###### INVITED REVIEW

## EDITOR'S SUGGESTION

2021, 70 (4): 048501.
doi: 10.7498/aps.70.20201799

Abstract +

To break through the conventional binary storage based on spin valves and magnetic tunnel junctions, multi-state storage has been successfully achieved in Hall balance. Meanwhile, logic operation can be realized in the storage cell of Hall balance to improve the operation efficiency. Therefore, the concept of Hall balance will benefit the device integration, which provides an effective insight into fabricating the development of spintronics. In this topical review article, firstly the background of memory based on Hall balance is introduced. Secondly, the concept and recent progress of Hall balance are briefly summarized. Thirdly, the manipulation of anomalous Hall resistance ratio (HRR) and its physical mechanism is systematically investigated. Furthermore, magnetic skyrmions and their dynamics in Hall balance are presented in detail. Finally, the application of Hall balance to other kinds of materials is discussed and prospects its future.

###### REVIEW

2021, 70 (4): 047301.
doi: 10.7498/aps.70.20201175

Abstract +

Through the research in recent decades, one has a comprehensive understanding of the thermoelectric properties of bulk and thin film materials, and made rapid progress of improving the thermoelectric figure of merit ZT, for instance, the maximum ZT values of bismuth telluride related materials, cuprous selenide related materials and tin selenide related materials all exceed 2. However, these bulk materials are still far from the requirements for their practical applications on a large scale. The theoretical calculations show that when bulk thermoelectric materials are made a low-dimensional nanostructured materials, such as two-dimensional nano-films and one-dimensional nanowires, their thermoelectric properties will be significantly improved. Taking silicon for example, when the bulk silicon is made silicon nanowires, the ZT value increases nearly a hundredfold. Hence, researches of the thermoelectric performances of materials with micro-nano structures have received great attention. However, the measurement of thermoelectric parameters of low-dimensional materials has brought challenges to researchers, for the traditional measurement methods or test platforms designed for bulk materials are no longer suitable for measuring thermoelectric parameters (thermal conductivity, electrical conductivity and Seebeck coefficient) of low-dimensional materials. Therefore, new measurement methods and test platforms need developing. In this case, micro-electromechanical system micro-suspended structure came into being. In this approach used are the separated samples and substrates, and isolated heat transfer channels, with which the thermal parameters of micro/nano materials can be accurately measured, and the sensitivity of thermal conductance can reach 10 PW/K. In this review, the structures of several micro-electromechanical systems used to measure the thermoelectric properties of low-dimensional nanostructures are introduced, including double suspended islands, single suspended islands and suspended four-probe structures. Meanwhile, the fabrication methods and measurement principles of these MEMS structures and thermoelectric properties of micro-nano structure materials are described in detail.

2021, 70 (4): 048503.
doi: 10.7498/aps.70.20201284

Abstract +

Lead halide perovskites have aroused widespread interest in recent years due to their superior optoelectronic properties, such as high absorption coefficient, high charge carrier mobility, high defect tolerance and high photoluminescence (PL) efficiency. However, one critical problem which potentially hampers their commercial applications is the toxicity caused by lead. To address this toxicity problem, a careful and strategic replacement of Pb

^{2+}with other nontoxic candidate elements represents a promising direction. Tin (Sn), currently the most promising alternative to lead due to its structure and properties, has received extensiveattention. In this review, some recent developments of Sn-based perovskites and their applications in light-emitting diodes are summarized. Firstly, some synthesis methods of Sn-based perovskite materials are introduced. Then, the crystal structures and photoelectric properties of Sn-perovskites in different valence states are analyzed. Then, the potential application of Sn-based perovskite materials in light-emitting devices is presented and some methods to improve the performance of Sn-based PeLEDs are also summarized. Finally, the significant challenges in these Sn-based PeLEDs are pointed out and their possible solutions are suggested. It is expected that this review can conduce to an in-depth understanding of Sn-based halide materials and their application in PeLEDs.###### GENERAL

## EDITOR'S SUGGESTION

2021, 70 (4): 040201.
doi: 10.7498/aps.70.20201520

Abstract +

Based on laser-induced breakdown spectroscopy and machine learning algorithms, ginseng origin identification model is established by principal component analysis algorithm combined with back-propagation (BP) neural network and support vector machine algorithm to analyze and identify ginseng from five different origins in northeast China (Daxinganling, Ji’an, Hengren, Shizhu, and Fusong). The experiment collects a total of 657 groups of laser-induced breakdown spectral data from five origins of ginseng at 200–975 nm, reduces the background continuous spectrum of the original spectral data by moving window smoothing method, labels the ginseng LIBS spectral elements according to the American NIST atomic spectral database. Eight characteristic spectral lines of 7 elements Mg, Ca, Fe, C, H, N and O are selected for principal component analysis according to characteristic spectral selection conditions. The cumulative contribution rate of the first three principal components of the original spectral data reaches 92.50%, which represents a large amount of information about the original ginseng LIBS spectrum, and the samples show a good aggregation and classification in the principal component space. After dimension reduction, the first three principal components are randomly selected in a ratio of 2 to 1 and divided into 438 test sets and 219 training sets, which are used as the input values of the classification algorithm. The experimental results show that the principal component analysis combined with the BP neural network algorithm and support vector machine algorithm can correctly identify 217 and 218 spectra of 219 spectra of the test set respectively, and the average recognition rate is 99.08% and 99.5% respectively. The modeling time of BP neural network is 11.545 s shorter than that of the support vector machine. Both models misjudged Ji'an Ginseng as Shi zhu ginseng, and the reason for this misjudgment is that the normalized intensity of H and O under Ca element ion emission spectrum are similar due to the proximity of Ji 'an to Shi Zhu in geographical environment. The study presented here demonstrates that laser-induced breakdown spectroscopy combined with machine learning algorithm is a useful technology for rapid identification of ginseng origin and is expected to realize automatic, real-time, rapid and reliable discrimination.

