## Vol. 66, No. 16 (2017)

##### 2017-08-20

###### GENERAL

2017, 66 (16): 160701.
doi: 10.7498/aps.66.160701

Abstract +

We report a rubidium atomic magnetometer based on pump-probe nonlinear magneto-optical rotation. The rubidium vapor cell is placed in a five-layer magnetic shield with inner coils that can generate uniform magnetic fields along the direction of pump beam, and the cell is also placed in the center of a Helmholtz coil that can generate an oscillating magnetic field perpendicular to the direction of pump beam. The atoms are optically pumped by circularly polarized pump beam along a constant magnetic field in a period of time, then the pump beam is turned off and a /2 pulse of oscillating magnetic field for 87Rb atoms is applied. After the above process, the individual atomic magnetic moments become phase coherent, resulting in a transverse magnetization vector precessing at the Larmor frequency in the magnetic field. The linearly polarized probing beam is perpendicular to the direction of magnetic field, and can be seen as a superposition of the left and right circularly polarized light. Because of the different absorptions and dispersions of the left and right circularly polarized light by rubidium atoms, the polarization direction of probing beam rotates when probing beam passes through rubidium vapor cell. The rotation of the polarization is subsequently converted into an electric signal through a polarizing beam splitter. Finally, the decay signal related to the transverse magnetization vector is measured. The Larmor frequency proportional to magnetic field is obtained by the Fourier transform of the decay signal. The value of magnetic field is calculated from the formula:B=(2/) f, where and f are the gyromagnetic ratio and Larmor frequency, respectively. In order to measure the magnetic field in a wide range, the tracking lock mode is proposed and tested. The atomic magnetometer can track the magnetic field jump of 1000 nT or 10000 nT, indicating that the atomic magnetometer has strong locking ability and can be easily locked after start-up.
The main performances in different magnetic fields are tested. The results show that the measurement range of the atomic magnetometer is from 100 nT to 100000 nT, the extreme sensitivity is 0.2 pT/Hz1/2, and the magnetic field resolution is 0.1 pT. The transverse relaxation times of the transverse magnetization vector in different magnetic fields are obtained, and the relaxation time decreases with the increase of the magnetic field. When the measurement range is from 5000 nT to 100000 nT, the magnetic field sampling rate of the atomic magnetometer can be adjusted in a range from 1 Hz to 1000 Hz. The atomic magnetometer in high sampling rate can measure weak alternating magnetic field at low frequency. This paper provides an important reference for developing the atomic magnetometer with large measurement range, high sensitivity and high sampling rate.

2017, 66 (16): 160702.
doi: 10.7498/aps.66.160702

Abstract +

A novel heterodyne polarization interference imaging spectroscopy (HPⅡS) based on a Savart polariscope is proposed in this paper. The HPⅡS is modified by introducing a pair of parallel polarization gratings into the static polarization interference imaging spectrometer. Because of the introduced parallel polarization gratings, the lateral displacements of the two beams split by the Savart polariscope vary with wavenumber. The frequency of the interferogram obtained on the detector is related to wavenumber. Like the spatial heterodyne spectrometer where the two end mirrors in a Michelson interferometer are replaced with two matched diffraction gratings, the zero frequency of the interferogram generated in HPⅡS corresponds to a heterodyne wavenumber instead of the zero wavenumber in a non-heterodyne spectrometer. Due to the heterodyne characteristics, a high spectral resolution can be achieved using a small number of sampling points. In addition, there is no slit in HPⅡS and it is an imaging Fourier transform spectrometer that records a two-dimensional image of a scene superimposed with interference curves. It is a temporally and spatially combined modulated Fourier transform spectrometer and the interferogram of one point from the scene is generated by picking up the corresponding pixels from a sequence of images which are acquired by scanning the scene. As a true imaging spectrometer, HPⅡS also has high sensitivity and high signal-to-noise ratio. In this paper, the basic principle of HPⅡS is studied. The optical path difference produced by the Savart polariscope and the parallel polarization gratings is calculated. The interferogram expression, the spectral resolution, and the spectrum reconstruction method are elaborated. As the relationship between the frequency of the interferogram and the wavenumber of the incident light is nonlinear, the input spectrum can be recovered using Fourier transform combined with the method of stationary phase. Also, the matrix inversion method can be used to recover the input spectrum. Finally, a design example of HPⅡS is given. The interferogram is simulated, and the recovered spectrum shows good agreement with the input spectrum. In the design example, the spectral range is 16667-18182 cm-1(550-600 nm), and the number of sampling points is 500. The spectral resolution of HPⅡS is 6.06 cm-1, which is 12 times smaller than that in a non-heterodyne spectrometer with the same spectral range and sampling numbers. HPⅡS has the advantages of compact structure, high optical throughput, strong stability, and high spectral resolution. It is especially suitable for hyperspectral detection with ultra-small, high stability, and high sensitivity.

2017, 66 (16): 160201.
doi: 10.7498/aps.66.160201

Abstract +

When Monte Carlo method is used to study many problems, it is sometimes necessary to sample correlated pseudorandom variables. Previous studies have shown that the Cholesky decomposition method can be used to generate correlated pseudorandom variables when the covariance matrix satisfies the positive eigenvalue condition. However, some covariance matrices do not satisfy the condition. In this study, the theoretical formula for generating correlated pseudorandom variables is deduced, and it is found that Cholesky decomposition is not the only way to generate multidimensional correlated pseudorandom variables. The other matrix decomposition methods can be used to generate multidimensional relevant random variables if the positive eigenvalue condition is satisfied. At the same time, we give the formula for generating the multidimensional random variable by using the covariance matrix, the relative covariance matrix and the correlation coefficient matrix to facilitate the later use. In order to verify the above theory, a simple test example with 33 relative covariance matrix is used, and it is found that the correlation coefficient results obtained by Jacobi method are consistent with those from the Cholesky method. The correlation coefficients are more close to the real values with increasing the sampling number. After that, the antineutrino energy spectra of Daya Bay are generated by using Jacobi matrix decomposition and Cholesky matrix decomposition method, and their relative errors of each energy bin are in good agreement, and the differences are less than 5.0% in almost all the energy bins. The above two tests demonstrate that the theoretical formula for generating correlated pseudorandom variables is corrected. Generating correlated pseudorandom variables is used in nuclear energy to analyze the uncertainty of nuclear data library in reactor simulation, and many codes have been developed, such as one-, two-and three-dimensional TSUNAMI, SCALE-SS, XSUSA, and SUACL. However, when the method of generating correlated pseudorandom variables is used to decompose the 238U radiation cross section covariance matrix, it is found that the negative eigenvalue appears and previous study method cannot be used. In order to deal with the 238U radiation cross section covariance matrix and other similar matrices, the zero correction is proposed. When the zero correction is used in Cholesky diagonal correction and Jacobi eigenvalue zero correction, it is found that Jacobi negative eigenvalue zero correction error is smaller than that with Cholesky diagonal correction. In future, the theory about zero correction will be studied and it will focus on ascertaining which correction method is better for the negative eigenvalue matrix.

## EDITOR'S SUGGESTION

2017, 66 (16): 160301.
doi: 10.7498/aps.66.160301

Abstract +

The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates.
In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.

2017, 66 (16): 160302.
doi: 10.7498/aps.66.160302

Abstract +

By presenting the quantum evolution with the trajectories of points on the Bloch sphere, the Majorana representation provides an intuitive way to study a high dimensional quantum evolution. In this work, we study the dynamical evolution of the nonlinear two-mode boson system both in the mean-field model by one point on the Bloch sphere and the second-quantized model by the Majorana points, respectively. It is shown that the evolution of the state in the mean-field model and the self-trapping effect can be perfectly characterized by the motion of the point, while the quantum evolution in the second-quantized model can be expressed by an elegant formula of the Majorana points. We find that the motions of states in the two models are the same in linear case. In the nonlinear case, the contribution of the boson interactions to the formula of Majorana points in the second quantized model can be decomposed into two parts:one is the single point part which equals to the nonlinear part of the equation in mean-field model under lager boson number limit; the other one is related to the correlations between the Majorana points which cannot be found in the equation of the point in mean-field model. This means that, the quantum fluctuation which is neglected in the mean-field model can be represented by these correlations. To illustrate our results and shed more light on these two different models, we discussed the quantum state evolution and corresponding self-trapping phenomenon with different boson numbers and boson interacting strength by using the fidelity between the states of the two models and the correlation between the Majoranapoints and the single points in the mean-field model. The result show that the dynamics evolution of the two models are quite different with small boson numbers, since the correlation between the Majorana stars cannot be neglected. However, the second-quantized evolution and the mean-field evolution still vary in both the fidelity population difference between the two boson modes and the fidelity of the states in the two models. The difference between the continuous changes of the second quantized evolution with the boson interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect is also discussed. These results can help us to investigate how to include the quantum fluctuation into the mean-field model and find a method beyond the mean field approach.