2021, 70 (4): 040301.
doi: 10.7498/aps.70.20201602

Abstract +

We study the entanglement dynamics of the three-qubit Dicke model by means of the adiabatic approximation and the exact diagonalization in the parameter regime where the qubit transition frequencies are far off-resonance with the radiation field and the interaction strengths reach the ultrastrong-coupling regime. The single-mode field is prepared in the coherent state and two typical states GHZ and W are chosen as the initial three-qubit states. In the process of evolution, the interaction between the quantized field and three-qubit system leads to the generation of entanglement between the field and qubits, as well as between different parties in the three-qubit system, i.e. the pairwise entanglement of two qubits and the tripartite entanglement, which are of ongoing interest in quantum information process. The generalized concurrence and negativity are adopted to quantify different kinds of entanglement. The qubit-field entanglement never reaches the maximum and no sudden death occurs in the the tripartite entanglement for GHZ state, but it is exactly the opposite for W state. This reflects that the tripartite entanglement of the GHZ state is more robust than W sate, which is the same as in the rotating wave approximation. The results beyond the rotating wave approximation show that the pairwise entanglement gradually decreases and vanishes in the evolution of both initial states, with the tripartite entanglement periodically reaching relatively high level. This means that the interaction in system supports the tripartite entanglement at the cost of pairwise entanglement. The conclusions provide theoretical reference for the robustness of entanglement state and quantum information processing using Dicke model.

2021, 70 (4): 040302.
doi: 10.7498/aps.70.20201652

Abstract +

$ {\left(a{a}^\dagger \right)}^{\pm n} $ and $ {\left({a}^\dagger a\right)}^{\pm n} $ in their normally and anti-normally ordered product forms by using special functions and general mutual transformation rules between normal and anti-normal orderings of operators. Furthermore, the Q- and P-ordered forms of power operators $ {\left(XP\right)}^{\pm n} $ and $ {\left(PX\right)}^{\pm n} $ are also obtained by the analogy method. Finally, some applications are discussed, such as the Glauber-Sudarshan $ P $ -representation of chaotic light field and the generating functions of even and odd bivariate Hermite polynomials.">Operator ordering is often fallen back on due to its convenience in quantum optics and quantum statistics, thus it is an important task to derive the various ordered forms of operators as directly as possible. In this paper we arrange quantum mechanical operators $ {\left(a{a}^\dagger \right)}^{\pm n} $ and $ {\left({a}^\dagger a\right)}^{\pm n} $ in their normally and anti-normally ordered product forms by using special functions and general mutual transformation rules between normal and anti-normal orderings of operators. Furthermore, the Q- and P-ordered forms of power operators $ {\left(XP\right)}^{\pm n} $ and $ {\left(PX\right)}^{\pm n} $ are also obtained by the analogy method. Finally, some applications are discussed, such as the Glauber-Sudarshan $ P $ -representation of chaotic light field and the generating functions of even and odd bivariate Hermite polynomials.

2021, 70 (4): 040303.
doi: 10.7498/aps.70.20201091

Abstract +

In the ocean atmosphere boundary layer far from the continent, marine aerosols generally include two types: sea salt aerosols and secondary marine aerosols. The sea salt aerosols, also called sea salt droplets, stay in the atmosphere for a short time. The sea salt aerosols are produced by the splashing of waves caused by sea breeze on the sea surface. Quantum satellite-to-ship communication is one of the important application scenarios of quantum secret communication. The quantum satellite-to-ship communication is an important part of building a global quantum communication network. In the South China Sea, because the change of wind speed will cause a sharp change in the concentration of aerosol particles and the sharp change of the concentration of aerosol particles can change its own extinction characteristics, the change of aerosol extinction characteristics will inevitably lead to a dramatic attenuation of the satellite-to-ship’s quantum link performance. However, the research on the relationship between wind speed on the sea surface and quantum satellite satellite-to-ship communication channel parameters has not been carried out so far. In this paper, based on the Gras model of wind speeds on the sea surface and aerosol, the quantitative relationship between wind speed and satellite-to-ship quantum channel error rate, channel capacity and channel average fidelity are established respectively. The simulation results show that when the transmission distance is constant, as the sea surface wind speed increases, the channel bit error rate increases; as the wind speed increases, the channel capacity of quantum satellite satellite-to-ship communication decreases; when the source probability is constant, as the wind speed increases, the average fidelity of the channel shows a decreasing trend. When the wind speeds are 4 m/s and 20 m/s, the oceanic atmospheric channel error rate, channel capacity, and channel average fidelity are respectively 4.62 × 10

^{–3}and 4.91 × 10^{–3}, 0.957 and 0.65, 0.999 and 0.974. It can be seen that the wind speed has a significant effect on the performance of maritime quantum communication. Therefore, when quantum communication over the ocean, in order to improve the reliability of communication, the parameters of the system should be adaptively adjusted according to the wind speed.
2021, 70 (4): 040304.
doi: 10.7498/aps.70.20201522

Abstract +

The gravity field is one of the basic physical fields of the Earth. Dynamic measurements could improve the efficiency of gravity surveying and mapping, and have very important applications in the fields of geological survey, geophysics, resource exploration, inertial navigation and so on. Currently, dynamic gravity measurements are mostly based on relative measurements. The dynamic relative gravimeters have the problem of zero drift, which affects the measurement performance. Dynamic absolute gravimeters can provide synchronous and co-site calibration for relative gravimeters and solve the problem of long drift. Therefore dynamic absolute gravimeters have attracted much attention. Based on a homemade atomic gravimeter and an inertial stable platform, a system of absolute gravity dynamic measurement has been built on a ship. The dynamic measurement experiments of absolute gravity under the state of ship-borne mooring have been carried out. It is found that the frequency of vibration noises of this ship is around 0.2 Hz, and the amplitude is about 1 Gal. In the case of harsh environment, the temperature and humidity of the used container have been controlled to be 25 ℃ and 70% via the air conditioning. Then, a continuous gravity measurement of 5 hour has been taken, and the peak to peak value of 80 mGal has been achieved. The values of gravity have no drifts at all during the measurements. Besides, the sensitivity of gravity measurement has been evaluated to be 16.6 mGal/Hz

^{–1/2}under the environment of ship-borne mooring. A resolution of 0.7 mGal could be reached with an integration time of 1000 s. The stability of this system has been estimated after the measurement of absolute gravity for two weeks, and the change of absolute gravity values is about 0.5 mGal. Finally, in order to evaluate the accuracy of the dynamic measurement of absolute gravity, the measured average value of absolute gravity at ship-borne has been compared with the value of the high-precision absolute gravity reference point of the pier, and the results are estimated to be (–0.072 ± 0.134) mGal. The results of this paper could provide a new solution for the simultaneous and co-site calibration of the ocean relative gravimeter on the same ship.
2021, 70 (4): 040501.
doi: 10.7498/aps.70.20201346

Abstract +

In this paper we propose a class of 8th-order potential function, and discuss the bifurcation characteristic of such a system in detail. Then, a symmetric quad-stable system consisting of two small-scale bistable potentials on the left and right and an intermediate barrier is obtained. In order to analyze the quad-stable system characteristic effectively, under the combined action of periodic force and random force, the approximate analytical expression of the quad-stable system output response is established. Meanwhile, from the viewpoint of the energy, the work which is a process quantity is introduced to describe the capacity for work between the large-scale and small-scale bistable potential. It is found that the double stochastic resonance phenomenon does exist in the quad-stable system. The theoretical analysis and numerical simulation results indicate that when the height of the intermediate barrier is higher than the barrier height of the two small-scale bistable potentials on the left and right, as the noise intensity increases, the response of the quad-stable system transforms a small-amplitude vibration restricted in a small-scale bistable subsystem into a large-amplitude vibration across the intermediate barrier, and the work done by the periodic force presents a double-peak curve. To be more specific, as the noise intensity gradually increases from zero, the system response is first confined to a small-scale bistable potential. Under the joint action of the small-scale bistable potential, periodic force and random force, the small-scale stochastic resonance phenomenon occurs, and the first resonance peak appears. With the noise intensity increasing even further, the system response turns into the large-amplitude vibration between two small-scale bistable subsystems, resulting in the large-scale stochastic resonance phenomenon and a higher resonance peak. Thus, the work done by periodic force has the peak values at two different noise intensities, which means that the noise can induce the double stochastic resonance phenomenon in the quad-stable system. More importantly, it can be found that the small-scale stochastic resonance can enhance the effect of large-scale stochastic resonance.

2021, 70 (4): 040502.
doi: 10.7498/aps.70.20201059

Abstract +

There are many resonance phenomena in a nonlinear dynamical system subjected to forced excitation, especially the excitation with multiple frequencies. Duffing oscillator subjected to the excitation with multiple frequencies may exhibit some complex resonance phenomena, such as simultaneous resonance and combination resonance. In this paper, the simultaneous primary and super-harmonic resonance of Duffing oscillator is studied, and it is analyzed in periodic motion and chaotic motion. Firstly, the approximate analytical solution is obtained by the method of multiple scales, and the correctness and accuracy of the analytical solution are verified through numerical simulation. Furthermore, the amplitude-frequency equation and phase-frequency equation of the steady-state response are derived from the approximate solution, and the stability of the steady-state response is analyzed based on Lyapunov’s first method. It is found that there are at most two stable periodic solutions and one unstable periodic solution. The effects of nonlinear stiffness on steady-state response is also analyzed through numerical simulation. However, the approximate solution obtained by the singular perturbation method is not sufficient to describe the global characteristics of the system, therefore, the necessary condition for the chaos in the sense of Smale horseshoes is derived based on the Melnikov method. Finally, one-demonstrational system that meets the condition of simultaneous resonance is analyzed through numerical simulation, and the bifurcation diagram shows the two thresholds of the demonstration system. At the first threshold, the heteroclinic orbit of the system breaks, and the system goes to chaos in crisis way. At the second threshold, the crisis reappears and the new strange attractor appears. The variation of the first critical value under various frequency combinations is investigated based on the Melnikov method, and the results are compared with the results of numerical simulation. The analytical and numerical results are qualitatively the same although there is a quantitative difference between them.

2021, 70 (4): 040503.
doi: 10.7498/aps.70.20201499

Abstract +

Phase change materials can absorb, store and release heat with their latent heat capacity. Meanwhile, their temperature fluctuation during phase changing is small, so they can realize temperature control and be used for thermal management. But their low thermal conductivity and easy leakage problem seriously restrict their performance. Graphene aerogel have a large specific surface area because of its rich porous structure, and can absorb phase change materials to solve the leakage problem. Meanwhile, the high thermal conductivity of graphene can improve the thermal conductivity of phase change materials. At the same time, the black of graphene aerogel itself has good light absorption performance. Combined with phase change material, the resulting composite phase change material can make full use of the sunlight to achieve photo-thermal transformation and energy storage. Composite phase change material can release heat at night when there is no solar energy, making up for the intermittency of solar energy. Herein, graphene aerogel was prepared by reduction self-assembly and freeze-drying method, and composite phase change material was prepared by vacuum impregnation method. The graphene aerogel composite phase change materials with different mass fraction were prepared by using n-octadecane as phase change material. The thermal conductivity of the sample with 13.99 wt% graphene aerogel content was 306.2% higher than that of pure octadecane, and the latent heat of melting and solidification decreased by 13.8% and 10.8% respectively. Simultaneously, molecular dynamics simulation results show that the introduction of graphene aerogels will increase to a certain extent is octadecane molecular order and consistency, which in the same temperature of composite phase change materials are octadecane than pure octadecane molecules have more concentrated at the end of the distance and the torsion angle, radial distribution function and the diffusion coefficient is relatively low, that the introduction of graphene materials can promote positive octadecane coefficient of thermal conductivity.

2021, 70 (4): 040601.
doi: 10.7498/aps.70.20201225

Abstract +

Optical frequency combs of the femtosecond laser have been widely used in time-frequency technology and precision spectrum measurement. The absolute ranging technology derived from time-frequency characteristics of the optical frequency comb is expected to become the incomparable means of length metrology and distance measurement in the future due to its traceability to time-frequency standard and capability of large scale and high precision. This paper proposes a real-time absolute ranging method with multi-wavelength interferometry referenced to optical frequency comb, which enables multiple continuous-wave lasers to be synchronously calibrated to selected modes of the frequency comb by means of optical phase-locked loop. With synchronous phase measurement and calculation with excess fraction algorithm, absolute distance measurement by multi-wavelength interferometry is ultimately fulfilled. The proposed measurement method can not only retain high resolution and high accuracy of traditional laser interferometry, but also can be traced to a time-frequency reference, which is of metrological significance to high-precision length and distance measurement, especially to the definition of “meter” for physical reproduction. Measured results for ranging experiments have proved that the non-ambiguity range of the four-wavelength interferometer reaches 44.6 mm, and fluctuations of air refractive index cause the non-ambiguity range change with the order of nanometers. Through theoretical analysis, it is pointed out that the non-ambiguity range of the multi-wavelength interferometer in the actual measurement environment is restricted by the calculated error of air refractive index, especially the estimation accuracy and fluctuation degree of the refractive index relationship between wavelengths. And in a good laboratory conditions, the non-ambiguity range of real-time absolute ranging by frequency-comb-calibrated multi-wavelength interferometry can reach several meters or even tens of meters. At the same time, a 2-meter linear displacement comparison has been carried out, the P.V. value of the residual errors for linear fitting is 36.1 nm, and such residual errors match the magnitude of uncertainty of air refractive index calculated by empirical formula, which prove that the multi-wavelength interferometry can perform meter-level absolute ranging. The proposed research can be directly applied to precision manufacturing of large-scale semiconductors up to several meters, and is beneficial to promoting the accuracy of laser ranging for space mission.