2017, 66 (16): 160501.
doi: 10.7498/aps.66.160501

Abstract +

A lot of studies of control highlight fractional calculus in modeling systems and designing controllers have been carried out. More recently, a lot of chaotic behaviors have been found in fractional-order systems. Then, controlling the fractional-order systems, especially controlling nonlinear fractional-order systems has become a hot research subject. The design of state estimators is one of the essential points in control theory. Time delays are often considered as the sources of complex behaviors in dynamical systems. A lot progress has been made in the research of time delay systems with real variables. In recent years, fractional-order time-delay chaotic synchronization and chaotic secure communication have received ever-increasing attention. In this paper we focus our study on the synchronization of fractional-order time-delay chaotic systems and its application in secure communication. Firstly, based on the Lipschitz condition, the nonlinear fractional-order time-delay system is proposed. Secondly, the fractional-order time-delay observer for the system is constructed. The necessary and sufficient conditions for the existence of the fractional-order observer are given by some lemmas. Thirdly, the synchronous controller is designed based on the state observer and the stability theory of fractional-order system. Instead of the state variables, the output variables of drive system and response system are used to design the synchronous controller, which makes the design much more simple and practical. With the Lyapunov stability theory and fractional order matrix inequalities, the method of how to obtain the parameters of the controller is presented. The sufficient conditions for asymptotical stability of the state error dynamical system are derived. After that, with the Chen fractional-order time-delay chaotic system, the synchronous controller is designed to make the system run synchronously. Finally, the proposed approach is then applied to secure communications, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. With the observer design technique, a chaotic receiver is then derived to recover the information signal at the receiving end of the communication. In the conventional chaotic masking method, the receiver is driven by the sum of the information signal and the output of the transmitter, whose dynamics is autonomous. The simulation results show that the design of the synchronous controller works effectively and efficiently, which implies that the proposed fractional order time-delay observer in this paper runs effectively. The proposed method is able to be applied to other fractional order time-delay chaos systems, and also to chaotic secure communication system.

2017, 66 (16): 160502.
doi: 10.7498/aps.66.160502

Abstract +

Heart rate is one of the most easily accessed human physiological data. In recent years, the analysis of sleep function based on heart rate variability has become a new popular feature of wearable devices used for daily health management. Consequently, it is needed to explore various types of short-term characteristic parameters which can be applied to the heartbeat interval time series within the standard sleep staging time window (about 30 s). Utilizing the recently reported limited penetrable horizontal visibility graph (LPHVG) algorithm, together with a weighted limited penetrable horizontal visibility graph (WLPHVG) algorithm proposed in this paper, the short-term heartbeat interval time series in different sleep stages are mapped to networks respectively. Then, 6 characteristic parameters, including the average clustering coefficient C, the characteristic path length L, the clustering coefficient entropy Ec, the distance distribution entropy Ed, the weighted clustering coefficient entropy ECw and the weight distribution entropy Ew are calculated and analyzed. The results show that the values of these characteristic parameters are significantly different in the states of wakefulness, light sleep, deep sleep and rapid eye movement, especially in the case of the limited penetrable distance Lp=1, indicating the effectiveness of LPHVG and WLPHVG algorithm in sleep staging based on short-term heartbeat interval time series. In addition, a preliminary comparison between proposed algorithm and the basic visibility graph (VG) algorithm shows that in this case, the LPHVG and WLPHVG algorithm are superior to the basic VG algorithm both in performance and in calculation speed. Meanwhile, based on the LPHVG and WLPHVG algorithm, the values of network parameters (the clustering coefficient entropy Ec and the weighted clustering coefficient entropy ECw) are calculated from heartbeat interval time series of healthy young and elder subjects in different sleep stages, to further study the aging effect on and sleep regulation over cardiac dynamics. It is found that despite an overall level difference between the values of Ec and ECw in young and elder groups, the stratification patterns across different sleep stages almost do not break down with advanced age, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. In addition, compared with the clustering coefficient entropy Ec based on LPHVG algorithm, the weighted clustering coefficient entropy ECw based on WLPHVG algorithm shows higher sensitivity to discriminating subtle differences in cardiac dynamics among different sleep states. Overall, it is shown that with the simple mapping criteria and low computational complexity, the proposed method could be used as a new auxiliary tool for sleep studies based on heart rate variability, and the corresponding network parameters could be used in wearable device as new auxiliary parameters for sleep staging.

###### NUCLEAR PHYSICS

2017, 66 (16): 162901.
doi: 10.7498/aps.66.162901

Abstract +

The optical system is one of the main components of an ion thruster, which consists of electrically biased multi-aperture grids. The grid design is critical to the ion thruster operation since its transparency has an important influence on the thruster efficiency and thrust. To further optimize the optical system performance and evaluate effectively the efficiency of ion thruster, the optical transparency radial distribution of ion thruster is analyzed and discussed in experiment and simulation. The process of beam extraction is simulated by the particleincell-Monte Carlo collision (PIC-MCC) method, and the movement of the ions is investigated by the PIC method while the collisions of particles are handled by the MCC method. Then the interdependency among the transparency of screen grid, the accelerator grid, optics system and the number of ion extracted is analyzed. Taking into account the distribution of ion density at the exit of discharge chamber, the radial distribution of the screen grid transparency, accelerator grid transparency and optical system transparency are acquired. An experiment is performed to verify the simulation based derivation, indicating the good agreement between experimental and simulation results. The results show that the radial distribution of screen grid transparency increases gradually along the radial direction and has a good central axial symmetry, and its minimum value is located in the center of the thruster while the maximum value is near the margin region of screen gird. The radial distribution of accelerator grid transparency is opposite to that of the screen grid transparency, which decreases along the radial direction, and its maximum value is located at the axis of the thruster. The radial distribution of optical system transparency is the same as that of the screen grid transparency. And its minimum value is in the center of optics system, which indicates that the effect of accelerator grid transparency on the optical system transparency is little. In addition, the study also finds that the total optical transparency of ion thruster decreases slowly as the beam current increases. This work will provide a lot of support for the optimal design of ion thruster optics system.

###### ATOMIC AND MOLECULAR PHYSICS

2017, 66 (16): 163102.
doi: 10.7498/aps.66.163102

Abstract +

Switching of vanadium dioxide (VO2) from low-temperature insulating phase to high-temperature rutile phase can be induced by photons with a certain energy. Photoinduced insulator-metal transition is found experimentally in VO2 polycrystalline film by photos with energy even below 0.67 eV. However, insulator-metal transition in single crystal can only be induced when photo energyis above 0.67 eV. In order to understand these experimental phenomena, we make a first-principle study on low-temperature non-magnetic M1 phase of VO2 with oxygen vacancy by density functional theory calculations based on the Heyd-Scuseria-Ernzerhof screened hybrid functional. According to symmetry, M1 phase has two kinds of different oxygen vacancies, O1 and O2 vacancies. Calculations are made on structures and electronic properties of nonmagnetic M1 phases with O1 and O2 vacancies, respectively. The present theoretical results show that neither the short vanadium-vanadium (VV) bond length near O1 or O2 vacancy nor the lattice parameters almost change but the long VV bond length near O1 or O2 vacancy decreases due to the oxygen vacancy. The long VV bond lengths near O1 and O2 vacancies are about 2.80 and 2.95 , respectively, but the long VV bond length is 3.17 in pure M1. The insulating band gap is opened between V 3d bands, and hybridization happens between V 3d and O 2p orbitals. Furthermore, the present theoretical results demonstrate that the band gap of pure nonmagnetic M1 is 0.68 eV while M1 with O1 vacancy, O2 vacancy, and two oxygen vacancies including O1 and O2, have band gaps of 0.23 eV, 0.20 eV, and 0.15 eV, respectively. The band gap decreases probably because oxygen vacancy results in the decease of the long VV bond length near it. The present results can explain the experimental results well.

2017, 66 (16): 163101.
doi: 10.7498/aps.66.163101

Abstract +

Based on consistent basis set aug-cc-pV5Z, five low-lying potential energy curves and transition dipole moments X2∑+, A2Π, B2∑+, a4Π and b4∑+ of BD+ are calculated by using internally contracted multi-reference configuration interaction approach. According to the calculation results, ro-vibrational levels of theses electronic states are derived through solving the radial Schrödinger equation ro-vibrational equation, and then the molecular parameters, Franck-Condon factors (FCFs) and radiation life are obtained by fitting and calculations. The FCFs (f00=0.923) and radiation life for v"=0 (τ=235 ns) of A2Π-X2∑+ are suitable for achieving rapid laser cooling. Therefore, an optical-cycle for Doppler laser cooling scheme is proposed:the system includes the A2Π1/2(v'=0)-X2∑+(v"=0, 1), where the case of v'=0 contains 2 rotational levels, the cases of v"=0 and v"=1 contain 6 and 4 rotational levels, respectively. According to the proposal, we simulate the dynamic process of the molecular population in laser cooling. The BD+ can be decelerated from initial velocity of 100 m/s to 4.6 m/s (13 mK) after scattering 1150 photons during 5.4 ms.