2021, 70 (4): 040602.
doi: 10.7498/aps.70.20201442

Abstract +

–12. Then, the refractive index of helium in a range of 10

^{2}–10^{5}Pa is measured by the vacuum measuring device which is based on Fabry-Perot cavity, and the uncertainty of measurement is 9.59 × 10^{–8}. Finally, the discrepancy between the theoretical and measured values of helium refractive index is compared and analyzed. It can be concluded that the the uncertainty of helium refractive index measurement originates from the deformation of the cavity caused by helium permeation. Therefore, solving the problem of helium permeation is the key to establishing a new vacuum standard. In this paper, the change of cavity length caused by helium penetration in the cavity is corrected. The refractive index coefficient is corrected at various pressure points in a vacuum range of 10^{3}–10^{5}Pa, and its pressure-dependent expression is obtained The variation of cavity length caused by gas pressure is further quantified. The relationship between the change of cavity caused by gas pressure and that caused by the refractive index is obtained. The correction parameter of cavity length is calculated to be 3.12 × 10^{–2}. In the future experiment of helium refractive index measurement by means of Fabry-Perot cavity, the refractive index correction coefficient at each pressure point given in this paper can be used to correct the refractive index measurement results, thereby eliminating the influence of helium penetration on the refractive index measurement, and obtaining the gas pressure with high accuracy.">In the face of the historical change of international measurement system, the classical physics based physical standard corresponding to many measurement parameters develops toward "natural standard", namely quantum standard. In order to further improve the reproducibility and accuracy of vacuum value, the latest research uses quantum technology to realize the measurement and characterization of vacuum value. In this method, Fabry- Perot cavity is used to accurately measure the refractive index of the gas. The density can be calculated by the refractive index and inversed to obtain the corresponding vacuum value. The measurement of the gas refractive index is the key to the accuracy of the vacuum value. The macroscopic permittivity of nonpolar gases is related to the microscopic polarization parameters of atoms through quantum dynamics. In recent years, with the rapid development of ab initio theory and methods on the electromagnetic and thermodynamic properties of monatomic molecules, the calculation accuracy of relevant parameters was constantly improved, which can further reduce the measurement uncertainty of the above methods. In this paper, the theoretical value of helium refractive index is calculated accurately based on the first principle with known pressure and temperature. The relationship between gas pressure and refractive index is obtained, and the relative uncertainty of the theoretical value of refractive index is 6.27 × 10^{–12}. Then, the refractive index of helium in a range of 10^{2}–10^{5}Pa is measured by the vacuum measuring device which is based on Fabry-Perot cavity, and the uncertainty of measurement is 9.59 × 10^{–8}. Finally, the discrepancy between the theoretical and measured values of helium refractive index is compared and analyzed. It can be concluded that the the uncertainty of helium refractive index measurement originates from the deformation of the cavity caused by helium permeation. Therefore, solving the problem of helium permeation is the key to establishing a new vacuum standard. In this paper, the change of cavity length caused by helium penetration in the cavity is corrected. The refractive index coefficient is corrected at various pressure points in a vacuum range of 10^{3}–10^{5}Pa, and its pressure-dependent expression is obtained The variation of cavity length caused by gas pressure is further quantified. The relationship between the change of cavity caused by gas pressure and that caused by the refractive index is obtained. The correction parameter of cavity length is calculated to be 3.12 × 10^{–2}. In the future experiment of helium refractive index measurement by means of Fabry-Perot cavity, the refractive index correction coefficient at each pressure point given in this paper can be used to correct the refractive index measurement results, thereby eliminating the influence of helium penetration on the refractive index measurement, and obtaining the gas pressure with high accuracy.###### ATOMIC AND MOLECULAR PHYSICS

2021, 70 (4): 043101.
doi: 10.7498/aps.70.20201386

Abstract +

$\alpha _{\text{0}}^{\text{1}}{\beta _0}$ . For Li atoms, the present electric-dipole polarizability is in good agreement with the available theoretical and experimental results. However, the present hyperpolarizability is different from the other theoretical results significantly. Moreover, the hyperpolarizabilities calculated by different theoretical methods are quite different. The biggest difference is more than one order of magnitude. In order to explain the reason for these differences, we analyze the contributions of different intermediate states to the hyperpolarizability in detail. It is found that the sum of the contributions of the 2s→$\left( {n \geqslant 3} \right)$ and $\left( {n \geqslant 3} \right)$ to hyperpolarizability is approximately equal to that term of $\alpha _{\text{0}}^{\text{1}}{\beta _0}$ . The total hyperpolarizability, which is the difference between the sum of the contributions of the 2$\left( {n \geqslant 3} \right)$ and $\left( {n \geqslant 3} \right)$ to hyperpolarizability and $\alpha _{\text{0}}^{\text{1}}{\beta _0}$ , is relatively small. Consequently, this difference magnifies the calculated error. If the uncertainties of the transition matrix elements are less than 0.1%, the uncertainty of hyperpolarizability is more than 100%. Therefore, the differences of hyperpolarizabilities for the ground state of Li atoms, calculated by various theoretical methods, are more than 100% or one order of magnitude.">The wave functions, energy levels, and oscillator strengths of Be$\alpha _{\text{0}}^{\text{1}}{\beta _0}$ . For Li atoms, the present electric-dipole polarizability is in good agreement with the available theoretical and experimental results. However, the present hyperpolarizability is different from the other theoretical results significantly. Moreover, the hyperpolarizabilities calculated by different theoretical methods are quite different. The biggest difference is more than one order of magnitude. In order to explain the reason for these differences, we analyze the contributions of different intermediate states to the hyperpolarizability in detail. It is found that the sum of the contributions of the 2s→$\left( {n \geqslant 3} \right)$ and $\left( {n \geqslant 3} \right)$ to hyperpolarizability is approximately equal to that term of $\alpha _{\text{0}}^{\text{1}}{\beta _0}$ . The total hyperpolarizability, which is the difference between the sum of the contributions of the 2$\left( {n \geqslant 3} \right)$ and $\left( {n \geqslant 3} \right)$ to hyperpolarizability and $\alpha _{\text{0}}^{\text{1}}{\beta _0}$ , is relatively small. Consequently, this difference magnifies the calculated error. If the uncertainties of the transition matrix elements are less than 0.1%, the uncertainty of hyperpolarizability is more than 100%. Therefore, the differences of hyperpolarizabilities for the ground state of Li atoms, calculated by various theoretical methods, are more than 100% or one order of magnitude.