2017, 66 (16): 163601.
doi: 10.7498/aps.66.163601

Abstract +

Illustrated by the case of the planar clusters, we propose a new method to search the possible stable structures by combining the structural identification and Monte-Carlo tree algorithm. We adopt two kinds of model-potential to describe the interaction between atoms:the pair interaction of Lennard-Jones potential and three-body interaction based on the Lennard-Jones potential. Taking the possible triangular lattice fragment as candidates, we introduce a new nomenclature to distinguish the structures, which can be used for the rapid congruence check. 1) We label the atoms on the triangular lattice according to the distances and the polar angles. where a given triangular structure has a corresponding serial number in the numbered plane. Note that the congruent structures can have a group of possible serial numbers. 2) We consider all the possible symmetrical operations including translation, inversion and rotation, and obtain the smallest one for the unique nomenclature of the structure. In conventional search of magic clusters, the global optimizations are performed for the structures with given number of atoms. Herein, we perform the Monte-Carlo tree search to study the evolution of stable structures with various numbers of atoms. From the structures of given number of atoms, we sample the structures according to their energy with the importance sampling, and then expand the structures to the structures with one more atom, where the congruence check with the nomenclature is adopted to avoid numerous repeated evaluations of candidates. Since the structures various numbers of atoms are correlated with each other, a searching tree will be obtained. In order to prevent the over-expansion of branches, we prove the “tree” according to energy to make the tree asymmetric growth to retain the low energy structure. The width and depth of search is balanced by the control of temperature in the Monte-Carlo tree search. For the candidates with lower energies, we further perform the local optimization to obtain the more stable structures. Our calculations show that the triangular lattice fragments will be more stable under the pair interaction of Lennard-Jones potential, which are in agreement with the previous studies. Under the three body interaction with the specific parameter, the hexagonal lattice fragments will be more stable, which are similar to the configurations of graphene nano-flakes. Combining the congruence check and Monte-Carlo tree search, we provide an effective avenue to screen the possible candidates and obtain the stable structures in a shorter period of time compared with the common global optimizations without the structural identification, which can be extended to search the stable structure for materials by the first-principles calculations.

###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2017, 66 (16): 164205.
doi: 10.7498/aps.66.164205

Abstract +

For high performance clock, optical lattice is introduced to generate periodic trap for capturing neutral atoms through weak interactions. However, the strong trapping potential can bring a large AC Stark frequency shift due to imbalance shifts for the upper and lower energy levels of the clock transition. Fortunately, it is possible to find a specific “magic” wavelength for the lattice light, at which the first-order net AC Stark shift equals zero. To achieve high stability and accuracy of a neutral atomic optical clock, the frequency of the lattice laser must be stabilized and controlled to a certain level around magic wavelength to reduce this shift.#br#In this paper, we report that the frequency of lattice laser is stabilized and linewidth is controlled below 1 MHz with transfer cavity scheme for ytterbium (Yb) clock. A confocal invar transfer cavity mounted in an aluminum chamber is locked through the Pound-Drever-Hall (PDH) method to a 780 nm diode laser stabilized with modulation transfer spectroscopy of rubidium D2 transition. It is then used as the locking reference for the lattice laser. This cavity has a free spectral range of 375 MHz, as well as fineness of 236 at 780 nm, and 341 at 759 nm. Because neither of the wavelengths of 759 nm and 780 nm is separated enough to use optical filter, they are coupled into the cavity with transmission and reflection way respectively, and the two PDH modulation frequencies are chosen differently to avoid possible interference.#br#The stabilization of the 759 nm lattice laser on transfer cavity can stay on for over 12 hours without escaping or mode hopping. To estimate the locking performance of the system, a beat note with a hydrogen maser-locked optical frequency comb is recorded through a frequency counter at 10 ms gate time for over 3 hours. This beat note shows that the frequency fluctuation is in a range of 10 kHz corresponding to a stability of 2×10-11 level with 0.1 s averaging time, but goes up to 150 kHz corresponding to a stability of 3.6×10-10 at 164 s averaging time. The long-term drift can be the result of air pressure fluctuation on the transfer cavity, or the bad stability of the optical comb in the measurement process. However, current locking performance is still enough for the requirement of 10-17 clock uncertainty.#br#In conclusion, we succeed in realizing frequency stabilization and control for the lattice laser of Yb clock with the transfer cavity scheme. The result shows that the short-term stability is around 10-11 level, though a mid-long-term drift exists. However, the stability of 3.6×10-10 over 164 s can still promise a 10-17 uncertainty for the Yb clock. And, it can be reduced if the averaging time is long enough. The work can be further improved by installing the transfer cavity into vacuum housing for better stability in future.

2017, 66 (16): 164202.
doi: 10.7498/aps.66.164202

Abstract +

Partially coherent beams with nonconventional correlation functions have been extensively studied due to their wide and important applications in free-space optical communication, particle trapping, image transmission and optical encryption. Here, we study the propagation of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam (cGBCB) in detail. Analytical expressions for the cross-spectral density function of cGBCBs through paraxial ABCD system are derived based on the extended Huygens-Fresnel integral. By use of the derived formulae, the intensity distribution properties of a nonuniform cGBCB on propagation in free space are analytically investigated. Some numerical calculation results are presented and discussed graphically. It is found that when the root-mean-square correlation width δ and the parameter controlling the degree of coherence profiles β are appropriately chosen, the intensity distribution of the nonuniform cGBCB displays self-splitting properties during propagation. We point out that rather than a simple duplication, the self-splitting behaviour consists of a complex process in which the dark hollow pattern for cGBCB is gradually filled in the centre at first, then starts to split with increasing the propagation distance, and most impressively, an evolution process from a single dark hollow beam in the source plane to quadruple dark hollow profiles in certain propagation ranges can be realized. The influence of correlation function on the evolution properties of the intensity distribution is investigated, demonstrating that the values of parameters δ and β of the correlation function play a critical role in inducing the self-splitting effect for nonuniform cGBCB on propagation in free space. Therefore, it is clearly shown that modulating the correlation function of a partially coherent beam can alter the coherence length and the degree of nonuniformity, and thus provides an effective way of manipulating its propagation properties. We also find the evolution speed of the intensity distribution can be greatly affected by the topological charge n of the beam function and the parameter R controlling the hollow size of cGBCB in source plane, e. g. the intensity distribution evolves into quadruple dark hollow profiles more slowly with larger n or smaller R. As is well known, the dark-hollow intensity configurations are useful in many applications and have been extensively studied both theoretically and experimentally. Therefore, the results drawn in the paper develop an alternative way to realize dark-hollow beam array, and further pave the way for dark hollow beam applications in long-distance free-space optical communications.

2017, 66 (16): 164203.
doi: 10.7498/aps.66.164203

Abstract +

Ptychography provides an extremely robust and highly convergent algorithm to reconstruct the specimen phase with a wide field of view. The resolution and accuracy of ptychography are severely restricted by the uncertainty of the position error that includes the scanning position and axial distance error. In fact, it is difficult to accurately measure the distance between the target plane and entrance pupil of charge-coupled device (CCD) or complementary metal oxide semiconductor, which results in the axial distance error. The axial distance error can blur the reconstructed image, degrade the reconstruction quality and reduce the resolution. In order to analyze the effect of the axial distance error, the model for axial distance error is derived based on the amplitude constraint in CCD and Fresnel diffraction integral. This model indicates that the axial distance error can cause a stretching deformation of the retrieved image, which is similar to the defocusing effect caused by different axial distances in holography. In this paper, we propose a method of correcting the axial distance error by using the image information entropy in an iterative way to obtain the accurate axial distance and retrieve the distinct image. The correction method based on the image information entropy is composed of four parts:the initial calculation, the determination of the direction search, the axial error correction and the reconstruction of the distinct image. The initial calculation part is to ensure that the intensity of the reconstructed object tends to be stable before entering into the other processing parts. The search direction portion is to indicate that the initial axial distance is greater than the actual axial distance, or less than the actual axial distance. The axial error correction section is to calculate the sharpness values of the image at different axial distance, and find the peak position of the sharpness distribution that corresponds to the position of the clearest image. The axial distance can be taken from the peak position. The obtained axial distance is again taken into account in the ptychography algorithm to eliminate the axial distance error and obtain the distinct reconstructed image. In this paper, some simulations are conducted to verify the feasibility of the proposed method. The effect of the axial distance error is analyzed. The image energy variation, the Tamura coefficient and the image information entropy are selected as the image definition evaluation functions in our paper. We compare the distributions of three image definition evaluation functions in the correction process of the axial distance error. It is found that the image information entropy has higher sensitivity than the other image definition evaluation functions. Finally, both simulation and experiment have proved the feasibility of axial distance error correction based on image information entropy.