*n*p_{j}*n*p*→*_{j}*n*d_{j}*s*→*n*p_{j}*n*p*→*_{j}*n*d_{j}^{+}ions and Li atoms are calculated by using a relativistic potential model, which is named the relativistic configuration interaction plus core polarization method (RCICP). The calculated energy levels in this work are in good agreement with experimental levels tabulated in NIST Atomic Spectra Database, and the difference appears in the sixth digit after the decimal point. The present oscillator strengths are in good agreement with the existing theoretical and experimental results. By means of these energy levels and oscillator strengths, the electric-dipole static polarizabilities and hyperpolarizabilities of the ground states are determined. The contributions of different intermediate states to the hyperpolarizabilities of the ground state are further discussed. For Be^{+}ions, the present electric-dipole polarizability and hyperpolarizability are in good agreement with the results calculated by Hartree-Fock plus core polarization method, the finite field method and relativistic many-body method. The largest contribution to the hyperpolarizability is the term of*n*p_{j}*n*p*→*_{j}*n*d_{j}*s*→*n*p_{j}*n*p*→*_{j}*n*d_{j}###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2021, 70 (4): 044201.
doi: 10.7498/aps.70.20201331

Abstract +

$0.8 \times {10^{ - 14}}$ to $1.4 \times {10^{ - 14}}\;{{\rm{cm}}^{ - 2}}$ , the resonant frequency of transparent window increases 7.5628 THz. In a dual-band PIT model, under the same change of relaxation rate, the resonant frequencies of the two transparent windows increase 6.8593 and 9.1457 THz, at the same time, and the resonant frequencies of the three transparent windows in triple-band PIT model increase 6.8593, 8.7939 and 11.2563 THz respectively. In addition to the resonant frequency, the transmittance at the dip frequency in each model gradually decreases, and the depth of depression gradually increases. Finally, the sensing characteristics of the single-band PIT model are further studied. When the refractive index of the background changes from small to large, the dip frequency and the resonant frequency of the transparent window will be significantly red-shifted. The change of frequency is approximately linear with refractive index. The model has a sensitivity of 6110.6 (nm/RIU) and a figure of merit of 7.39 (1/RIU) which is better than the same type of sensor. This model provides a theoretical reference for designing the multiband filtering and ultrasensitive sensors. "> In this paper, we propose three plasmon-induced transparency(PIT) hybrid models based on the coupling of black phosphorus (BP) nanorods. By using the bright-bright mode coupling between BP nanorods with different lengths, and according to the weak hybrid effect after the detuning of each bright mode unit, we can trigger the single-band, dual-band and triple-band PIT effects. Secondly, by changing the relaxation rate of BP, the resonant frequency can be adjusted in each PIT model. When the relaxation rate of BP changes from small to large, the resonance frequencies of the transparent windows in those three PIT models all increase and the blue shifts occur. In a single-band PIT model, when the relaxation rate of BP changes from $0.8 \times {10^{ - 14}}$ to $1.4 \times {10^{ - 14}}\;{{\rm{cm}}^{ - 2}}$ , the resonant frequency of transparent window increases 7.5628 THz. In a dual-band PIT model, under the same change of relaxation rate, the resonant frequencies of the two transparent windows increase 6.8593 and 9.1457 THz, at the same time, and the resonant frequencies of the three transparent windows in triple-band PIT model increase 6.8593, 8.7939 and 11.2563 THz respectively. In addition to the resonant frequency, the transmittance at the dip frequency in each model gradually decreases, and the depth of depression gradually increases. Finally, the sensing characteristics of the single-band PIT model are further studied. When the refractive index of the background changes from small to large, the dip frequency and the resonant frequency of the transparent window will be significantly red-shifted. The change of frequency is approximately linear with refractive index. The model has a sensitivity of 6110.6 (nm/RIU) and a figure of merit of 7.39 (1/RIU) which is better than the same type of sensor. This model provides a theoretical reference for designing the multiband filtering and ultrasensitive sensors.

2021, 70 (4): 044202.
doi: 10.7498/aps.70.20201623

Abstract +

Algebraic topology, algebraic geometry, and category theory are new branches of mathematics that have developed in the last hundred years and have had profound collisions with modern physics in recent decades. A large number of topological phenomena are found in systems such as viruses, bacteria, fingerprints, fish school, typhoons, and the galaxies. Topological phenomena play a significant role in the spatial distribution of viral particles, the formation of nanovesicles of polymer, and Bose-Einstein condensates. In this paper, based on Landau-de Gennes theory, models have been constructed to simulate the topological charge distribution and other topological phenomena in liquid crystals. The research indicates that as the radius of the liquid crystal panel grows, the ratio of the optimal distance between the topological charge to the radius gradually increases and tends to stabilize. The size of the disc affects the equilibrium position of the topological load. The relative equilibrium position of topological load is between 0.542 and 0.558, in which the ratio of the distance between the two +1/2 topological loads in the 0–5 mm disc increases from 0.542 to 0.558, and then in the 5–12 mm section the ratio is almost stable at 0.558. As the size of the disc increases, the influence of the boundary anchoring energy decreases, and the equilibrium position, i.e. the distance between the two topological charges and the diameter of the disc, approaches a constant value. This equilibrium position is the result of the repulsive force of the disc boundary on the +1/2 topological load and the repulsive force between the two topological loads. The angle between two topological charges in a liquid crystal disc is between 140° and 180°. The trajectory of the topological charge is the process of finding the lowest free energy point, and the end of the trajectory is in the region of minimum free energy. The result is instructive significance in the design of classification containers by using topological charge condensate effect. And it is helpful to further understand the topological phenomena in soft materials including topological colloids, liquid crystals, and liquid crystal copolymers.