2017, 66 (16): 164204.
doi: 10.7498/aps.66.164204

Abstract +

The energy transfer phenomenon between Nd3+ and Yb3+ generates the research interest in Nd3+/Yb3+ co-doping, because it provides a straight-forward way to combine the features of Nd3+ and Yb3+ to develop some potential applications,such as solar cells,high energy pulse and tunable lasers.Substantial research work has been conducted to study the spectroscopic properties of Nd3+/Yb3+ in different glasses,crystal and ceramic host materials.However,it is still not very clear about the laser properties of the Nd3+/Yb3+ co-doping system,especially the high rare-earth solubility phosphate glass.This work reports the stimulated emission and laser properties of an Nd3+/Yb3+ co-doped phosphate glass fiber under singly 970 nm and 808 nm LD pumping.The molar doping ratio of Nd3+:Yb3+ is 4:1.Using the free-space coupled method,the laser properties of the co-doped fiber under 970 nm pump are tested first in a laser cavity comprised of a butt-coupled dichroic mirror with high reflectivity (≥ 99.5%) and a cleaved fiber ended with~4.6% Fresnel reflectivity.It is found that with the increase of 970 nm pump power (P970) two discrete laser peaks and one peak located at 1053 nm with a larger threshold can be observed for fiber length equal to and less than 0.7 m.The 1053 nm laser is produced by Yb3+ → Nd3+ energy transfer,and its lasing threshold decreases with increasing fiber length in this length region.Then,the amplified spontaneous emission (ASE) spectra for fiber lengths of 0.35 m,0.9 m and 5.0 m under 970 nm pumping are tested by cutting 6° at the output port.The test results indicate that the Yb3+ → Nd3+ energy transfer has a modulation effect on fiber spectrum,and the modulation becomes more obvious for a longer fiber length.A two-fold promotion mechanism is suggested to explain the modulation effect:1) the reabsorption effect of Yb3+ leading to relatively lifetime prolongation increases the Yb3+ → Nd3+ energy transfer efficiency;2) the red-shifted oscillator laser wavelength leads to a larger emission cross section difference between Nd3+ and Yb3+.Besides,the measurement results in 0.35-m-long fiber also suggest that the 1053 nm laser in fiber laser test may be due to a fiber temperature raising effect during the increase of P970.The laser properties and ASE spectra of the fiber under 808 nm pumping have been studied in the same fiber test setup.However,the tested results are quite different from the 970 nm pumping case. Only one lasing peak at 1053 nm is detected,and it is found that the peak is not dependent on the 808 nm pump power (P808) nor the fiber length.To explain this phenomenon,one energy transfer model with taking into consideration the stimulated emission of Nd3+ is derived.According to this theoretical model,Nd3+ → Yb3+ energy transfer efficiency fast decreases with the increase of simulated emission intensity of Nd3+.This explanation is experimentally supported by a 0.05-m-long Nd3+/Yb3+ co-doped phosphate glass fiber with varying P808.Therefore,the adoption of Nd3+ to sensitize Yb3+ for developing some laser applications needs to consider the suppression effect of Nd3+ stimulated emission on Nd3+ → Yb3+ energy transfer.

2017, 66 (16): 164301.
doi: 10.7498/aps.66.164301

Abstract +

As a new treatment modality with little thermal damage and few cell metastases to surrounding normal tissues, high intensity focused ultrasound (HIFU) therapy is considered to be one of the most promising technologies for tumor therapy in the 21st century. However, noninvasive temperature monitoring for the focal region exhibits great significance of precise thermal dosage control in HIFU treatment. By combining electrical impedance measurement and HIFU, an electrical impedance tomography (EIT) based temperature monitoring method using surface voltages is proposed to reconstruct the distribution of electrical conductivity inside the focal plane on the basis of the temperature dependent electrical impedance of tissues. In theoretical study, a comprehensive system of EIT measurement during HIFU therapy is established. With the consideration of acoustic absorption in viscous tissues, three-dimensional Helmholtz equation for HIFU is simplified into two-dimensional axisymmetric cylindrical coordinates, and the characteristics of temperature rising in the focal region are derived using Pennes bio-heat transfer equation. Then, by introducing the temperature-conductivity relation into tissues, the processing methods for electrical field and surface voltage in the focal region are constructed with constant current injection from two symmetrical electrodes. In simulation study, by applying the experimental parameters of the focused transducer, the distributions of acoustic pressure and temperature are simulated at a fixed acoustic power, and then the corresponding distributions of conductivity in the focal plane are achieved at different treatment times for centric and eccentric focusing. Furthermore, with the simulations of current density and electrical potential generated by the rotating current injection from 16 pairs of symmetrical electrodes, 32×32 voltages are detected by the 32 surface electrodes placed around the focal plane of the model. In conductivity image reconstruction, the modified Newton-Raphson (MNR) algorithm is employed to conduct iterative calculation. It shows that with the increase of HIFU treatment time, the electrical conductivity in the focal region increases accordingly and reaches a maximum value in the center due to the highest acoustic pressure and the most energy accumulation. It is proved that not only the position of the focal center, but also the conductivity distribution inside the focal region can be restored accurately by the proposed EIT based reconstruction algorithm. The favorable results demonstrate the feasibility of temperature monitoring during HIFU therapy, and also provide a new method of evaluating the noninvasive efficacy and controlling the dose based on electrical impedance measurements.

2017, 66 (16): 164701.
doi: 10.7498/aps.66.164701

Abstract +

In this paper, we present a smoothed particle hydrodynamics (SPH) method for modeling multiphase flows. The multiphase SPH method includes a corrective discretization scheme for density approximation around the fluid interface to treat large density ratio, a small repulsive force between particles from different phases to prevent particles from unphysically penetrating fluid interface, and a newly-developed hyperbolic-shaped kernel function to remove possible stress instability. This multiphase SPH method is then used to study the single-and multi-mode Rayleigh-Taylor instability problems. A comparison between our results with the results from existing literature shows that our results are obviously better than most available results from other SPH simulations. The present results are close to those by Grenier et al. while the present multiphase SPH method is simpler and easier to implement than that in the work by Grenier et al. (Grenier, et al. 2009 J. Comput. Phys. 228 8380). For the single-mode Rayleigh-Taylor instability, the evolutions of the interface pattern and vortex structures, and the penetration depth each as a function of time are investigated. For the multi-mode Rayleigh-Taylor instability, the merging of small structures into a large structure during the evolution of the interface is studied. The horizontal average density and the penetration each as a function of height are also studied.

2017, 66 (16): 164702.
doi: 10.7498/aps.66.164702

Abstract +

Collapse of a confined bubble is the core problem of bubble dynamics. The recent study has shown that the collapse of macroscopic bubble may drive the motion of suspended particle with the similar size, but, there has still been a lack of the relevant study on a microscale. In the experiment about the bubble driven micro-motor, the locomotion of motor pushed by microjetting has been noticed. However, due to the limitation of experimental conditions, it is difficult to reveal the details of propulsion mechanism. In this paper, the volume of fluid based numerical method is adopted to simulate the interaction process between a collapsing microbubble and the suspended particle nearby. The spatial distribution and the time evolution of flow field are obtained, and the velocity that the micromotor could be achieved is deduced by integrating the impulsive force. The results show that when the bubble size is fixed, the interaction force is inversely proportional to the size of microparticle and the gap between microparticle and bubble. The Kelvin impulse theorem is used to clarify the difference between the interaction on a macroscopic scale and that on a microscopic scale. This study not only extends the scope of cavitation dynamics, which reveals the characteristics of interaction between bubble and particle on a microscale, but also is significant for improving the efficiency of self-propelled micro-motor.

2017, 66 (16): 164201.
doi: 10.7498/aps.66.164201

Abstract +

The vector Kirchhoff integral theorem (VKI) is an important formula in electromagnetic (EM) theory,especially it is a basis of the optical diffraction theory.Recently,it has been found that there exist some flaws in the proofs presented in the literature.There are mainly two types of methods to prove the VKI.The first type of method is to employ the vector analysis to prove the VKI directly.Some flaws of this type of proof presented in the literature have been found and pointed out in this paper.The second type of method is to employ the scalar Kirchhoff Integral (SKI) to directly obtain the VKI. The SKI was first derived by Kirchhoff (1882).In spite of its mathematical inconsistency and its physical deficiencies, the SKI works remarkably well in the optical domain and has been the basis of most of the work on diffraction.However, the proofs for SKI usually need the scalar radiation conditions.The scalar radiation condition was first proposed by Sommerfeld to ensure the uniqueness of the solution of certain exterior boundary value problems in mathematical physics. But whether the scalar radiation conditions were suitable for the EM was not sure.In fact,for electromagnetic field,we have another vector radiation conditions which have been verified to be adaptable for all the radiation and scattering fields.It is difficult to obtain the scalar radiation conditions directly by just separating three Cartesian directions from the vector one,because the different scalar components are coupled together after the rotation and cross product operation.Actually,few strict proofs could be found to support the fact that EM satisfies the scalar radiation condition. So as the supplementary,the scalar radiation conditions will be derived in detail with far-field approximation method in this paper.To avoid using the scalar radiation condition which may bring some non-rigorousness,we perform a new strict proof for the VKI by using the vector analysis identities.
The rest of this paper is organized as follows.In Section 2,the different proofs presented in the classical books will be analyzed in detail.The flaws existing in these proofs will be pointed out.After that,in Section 3,based on the Stratton-Chu formula,a new strict proof will be given with using the vector identities.In Section 4,a sensitivity analysis is numerically performed to confirm our demonstration.Finally,the conclusions are drawn from the present study in Section 5.The scalar radiation conditions will be discussed in the appendix.

2017, 66 (16): 164501.
doi: 10.7498/aps.66.164501

Abstract +

Numerical characteristics of the Hilber-Hughes-Taylor- (HHT-) method for the differential-algebraic equations (DAEs) in impact dynamics of flexible multibody systems are investigated. The research is based on a dynamic process of a flexible beam rotating about a fixed axis, whichis under the action of gravity and collides with a rigid plane. Therefore, the dynamic transformation and solution of flexible multibody system are divided into two parts. The Lagrange's equations of the second kind are used to derive the dynamic equations before and after impact, whereas the contact constraint method (CCM) is adopted to simulate the contact process. Compared with other methods, the CCM can describe the contact process accurately and avoid choosing the additional parameters. A set of the differential equations are transformed into a set of the DAEs due to the added constraint equations into impact process. Normally the dynamic equations of the flexible multibody system are index-3 DAEs. Solving a system of the index-3 DAEs directly by an integration algorithm would be subject to ill-conditioning and poor global convergence properties, so it is reasonable to find the methods that avoid both drawbacks and dependence on the constraint information. In order to solve this complex process, the HHT- method is used in the impact dynamic simulation by introducing the Gear-Gupta-Leimkuhler formulation. The coefficient of the HHT- method can be used to control the numerical dissipation, and it also represents asymptotic annihilation of the high frequency response. The smaller the value of , the more the damping is induced in the numerical solution. The Baumgarte's stabilization method is the most famous one for index-3 DAEs. Unfortunately, no general way can be adopted to determine the coefficients of the Baumgarte's stabilization method. It is the main reason for the numerical stability problems. It is necessary to study the influences of coefficients of the former two methods. Simultaneously, the simulation results from the HHT- method are compared with those from the Baumgarte's stabilization method to calculate the CCM model, and the Newmark method is used to solve the ODEs by using the continuous contact force model. The influence of the modal truncation N on the numerical method is also taken into account. Furthermore, the influences of N and the coefficient of HHT- method on the velocity and acceleration constraints in the multibody system are analyzed. Results have shown that the choice of the stabilization coefficients exerts a greater influence on the simulation results, such as the dynamic responses and the constraints, than that of the coefficient . Meanwhile, the HHT- method has an influence on the choice of coefficient and numerical damping properties. This numerical damping property can reduce the effect of high order modes induced by impact. Finally, the increase of N causes the sharpening default of both velocity and acceleration constraints.

2017, 66 (16): 164703.
doi: 10.7498/aps.66.164703

Abstract +

Magnetic fluid is a stable suspension of solid phase magnetic particles of diameter about 10 nm in a nonmagnetic carrier fluid like water or alcohol. Nowadays, the magnetic fluid is widely used in industry areas such as sealing, damping, lubricating, sound regulation, heat dissipation, and MHD beneficiation. Researchers have paid great attention to the behaviors of non-magnetic particles (NPs) in the magnetic field because magnetic fluid containing NPs can form different microstructures, which are easily controlled by applying a magnetic field. In order to appropriately use the properties of magnetic fluid in industry, it is necessary to study the interaction among NPs in detail. In this paper, a multi-physical numerical model is employed to investigate the sedimentation of two NPs in magnetic fluid subjected to an applied magnetic field. The magnetic fluid flow is simulated by lattice Boltzmann method, and magneto hydrodynamics is calculated with a self-correcting procedure of a Poisson equation solver, which enables the Ohm's law to satisfy its conservation law. A dipole force model is used to obtain the dipole interaction force between particles. In addition, as the permeability of the magnetic fluid is quite different from those of the NPs and magnetic fluid, correctly establishing the conjugate boundary condition of the magnetic intensity at the interface between the particles and surrounding fluid is a key because it affects the magnetic induction in the fluid-structure interaction area. A smooth transition scheme of the conjugate boundary condition for magnetic intensity at the interface between the particles and surrounding fluid is used in this work. The aim of this work is to investigate sedimentation of two NPs in magnetized magnetic fluid. By changing the ratio of magnetic permeability and the magnetic parameter, it is found that altering the ratio of magnetic permeability is more effective to change the trajectories of NPs, while changing the magnetic parameter can just give rise to a slight transform of particle trajectories. This can provide good theoretical support for the application of magnetic fluid in industry area, because the results in the present simulation can quantitatively analyze the controlling of the movement of NPs.

###### CONDENSED MATTER:STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

## EDITOR'S SUGGESTION

2017, 66 (16): 166801.
doi: 10.7498/aps.66.166801

Abstract +

Monocrystalline graphene is expected to become a core material for the next-generation flexible electronic device, owing to its superior mechanical and electrical properties. Therefore, it is essential to analyze the interfacial mechanical property of the composite structure composed of large-scale monocrystalline graphene, prepared by chemical vapor deposition (CVD), and flexible substrate in experiment. Recent years, micro-Raman spectroscopy has become a useful method of micro/nano-mechanics for the experimental investigations on the properties of low-dimensional nanomaterials, such as carbon nanotube (CNT), graphene, molybdenum disulfide (MoS2). Especially, Raman spectroscopy is effectively applied to the investigations on the mechanical behaviors of the interfaces between graphene films and flexible substrates. Among these researches, most of the measured samples are small-scale monocrystalline graphene films which are mechanically exfoliated from highly oriented pyrolytic graphite, a few ones are the large-scale single-layer polycrystalline graphene films prepared by CVD. There is still lack of study of the large-scale single-layer monocrystalline graphene. In this work, micro-Raman spectroscopy is used to quantitatively characterize the behavior of interface between single-layer monocrystalline graphene film prepared by CVD and polyethylene terephthalate (PET) substrate under uniaxial tensile loading. At each loading step from 0 to 2.5% tensile strain on the substrate, the in-plane stress distribution of the graphene is measured directly by using Raman spectroscopy. The interfacial shear stress at the graphene/PET interface is then achieved. The experimental result exhibits that during the whole process of uniaxial tensile loading on the PET substrate, the evolution of the graphene/PET interface includes three states (adhesion, sliding and debonding). Based on these results, the classical shear-lag model is introduced to analyze the interfacial stress transfer from the flexible substrate to the single-layer graphene film. By fitting the experimental data, several mechanical parameters are identified, including the interface strength, the interface stiffness and the interface fracture toughness. The Raman measurements and result analyses are carried out on the samples whose single-layer graphene films have different lengths. It is shown that the stress transfer at the graphene/PET interface controlled by the van der Waals force has obvious scale effect compared with the graphene length. The interface strength, viz. the maximum of the interfacial shear stress, decreases with the increase of the graphene length. While the graphene length has no effect on the debonding strain or the strain transfer limit of graphene/PET interface. Combining with other previous studies of the large-scale single-layer graphene shows that the mechanical parameters of the interface between graphene and flexible substrate have no relation no matter whether the graphene is monocrystalline or polycrystalline.

2017, 66 (16): 166101.
doi: 10.7498/aps.66.166101

Abstract +

Recent years there has been aroused a growing interest in designing two-dimensional (2D) structures of carbon allotropes, owing to the great success in graphene. The T-graphene is a newly proposed 2D carbon allotrope possessing tetragonal symmetry other than hexagonal symmetry of graphene. Also, the energetic and dynamical stabilities of T-graphene have been revealed. So motivated, we investigate the structural stabilities and electronic properties of T-graphene and especially its derivatives-n(n=1-5) by using the first-principle calculation based on the density function theory. By changing the atomic number (n) of the linear carbon chains connecting the two tetragon rings of T-graphene, a series of sp-sp2 hybrid structures can be formed, which is named T-graphene derivatives-n. The calculation results show that the structural stabilities, chemical bond types and electronic structures of these materials depend greatly on the parity of n. Owing to a strong π-bond formed by eight carbon atoms in T-graphene, it becomes the one with the lowest energy in all these materials studied in this work. An interesting phenomenon is found that the T-graphene derivatives-n with even n are dynamically stable as witnessed by the calculated phonon spectra without imaginary modes, while those with odd n are dynamically unstable. The metallic behaviors are present in the T-graphene derivatives-n with even carbon atoms in the linear carbon chains, showing an alternating single and triple C–C bonds. Besides, we observe that the metallicity of the T-graphene derivatives-n with even n becomes stronger as n increases. On the other hand, the linear carbon chains with odd carbon atoms are comprised of continuous C=C double bonds. These T-graphene derivatives-n with odd n also show metallic behaviors, but turn into magnetic materials (except for n=1), the magnetic moments are about 0.961μB (n=3) and 0.863μB (n=5) respectively, and ferromagnetic ordering is the only possibility for the magnetism, which rarely occurs in carbon material. Our first-principle studies indicate that the introducing carbon chains between the tetragonal carbon rings of T-graphene constitute an efficient method to obtain new two-dimensional carbon allotrope. With different numbers (even or odd) of carbon atoms on the chains, the constructed 2D carbon allotropes could show contrasting dynamical and magnetic properties. These findings provide a theoretical basis for designing two-dimensional carbon materials and carbon-based nanoelectronic devices.