## EDITOR'S SUGGESTION

2021, 70 (4): 044203.
doi: 10.7498/aps.70.20201403

Abstract +

The 193-nm immersion step-and-scan projection lithography tool is the most critical equipment in the high-volume manufacturing of integrated circuit with 45nm technology nodes and beyond. With the increase of numerical aperture (NA) of the projection lens, the resolution of lithography tool can be enhanced effectively. However, the polarization effect of the optics in an exposure system is more significant in high NA immersion lithography, which influences the lithographic imaging quality greatly. Thus, the polarization parameters of the immersion exposure system should be controlled -accurately for ensuring the lithographic imaging quality. With the advantages of miniaturization and high-accuracy online detection, the grating is applied to the polarization detection of the immersion lithography tools. A bilayer metallic grating polarizer with compact structure and excellent polarization performance is designed based on the inverse polarization effect and transmission enhancement effect on TE-polarized light. Rigorous coupled-wave theory and finite-different time-domain method are used to design the bilayer metallic grating polarizer. The former is used for analyzing the initial structure parameters of the grating, and the latter is used for acquiring the cross-sectional electromagnetic field of the structure. The initial parameters of the grating are calculated based on the surface plasmons resonance and Fabry-Perot-like theory. The influence of geometrical parameters of the grating on its polarization performance is analyzed. The simulation results show that the enhancement of TE-polarized light transmittance is mainly modulated by the middle layer height of the grating. Firstly, the TE-polarized light transmission is enhanced by the standing wave in the bottom medium cavity, and further enhanced by the top optical funnel formed. However, the transmission suppression of TM-polarized light is mainly caused by the low frequency mode of charge movement formed by surface plasmons. For the designed grating polarizer, the transmittance of TE-polarized light is 56.8%, and the extinction ratio is 65.6 dB at normal incidence. Comparing with previous metal grating polarizer, the extinction ratio of the designed grating is increased by four orders of magnitude.

2021, 70 (4): 044301.
doi: 10.7498/aps.70.20201385

Abstract +

Measurement of the bubble size distribution (BSD) and the void fraction in bubbly liquids is very important for many areas, such as ocean science, cavitation inception studies, and military applications. The methods of using acoustical attenuation caused by bubbly liquid to estimate the BSD can date back to Medwin’s research in which the resonant bubble approximation (RBA) was proposed [Medwin H 1970

*J.Geophys.Res*.**75**599]. In the traditional theory, the methods used to invert the acoustical attenuation for obtaining the BSD are well developed and useful for the low void fraction. However, the comparison between the results from the conventional methods and the experimental results is not satisfactory when the void fraction is higher than 10^{–5}. In fact, the frequency dispersion and the bubble interaction in bubbly liquid should be considered in the process of inverting the BSD for the high-density bubble group. In this paper, the relationship between the attenuation and the phase velocity of bubbly liquid is analyzed based on the effective medium theory, and the bubbles’ interaction is considered by calculating the change of vibration parameters of bubbles. On this basis, we propose an iterative method to accurately determine the BSD of the high-density bubble group. In this iterative method, the errors of the inversion results are reduced by estimating the phase velocity and the vibration parameters of bubbles from sound attenuation. This iterative method is numerically tested for the bubble distributions of log-normal and power-law functions. The simulation results are in good agreement with the given bubble distributions for the void fractions higher than 10^{–3}. Further, the influence of the frequency dispersion and the bubble interaction on inversion results are discussed. Compared with the experimental data, the inversion results calculated by the iterative method show that considering the dispersion can significantly reduce the errors, when the void fraction of bubbly liquid increases up to 10^{–5}. And the correction to bubble damping coefficient and resonance frequency have an important effect on the inversion result when the void fraction of bubbly liquid is higher than 10^{–3}, indicating that the iterative method proposed by this paper can be a useful tool for inverting the BSD of the high-density bubble group in the liquid.
2021, 70 (4): 044302.
doi: 10.7498/aps.70.20201111

Abstract +

$\left(({L}/{\lambda }) < 0.1\right)$ and small loops $\left(2\pi ({R}/{\lambda }) < 0.1\right)$ . The new transmitting and receiving sensors are designed based on the effective length of the electromagnetic vector sensor in practical engineering application. Firstly, the Parallel Factor trilinear alternating least square algorithm is proposed to make full use of the spatial-temporal tensor model for received data after matching filtering. And, the closed-form automatically paired two dimensional Direction of Departure and two dimensional Direction of Arrival can be obtained with the aid of the Parallel Factor trilinear alternating least square algorithm. Furthermore, due to the vector-cross-product Poynting-vector algorithm is failed in the condition of the new designed electromagnetic vector sensors with long dipoles and large loops, an efficient blind estimation method without requiring the prior knowledge of the dipoles’ electric length ${L}/{\lambda }$ and loops’ electric radius ${R}/{\lambda }$ is detailed derived to deal with the estimation of the transmitting azimuth angle, transmitting polarization angle, transmitting polarization phase difference, receiving azimuth angle, receiving polarization angle and receiving polarization phase difference. And, the estimated transmitting azimuth angle, transmitting polarization angle, transmitting polarization phase difference, receiving azimuth angle, receiving polarization angle and receiving polarization phase difference are also automatically paired without additional angle parameter pair matching process. Finally, the expression of the Cramer Rao Bound is detailed derived for the designed new bistatic electromagnetic vector sensors multiple-input multiple-output radar. The detailed derived Cramer Rao Bound can provide a benchmark for angle parameter and polarization parameter estimation performance. Additionally, simulation results are conducted to verify the better angle parameter and polarization parameter estimation accuracy of the proposed method for the new designed bistatic electromagnetic vector sensors multiple-input multiple-output radar with long dipoles and large loops. Through theoretical analysis and simulation results, it is can be founded that the length of the electric dipole and the circumference of the loops should be suitable selected to guarantee a better estimation accuracy. Thus, the interesting work in this paper can further promote the engineering application of electromagnetic vector sensor in bistatic multiple-input multiple-output radar.">In this paper, a new designed bistatic electromagnetic vector sensors multiple-input multiple-output radar with long dipoles and large loops is proposed to avoid the low inefficient electromagnetically radiation efficiency of original bistatic electromagnetic vector sensors multiple-input multiple-output radar with short dipoles $\left(({L}/{\lambda }) < 0.1\right)$ and small loops $\left(2\pi ({R}/{\lambda }) < 0.1\right)$ . The new transmitting and receiving sensors are designed based on the effective length of the electromagnetic vector sensor in practical engineering application. Firstly, the Parallel Factor trilinear alternating least square algorithm is proposed to make full use of the spatial-temporal tensor model for received data after matching filtering. And, the closed-form automatically paired two dimensional Direction of Departure and two dimensional Direction of Arrival can be obtained with the aid of the Parallel Factor trilinear alternating least square algorithm. Furthermore, due to the vector-cross-product Poynting-vector algorithm is failed in the condition of the new designed electromagnetic vector sensors with long dipoles and large loops, an efficient blind estimation method without requiring the prior knowledge of the dipoles’ electric length ${L}/{\lambda }$ and loops’ electric radius ${R}/{\lambda }$ is detailed derived to deal with the estimation of the transmitting azimuth angle, transmitting polarization angle, transmitting polarization phase difference, receiving azimuth angle, receiving polarization angle and receiving polarization phase difference. And, the estimated transmitting azimuth angle, transmitting polarization angle, transmitting polarization phase difference, receiving azimuth angle, receiving polarization angle and receiving polarization phase difference are also automatically paired without additional angle parameter pair matching process. Finally, the expression of the Cramer Rao Bound is detailed derived for the designed new bistatic electromagnetic vector sensors multiple-input multiple-output radar. The detailed derived Cramer Rao Bound can provide a benchmark for angle parameter and polarization parameter estimation performance. Additionally, simulation results are conducted to verify the better angle parameter and polarization parameter estimation accuracy of the proposed method for the new designed bistatic electromagnetic vector sensors multiple-input multiple-output radar with long dipoles and large loops. Through theoretical analysis and simulation results, it is can be founded that the length of the electric dipole and the circumference of the loops should be suitable selected to guarantee a better estimation accuracy. Thus, the interesting work in this paper can further promote the engineering application of electromagnetic vector sensor in bistatic multiple-input multiple-output radar.

2021, 70 (4): 044401.
doi: 10.7498/aps.70.20201546

Abstract +

Supercritical fluids are widely used in engineering technology, and the flow and heat transfer characteristics are very important for engineering design. However, due to the fact that the physical micro- and macroscopic behaviors of supercritical fluids are still open, neither the heat transfer mechanism nor the flow mechanism of supercritical fluids has been well revealed. It is widely believed that liquid-like (LL) and gas-like (GL) supercritical fluid are two phases distinguishable on a molecular scale. Only recently, has it become clear that the macroscopic transition from LL to GL supercritical state, when crossing the Widomline, is successfully detected in experiment, and explained based on the pseudo-boiling concept. In this paper, the abnormal flow and heat transfer behavior of supercritical CO

_{2}are studied based on the pseudo-boiling theory. On the assumption that the transition from LL to GL is heterogeneous, an analysis method for pseudo-boiling heat transfer is developed from classical dimensional analysis and subcritical subcooled boiling theory of models. To analyze the pseudo-boiling resulting in heat transfer deterioration process of supercritical fluid, two dimensionless numbers which are*π*= (*q*_{w}·*ρ*_{l})/(*G*·Δ*i*·*ρ*_{g}) and*π*_{13}= (*q*_{w}·*β*_{pc}·*d*_{i})/*λ*_{g}are proposed to explain the anomalous heat transfer characteristics in vertical upward heating flow. The former*π*reflects the rate of conversion between gas-like and liquid-like fluid. The larger gas-like conversion rate promotes the rapid production of more high-temperature fluid in the near-wall region, and the latter*π*_{13}characterizes the temperature gradient of gas-like film near the wall: the larger temperature gradient causes the gas film to cover the wall surface. The heat transfer deterioration may occur when the cooler liquid-like fluid of the core region cannot rewet the hot wall adequately. The new dimensionless numbers can successfully explain the heat transfer deterioration of supercritical fluid flow induced by pseudo-boiling. Our work paves the way to understanding the heat transfer and flow for supercritical fluids which establishes a relation among the internal flow, heat transfer field characteristics, boundary conditions and physical properties based on the pseudo-boiling theory preliminarily. The results of dimensional analysis can be applied to the similarity theory analysis of different fluids, which is of significance for promoting the theoretical research of supercritical fluid heat transfer on the basis of pseudo-boiling concept.
2021, 70 (4): 044701.
doi: 10.7498/aps.70.20201358

Abstract +

To acquire the unique behavioral characteristics that droplets impact the Janus particle (amphiphilicity) sphere surface, a series of collision experiments is conducted by using Janus particles with a diameter of 5.0 mm. These Janus particles are prepared by chemical treatment of the copper particles. Water droplets with a diameter of 2.0 mm are used to impact hydrophbilic surface, hydrophobic surface and hydropholic-hydropholic boundary of Janus particle, under four Weber numbers which are 2.7, 10, 20 and 30, the corresponing Reynold numbers are 621.8, 1191.9, 1589.2 and 2185.1. The results show that the collision process can be divided into four stages: spread, retraction, oscillation and rebound. Under different Weber numbers, the behavioral characteristics of droplets are mainly affected by the surface wettability. On the hydrophbilic surface, the droplets exhibit the spreading characteristics, with increasing time the spreading coefficient gradually increases and finally tends to be stable. As Weber number increases, the difference in spreading coefficient for droplet under adjacent Weber number gradually decreases, indicating that droplets spreading is mainly affected by inertia. On the hydrophobic surface, the spreading coefficient on the figure presents a "parabola" shape. Droplets spreading takes the same time to reach the maximum spreading coefficient under different Weber numbers. However, when droplets impact the hydropholic-hydropholic boundary, droplets show spreading and rebound behavioral characteristics simultaneously. At the beginning of droplets spreading, the spreading coefficient has almost the same value on both sides of the hydropholic-hydropholic boundary. With the increase of time, part of droplets on the hydrophobic are attracted by the hydrophbilic side surface and go into hydrophbilic side zone. In order to explain this phenomenon, the concept of line tension is introduced and the line tension on the hydrophilic side is found to be less than that on the hydrophobic side by analyzing the forces on both sides of the droplets. Based on energy balance and force analysis, it is found that the mutual conversion of droplet kinetic energy and surface energy are the key factor to make droplets spread. The droplets possess the unique behavioral characteristics and reach an equilibrium state under the combined influence of gravity, inertial force, surface tension, viscous force, and contact force.