2017, 66 (16): 166201.
doi: 10.7498/aps.66.166201

Abstract +

Mg2Ge with anti-fluorite structure at ambient pressure is characterized as a narrow band semiconductor and increasing pressure results in a decrease of the gap. In this work, the band structure of anti-fluorite Mg2Ge under high pressure is studied by first principles calculations, which suggests that Mg2Ge becomes metallic at 7.5 GPa as a result of band gap closure. The enthalpy difference between anti-fluorite phase and anti-cotunnite phase under high pressure is calculated by the first-principles plane-wave method within the pseudopotential and generalized gradient approximation. The results show that Mg2Ge undergoes a phase transition from the anti-fluorite structure to anti-cotunnite structure at 11.0 GPa. Then we investigate experimentally the pressure-induced metallization of Mg2Ge by electric resistance measurement in strip anvil cell and Raman spectroscopy by diamond anvil cell. The pressure distribution is homogeneous along the central line of the strip anvil and the pressure is changed ccontinuously by using a hydraulically driven two-anvil press. Raman scattering experiment is performed at pressure up to 21.1 GPa on a back scattered Raman spectrometer. The wavelength of excitation laser is 532 nm. No pressure-transmitting is used and pressure is determined by the shift of the ruby luminescence line. It is found that neither a discontinuous change of electrical resistance at 8.7 GPa nor Raman vibration modes of Mg2Ge appear above 9.8 GPa. The disappearance of the Raman vibration mode is ascribed to the metallization since the the free carrier concentration rises after metallization has prevented the laser light from penetrating into the sample. We compare these results with those of resistivity measurements in diamond anvil cell. Li et al.[2015 Appl. Phys. Lett. 107 142103] reported that Mg2Ge becomes metallic phase at 7.4 GPa and is transformed into metallic anti-cotunnite phase at around 9.5 GPa. We speculate that the discontinuous change in electric resistance at 8.7 GPa is ascribed to the gap closure of anti-fluorite phase and Mg2Ge may transform into the anti-cotunnite phase above 9.8 GPa.

## EDITOR'S SUGGESTION

2017, 66 (16): 166301.
doi: 10.7498/aps.66.166301

Abstract +

Group-ⅢA metal-monochalcogenides have been extensively studied due to their unique optoelectronic and spin electronic properties. To realize the device applications, modifying their magnetic properties is desirable. Atomic doping and vacancy defects have been proven to produce itinerant ferromagnetism and half-metallicity in GaSe monolayer. Relatively, the magnetic modification by adsorbing foreign atoms is rarely reported. Traditional ferromagnetic material, Fe element, possessing high electronic polarizability and high Curie temperature, becomes the best option of adsorbate. In this work, Fen(n=1, 2) atoms adsorbed GaSe monolayer systems are constructed, and the spin electronic properties are systematically studied through the density function theory. Based on the geometric configuration of fully relaxed 33 GaSe supercell, three highly symmetrical sites, i.e., the hollow site, the top site of Se atom, and the top site of Ga atom are inspected to search for the stable absorption positions of Fen atoms. Computation results of adsorption energies indicate that the top site of Ga atom is preferred for single Fe atom, and the hollow site near the first Fe adatom is the most stable site serving as adsorbing the second Fe atom. Based on the most stable configuration, the spin electronic properties are studied. For the single Fe adsorbed system, the valence band maximum moves to point, resulting in a direct-band-gap. The strong orbit coupling effect between Fe adatom and its nearest Ga and Se atoms causes un-coincident majority and minority spin channels. Two impurity bands are located near the Fermi level and contribute only to the minority spin channel, producing a half-metallicity with a 100% spin polarization in the system. Bader charge analysis and spin-resolved partial density of states suggest that the spin polarization is mainly attributed to the transfer of Fe-3d electrons, and the hybridizations of Fe-3d, Se-4p, and Ga-4p states. Charge transfer from the Fe adatom to GaSe generates an n-type doping and an antiferromagnetic coupling between Fe and vicinal Ga and Se atoms. For the two-Fe-atoms adsorbed GaSe monolayer, the spin electronic states are found to be mainly located between the two Fe adatoms, leading to the reduction of the charge transfer from Fe to GaSe ML. As the original single spin channel turns into two spin channels (majority spin channel and minority spin channel) near the Fermi level, the ferromagnetic coupling between Fe atom and the vicinal Se atoms turn into antiferromagnetic coupling and the spin polarization falls to 0%. Therefore, the spin properties of GaSe monolayer can be controlled by modifying the number of adsorbed Fe atoms. These results reveal the formation and transform of the spin electronic properties of typical ferromagnetic/GaSe adsorption system, which offers some advice for designing and constructing the two-dimensional spin nanostructures.

###### CONDENSED MATTER:ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

2017, 66 (16): 167201.
doi: 10.7498/aps.66.167201

Abstract +

The Cu3SbSe4 compound is an environmentally friendly and low-cost medium-temperature thermoelectric material, which is featured by its low thermal conductivity. The disadvantage of this compound lies in its intrinsic poor electrical transport property. In order to improve the electrical conductivity of Cu3SbSe4, in this work we are to increase its carrier concentration by one to two orders of magnitude though elemental doping. The sample composition of Cu2.95GaxSb1-xSe4 is designed to increase the hole carrier concentration by introducing Cu vacancies and substituting Ga3+ for Sb5+. The Cu2.95GaxSb1-xSe4 (x=0, 0.01, 0.02 and 0.04) samples are prepared by melting-quench method. The X-ray diffraction analysis indicates that the obtained samples are of single-phase with the tetragonal famatinite structure, and the energy-dispersive X-ray spectroscopy results show that the actual compositions of the samples are very close to their nominal compositions. The effect of Ga doping on the thermoelectric performance of Cu3SbSe4 compound is investigated systematically by electrical and thermal transport property measurements. According to our experimental results, the hole concentration of the sample is efficiently increased by substituting Sb with a small amount of Ga (x=0.01), which can not only substantially improve the electrical conductivity but also suppress the intrinsic excitation of the sample. The maximum power factor reaches 10 μW/cm·K2 at 625 K for the Ga doped sample with x=0.01, which is nearly twice as much as that of the sample free of Ga. Although the carrier concentration further increases with increasing Ga content, the hole mobility decreases dramatically with the Ga content increasing due to the increased hole effective mass and point defect scattering. Thus, the electrical transport properties of the samples deteriorate at higher Ga content, and the maximum power factors for the samples with x=0.02 and 0.04 reach 9 and 8 μW/cm·K2 at 625 K, respectively. The lattice thermal conductivities of the samples basically comply with the T-1 relationship, suggesting the phonon U-process is the dominant scattering mechanism in our samples. For the samples with x=0 and 0.01, the lattice thermal conductivities at high temperature deviate slightly from the T-1 curve due to the presence of intrinsic excitation. However, these deviations are eliminated for the samples with x=0.02 and 0.04 because the bipolar effect is effectively suppressed with the increasing of Ga content. Thus, Ga doping can reduce the bipolar thermal conductivity at high temperature by increasing the hole carrier concentration. Furthermore, the point defects introduced by Ga doping can also enhance the scattering of high-frequency phonons, leading to slightly reduced lattice thermal conductivities of Ga-doped samples at higher temperature. Finally, a maximum ZT value of 0.53 at 664 K is achieved in Ga-doped sample, which is 50% higher than that of the sample free of Ga.

2017, 66 (16): 167301.
doi: 10.7498/aps.66.167301

Abstract +

In order to reduce the high electric field peak near the gate edge and optimize the non-uniform surface electric field distribution of conventional AlGaN/GaN high electron mobility transistor (HEMT), a novel AlGaN/GaN HEMT with a partial GaN cap layer is proposed in this paper. The partial GaN cap layer is introduced at the top of the AlGaN barrier layer and is located from the gate to the drain drift region. A negative polarization charge at the upper hetero-junction interface is induced, owing to the polarization effect at the GaN cap layer and AlGaN barrier layer interface. Hence, the two dimensional electron gas (2DEG) density is reduced. The low-density 2DEG region near the gate edge is formed, which turns the uniform distribution into a gradient distribution. The concentration distribution of 2DEG is modified. Therefore, the surface electric field distribution of AlGaN/GaN HEMT is modulated. By the electric field modulation effect, a new electric field peak is produced and the high electric field peak near the gate edge of the drain side is effectively reduced. The surface electric field of AlGaN/GaN HEMT is more uniformly redistributed in the drift region. In virtue of ISE-TCAD simulation software, the equipotential and the surface electric field distribution of AlGaN/GaN HEMT are obtained. For the novel AlGaN/GaN HEMT employing a partial GaN cap layer, the 2DEG is completely depleted from the gate to the drain electrodes, arising from the low-density 2DEG near the gate edge, while the 2DEG is partly depleted for the conventional AlGaN/GaN HEMT. The surface electric field distribution of the conventional structure is compared with the one of the novel structures with partial GaN cap layers of different lengths at a fixed thickness of 228 nm. With increasing length, the new electric field peak increases and shifts toward the drain electrode, and the high electric field peak on the drain side of the gate edge is reduced. Moreover, the breakdown voltage dependence on the length and thickness of the partial GaN cap layer is achieved. The simulation results exhibit that the breakdown voltage can be improved to 960 V compared with 427 V of the conventional AlGaN/GaN HEMT under the optimum conditions. The threshold voltage of AlGaN/GaN HEMT remains unchanged. The maximum output current of AlGaN/GaN HEMT is reduced by 9.2% and the specific on-resistance is increased by 11% due to a 2DEG density reduction. The cut-off frequency keeps constant and the maximum oscillation frequency shows an improvement of 12% resulting from the increased output resistance. The results demonstrate that the proposed AlGaN/GaN HEMT is an attractive candidate in realizing the high-voltage operation of GaN-based power device.

2017, 66 (16): 167501.
doi: 10.7498/aps.66.167501

Abstract +

Over past decades, Fe-based amorphous and nanocrystalline alloys have aroused a popular research interest because of their ability to achieve high saturation magnetic flux density and low coercivity, but the mechanisms for modifying annealing-induced magnetic properties on an atomic scale in amorphous matrix due to structural relaxation has not been enough understood. In this work, we study the effects of pre-annealing time on local structural and magnetic properties of Fe80.8B10P8Cu1.2 amorphous alloy to explore the mechanisms for structural relaxation, particularly the evolution of chemical short range order. The alloy ribbons, both melt spun and annealed, are characterized by differential scanning calorimetry, X-ray diffractometry, Mössbauer spectroscopy and magnetometry. The magnetic hyperfine field distribution of Mössbauer spectrum is decomposed into four components adopting Gaussian distributions which represent FeB-, Fe3P-, Fe3B- and α-Fe-like atomic arrangements, respectively. The fluctuation of magnetic hyperfine field distribution indicates that accompanied with the aggregation of Fe atoms, the amorphous structures in some atomic regions tend to transform from Fe3B- to FeB-like chemical short-range order with the pre-annealing time increasing, but the amorphous matrix begins to crystallize when the pre-annealing time reaches 25 min. Before crystallization, the spin-exchange interaction between magnetic atoms is strengthened due to the increase of the number of Fe clusters and the structure compaction. Thus, saturation magnetic flux density increases gradually, then shows a drastic rise when there appear α-Fe grains in the amorphous matrix. Coercivity first declines to a minimum after 5 min pre-annealing and then increases drastically. This is attributed to the fact that excess free volume and residual stresses in the melt spun sample are released out during previous pre-annealing, which can weaken magnetic anisotropy significantly, while the subsequent pre-annealing destroys the homogeneity of amorphous matrix, resulting in the increase of magnetic anisotropy. In addition, the separation of Cu atoms from the first near-neighbor shell of Fe atoms and the obvious decrease in the Fe-P coordination number suggest the formation of CuP clusters, which can provide heterogeneous nucleation sites for α-Fe and contribute to the grain refinement. Therefore, through controlling the pre-annealing time, we successfully tune the content values of CuP and Fe clusters in the amorphous matrix to promote the precipitation of α-Fe and refine grains during crystallization. For Fe80.8B10P8Cu1.2 nanocrystalline alloy, an enhancement of soft magnetic properties is achieved by a pre-annealing at 660 K for 5-10 min followed by a subsequent annealing at 750 K for 5 min.

2017, 66 (16): 167101.
doi: 10.7498/aps.66.167101

Abstract +

The strain engineering is an effective method to modulate the optical properties of germanium. The biaxial tensile strain has been extensively studied, most of the investigations focusing on biaxial tensile strain with equal in-plane strain at different crystal orientations, namely symmetric biaxial tensile strain. However, the effect of biaxial tensile strain with unequal in-plane strain at different crystal orientations, namely asymmetric biaxial tensile strain, has not been reported. In this paper, we systematically investigate the effect of asymmetric biaxial tensile strain on the band structure of Ge by using first-principle calculation.#br#We firstly calculate and analyze the dependence of band gap on strain for Ge with asymmetric biaxial tensile strain along three low Miller index planes, i.e., (001), (101) and (111). Then, we present the values of band gap and strain for some typical indirect-to-direct bandgap-transition-points under asymmetric biaxial tensile strain. Finally, we analyze the influence of biaxial tensile strain on the valance band structure. For the asymmetric biaxial tensile strain along the (001) plane, the indirect-to-direct band gap transition only occurs when the strain of one orientation is larger than 2.95%. For asymmetric biaxial tensile strain along the (101) plane, the indirect-to-direct band gap transition only occurs when the strain of one orientation is larger than 3.44%. Asymmetric biaxial tensile strain along the (111) plane cannot transform Ge into direct band gap material.#br#For asymmetric biaxial tensile strains along the (001) and (101) plane, the indirect-to-direct band gap transition points can be adjusted by changing the combination of in-plane strain at different crystal orientations. The value of bandgap of direct-band-gap Ge under biaxial tensile strain is inversely proportional to the area variation induced by application of strain. The asymmetric biaxial tensile strain along the (001) plane is the most effective to transform Ge into direct band gap material among the three types of biaxial strains, which are similar to the symmetric biaxial tensile strains.#br#In addition, the symmetric biaxial tensile strain will remove the three-fold degenerate states of valance band maximum, leading to a removal of the degeneracy between one heavy hole band and the light hole band. For biaxial tensile strain along the (001) and (101) plane, the asymmetric biaxial tensile strain could further remove the degeneracy between another heavy hole band and the light hole band.

2017, 66 (16): 167401.
doi: 10.7498/aps.66.167401

Abstract +

In order to inhibit the Gd/Ba substitution in the growth process effectively, a series of single domain GdBCO bulk superconductors with different ratios of BaO additions in the solid phase pellet is successfully fabricated by the modified top seeded infiltration growth technique on the basis of previous research. In the present work, the macroscopic feature, microstructure and critical current density (Jc) of the single domain GdBCO bulk superconductor are investigated in detail. From the top view of the surface of the single domain GdBCO bulk superconductor, all of the samples exhibit clearly the fourfold growth sector boundaries on their top surfaces, and spontaneous satellite grains are observed in none of these samples. It can be seen that the different ratio of BaO addition (from 1 wt% to 4 wt%) cannot affect the growth morphology of the single domain GdBCO bulk superconductor. At the same time, for observations of the microstructure, the small test specimens of dimensions about 2 mm2 mm2 mm are cut from the top surface of the singe domain GdBCO bulk superconductors with different BaO doping ratios and at a distance 5 mm away from the seed, then microstructure analysis is performed in the cleavage phane of the test specimen by using scanning electron microscope. For the sample with 1 wt% BaO doping, the derivative phase of GdBCO (Gd123ss) is found in the Gd123 superconducting matrix. To detect the atomic ratio of the Gd123ss, energy dispersive X-ray spectrometry measurement is carried out on the samples. It is shown that the atomic ratio of the Gd123ss phase is Gd:Ba:Cu=1.566:1.459:3, which proves successfully that the Gd123ss is a kind of phase with lack of barium. With the increase of BaO doping, the phenomenon of lack of barium is effectively controlled and, the nano Gd123ss phase is generated as the flux pinning centre which can be used to improve the superconducting properties in the growth process of GdBCO bulk superconductor. This results can be concluded that the proper doping ratio can control the element substitution effectively, and the solid solution phase can be greatly reduced to some extent, and the critical current can be improved to a certain extent when the amount of BaO added ranges from 2 wt% to 4 wt%, which is very helpful in inhibiting the Gd/Ba substitution and fabricating the high-quality single domain GdBCO bulk superconductors.

2017, 66 (16): 167701.
doi: 10.7498/aps.66.167701

Abstract +

In order to prepare black silicon material with excellent optical absorption performance for solar cell application, a micro/nano bilayer-structure is formed on the surface of textured silicon wafer by a silver assisted chemical etching method. It is found that the deeper nanoholes could form as the etching time is longer, and the surface reflectivity is reduced obviously due to the increased time of photon reflection from the nanowires. The incident light reflectivity of the prepared black silicon is significantly reduced to 2.3%, showing obviously better optical reflectance characteristics than general monocrystalline silicon wafer, especially in a wavelength range of 300-830 nm. Considering the fact that a large number of carrier recombination centers is introduced into the nanostructured crystal silicon surface, BiFeO3/ITO composite film is coated on the surface of the black silicon solar cell by magnetron sputtering process to optimize the surface defect states and improve the cell performance. The experimental results show that the lengths of the nanowires are predominantly in a range of 180-320 nm for the prepared black silicon with micro/nano double-layer structure. The reflectivity of the incident light is below 5% in a wavelength range from 300 nm to 1000 nm, and reaches a maximal value at about 700 nm. The reflectance increases slightly as BiFeO3/ITO composite film is coated on the surface of black silicon solar cell, but it is still much lower than that of general monocrystalline silicon solar cell. The open circuit voltage and short circuit current density of the black silicon solar cell increase respectively from 0.61 V to 0.68 V and from 28.42 mA/cm2 to 34.57 mA/cm2 after it has been coated with BiFeO3/ITO composite film, and the photoelectric conversion efficiency of the cell increases from 13.3% to 16.8% accordingly. The improvement in performance of black silicon solar cell is mainly due to the promotion of effective separation of photogenerated carriers, thereby enhancing the spectral response of black silicon solar cell in the whole wavelength range. This indicates that the spontaneously polarized BiFeO3 film can play a better role in improving the surface properties of black silicon solar cell. On the other hand, for the BiFeO3 film deposited on the surface of black silicon, a spontaneous polarization positive electric field could be produced, pointing from the film surface to the inside of the solar cell. This polarization electric field could also act as part of built-in electric field to contribute the photoelectric transformation of the black silicon solar cell, leading to the open circuit voltage of cell increasing from 0.61 V to 0.68 V.

2017, 66 (16): 167702.
doi: 10.7498/aps.66.167702

Abstract +

Photocatalytic technology is considered to be the most promising treatment technology of environmental pollution. In this technology, the electronhole pairs generated by the light-responsive materials under sunlight irradiation will produce the oxidation-reduction reactions with the outside world. At present, there are still a series of problems needed to be solved in the photocatalytic technology, among which the recombination of photogenerated electron-hole pairs is a very important limitation. In recent years, the ferroelectric materials have attracted much attention as a new type of photocatalyst because the spontaneous polarizations of ferroelectric materials are expected to solve the recombination problem of electronhole pairs in the catalytic reaction process. However, there are no systematic analyses of the specific mechanisms for ferroelectric materials. In this paper, we review the effects of ferroelectric polarization of ferroelectric materials on photocatalytic activity from three aspects. Firstly, the polarization can give rise to depolarization field and band bending, thereby affecting the separation rate of electron-hole pairs, and speeding up the transmission rate. Therefore, in the first part, the effects of depolarization field and energy band bending on catalytic activity are summarized. This can conduce to understanding the influence of polarization on catalytic activity more clearly from the intrinsic mechanism. Next, the built-in electric field induced by the polarization of ferroelectric material can increase the separation rate of photogenerated carriers and improve the catalytic activity. However, the static built-in electric field easily leads to free carrier saturation due to the electrostatic shielding, which reduces the carrier separation rate. Thus, in order to eliminate the electrostatic shielding, the effects of three external field including temperature, stress (strain) and electric field, which can regulate polarization, on the separation of electronhole pairs and photocatalytic activity are summarized in the second part. Finally, detailed discussion is presented on how to exert effective external fields, such as strain, temperature, and applied electric field, and how to study the force catalysis or temperature catalysis under the no-light condition according to the piezoelectricity effect and pyroelectric effect of ferroelectric material in the last part.

###### INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

2017, 66 (16): 168501.
doi: 10.7498/aps.66.168501

Abstract +

A human brain is a high-density neural network, which has~1011 neurons and~1015 synapses. Neuron as a basic information processing unit builds the biological neural network, and the realization of information transmission and integration depends on the synaptic connection between neurons. This information transfer and integration work is difficult to realize by relying on von Neumann computer, due to the computer only works according to the well-defined programs. To further simulate the imagery thinking of human brain neural network, the researchers begin with the information memory and processing mechanism of human brain neural network. A large number of microelectronic devices with human thinking characteristics are designed, such as memristor, atomic switch, phase change memory, and transistors. The oxide-based thin film transistor under the new material system is one of these devices, and has attracted the attention of researchers. The transistors working as the biological synapses, the gate electrode is regard as presynaptic input terminal, and the channel current is measured as postsynaptic output. Utilizing the proton gating behaviors, a series of synaptic behaviors, such as short-term and long-term memory, paired-pulse facilitation, and spike timing-dependent plasticity is mimicked successfully in these synaptic transistors.#br#With the progressing of science and technology, and the increasing of requirements for environmental protection, researchers pay more attention to the environmentally friendly solid electrolyte materials to fabricate oxide-based thin film synaptic transistor. Researchers have a major interest in starch, due to the low price, rich source, and excellent mechanical properties. Starch can be extracted from corn, potato, sweet potato and other starch-containing substances, and is generally insoluble in cold water, and gelatinized in boiling water. In this study, corn starch solid electrolyte is prepared on ITO glass by spin coating progress, and dried at a constant temperature at 30℃. The electrical performances of protonic/electronic hybrid IZO synaptic transistor gated by corn starch solid electrolyte are excellent, operation voltage, Ion/off ratio, field-effect mobility and subthreshold swing are 1.5 V, 1×107, 18.7 cm2·V-1·s-1 and 156.8 mV/dec., respectively. Due to the mobile proton migrating in corn starch solid electrolyte, the paired-pulse facilitation, learning and memory behaviors and high-pass filter of biological neural synaptic plasticity are realized successfully. The synaptic transistors have potential applications in the field of environment-friendly microelectronic devices to reduce the production costs. Therefore, the corn starch solid electrolyte gated proton/electron hybrid synaptic transistor as an artificial synapse can offer a suitable option to building the neural network.

2017, 66 (16): 168101.
doi: 10.7498/aps.66.168101

Abstract +

The NbC precipitated in steel is in favor of the heterogeneous nucleation of ferrite, which is affected by the alloying elements at the ferrite/NbC interface. However, it is difficult to clearly understand the effect of alloying elements on the ferrite/NbC interface behavior experimentally. Therefore, the first-principles calculation is employed to address this problem in this paper. First of all, the segregation behaviors of alloying element X (=Cr, Mn, Mo, W, Zr, V, Ti, Cu and Ni) on the ferrite(100)/NbC(100) interface are systematically explored. And then, we investigate the influences of these alloying elements on the property of the ferrite/NbC interface. The work of adhesion (Wad), interfacial energy (γint) and electronic structure of ferrite/NbC interface alloyed by these elements are also analyzed. The results show that the (Cr, V, Ti)-doped interfaces have negative segregation energies, which indicates that Cr, V and Ti are easily segregated at the ferrite/NbC interface. Conversely, the Mn, W, Mo, Zr, Cu and Ni are difficult to segregate at the interface. When Mn, Zr, Cu and Ni replace the Fe atoms in the ferrite/NbC interface, the adhesive strength of the interface will decrease, thus weakening the heterogeneous nucleation of ferrite on NbC surface. However, the introduction of Cr, W, Mo, V and Ti will improve the stability of the ferrite/NbC interface due to the larger Wad and lower γint. Therefore, the Cr, W, Mo, V and Ti on the ferrite side of the interface can effectively promote ferrite heterogeneous nucleation on NbC surface to form fine ferrite grain. The analysis of difference charge density indicates that after the introduction of Zr and Cu in ferrite/NbC interface, the interactions among interfacial Zr, Cu and C atoms was weaken. However, when Cr and W are introduced into the clean interface, the strong Cr-C and W-C non-polar covalent bonds are formed, which enhances the adhesion strength of the ferrite/NbC interface. In addition, the minimum Cr-C bonding length at the Cr-doped interface suggests that the interface has the highest interface strength. The Mulliken population analysis shows that for the (Cr, W, Mo, V, Ti)-doped interfaces, the transfer charges of Cr, W, Mo, V and Ti are 1.12, 0.84, 0.54, 0.33 and 0.28, respectively. Nevertheless, for the clean interface, the transfer charge of Fe is only 0.05. Therefore, the interactions among interfacial Cr, W, Mo, V, Ti and C atoms are stronger than that between interfacial Fe and C atoms, which is in good accordance with the above analysis.

###### GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

2017, 66 (16): 169201.
doi: 10.7498/aps.66.169201

Abstract +

Black carbon aerosols affect the shortwave and longwave radiation in climate in a strong yet uncertain way. In aging process, black carbon particles coated by co-emitted aerosols tend to reduce the shortwave radiative forcing of freshly emitted black carbon at the top of atmosphere (TOA), however, this effect is still unclear in the longwave range. Here in this work, we investigate the effect of black carbon aging on longwave radiative forcing. The freshly emitted black carbon aerosols are simulated to be fractal aggregates consisting of hundreds of small spherical primary particles, and these aggregated black carbon aerosols tend to be fully coated by the large sulfate particles after aging. The optical properties of these freshly emitted and internally mixed black carbon aerosols are simulated using the numerically exact superposition T-matrix method, and their longwave radiative forcings are calculated by the radiative transfer equation solver. The results indicate that the black carbon longwave radiative forcing at TOA is remarkably amplified (up to 3) by coating the large sulfate particles, while the black carbon shortwave radiative forcings decrease during their aging. Moreover, the thicker sulfate coatings tend to increase the longwave radiative forcings of black carbon aerosols at TOA. These findings should improve our understanding of the effect of black carbon aging on their longwave radiative forcings and provide guidance for assessing the climate change.