2021, 70 (4): 044702.
doi: 10.7498/aps.70.20201303

Abstract +

To reduce the run-off of fluid in sealing system, especially in the multiphase medium and extreme operating conditions, it is necessary to investigate the wetting and spreading behavior in silicon carbon (SiC) sealing face. Considering the sealing performance, ring-grooved structures with a varying depth (

*h*) and width (*w*) are fabricated on SiC substrates by laser marking machine. The radius of structure’ inner surface is 1.5 mm, less than the capillary length of water. Then, experimental equipment is designed to observe the profile and the spreading behaviors of droplet on the surface, and the wetting performance and pinning effect are discussed, and the influences of depth and width of ring-grooves on the wetting performance can be obtained. The results show that the contact angle (CA) and the advancing contact angle (ACA) of smooth SiC surface are 70° and 76.5°, respectively. And the values decrease to CA 50° and ACA 54° after laser processing, which may be due to the average roughness (Ra) increasing from 0.1 μm in smooth surface to 0.8 μm in laser machined surface, making the hydrophilic surface more hydrophilic. The CA on the edge of ring-grooves increases to 138.5°, the control of fluid can be realized. When the droplet spreads along the radius direction before reaching the edge of groove, its CA keeps 76.5°. Once it reaches the edge, the position of contact line remains constant or changes slowly along the wall of groove(we are more inclined to the latter), and thus making the CA increase with the droplet volume increasing, until reaching a maximum apparent contact angle (*θ*_{max}). And*θ*_{max}in the experiment is less than that from the Gibbs equation, which is perhaps because of the mechanical vibration, the roughness of the wall or the liquid viscosity effect. After that, the droplet collapses, and spreads along the groove area, or even flows over the outer edge of the ring groove. The influences of*h*and*w*of groove are then studied, showing that*θ*_{max}first increases linearly and then tends to be stable with the increase of*h*, and the depth of groove has a critical value (*h*_{c}) of 80 μm. When*h*<*h*_{c}, the droplet moves along the wall to the bottom of groove, the droplet collapses after reaching the bottom under the surface tension function. However, when*h*≥*h*_{c}, the droplet is in a stable condition, and collapses with the increase of volume. When*h*= 100 μm, a critical value of width (*w*_{c}) of 40 μm exists for the geometrical relationships of ACA in wall between*h*and*w*. If*w*is too small, the droplet will contact the outer diameter of ring groove, which finally makes the droplet collapse and spread on the smooth surface. The present research can conduce to understanding the pinning effect in the solid edge and the spreading behavior of droplets in SiC surface.###### PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

## EDITOR'S SUGGESTION

2021, 70 (4): 045101.
doi: 10.7498/aps.70.20201611

Abstract +

The accurate predicting of thermal conductivity of GaN semiconductors, especially GaN films, is of great importance for the thermal management in electronic devices. In this paper, a theoretical model based on the first-principles calculations and Debye-Callaway model is proposed to predict the thermal conductivity of GaN films, which is a function of temperature, isotope, point defects, dislocations, film thickness, and strain fields. Specifically, the coefficients in our theoretical model that used to capture umklapp scattering and phonon-isotope scattering are fitted with the data from first-principles calculations, and two sub-models for point defects scattering and dislocation scattering are discussed, respectively. The sub-model of boundary scattering with suppression function is introduced to describe the anisotropy of size effect, and the effect of in-plane strain (perpendicular to polar axis) is also discussed. The comparison between theoretical predictions and experimental data shows that the model performs well roughly in a large temperature range from 300 to 500 K, with an around 20% difference at room temperature. Our predicted temperature dependent thermal conductivity deviates slightly from the measurements, which may result from the lack of high-order phonon scattering in our model, e.g., four-phonon scattering. Our results also show that the first-principles calculations for GaN overestimates the influence of isotope scattering. We further study the thermal transport properties of GaN film which are influenced by the thickness, dislocation density, and point defect density through using the new theoretical model. Significant reduction of thermal conductivity is found to occur at a film thickness of 10 μm, which is consistent with the findings from the first-principles calculations. The isotope and defects including point defects and dislocations are found to have a weak influence on the thermal conductivity when the thickness of GaN film is larger than 100 nm, while the influence becomes significant for the film with and below 100 nm in thickness. In addition, dislocations and point defects start to reduce thermal conductivity significantly when the surface density of dislocations increases to 10

^{10}cm^{–2}and point defect density reaches10^{18}cm^{–3}.
2021, 70 (4): 045201.
doi: 10.7498/aps.70.20201391

Abstract +

${q_0}= 2.44$ on the magnetic axis and ${q_a}= 7.13$ on the plasma boundary. And, the minimum safety factor ${q_{\min }}$ is 1.60. The structure of this kind of weakly negative magnetic shear can generate higher radio of the plasma pressure to the magnetic pressure and it is the important feature of the advanced steady-state scenario. Using MARS code, for two cases: without wall and with ideal wall, the results of growth rates of the external kink modes for different values of ${\beta _{\rm N}}$ are obtained. The limit value of $\beta _{\rm N}^\text{no-wall}$ is 2.49 for the case without wall, and the limit value of $\beta _{\rm N}^\text{ideal-wall}$ is 3.48 for the case with ideal wall. Then, a parameter ${C_\beta } = \left( {{\beta _{\rm{N}}} - \beta _{\rm{N}}^{{\text{no-wall}}}} \right)/\left( {\beta _{\rm{N}}^{{\text{ideal-wall }}} - \beta _{\rm{N}}^{{\text{no-wall }}}} \right)$ is defined. The research results in this work show that with the plasma pressure scaling factor ${C_\beta } = 0.7$ and plasma rotation frequency ${\Omega _{0}} = 1.1\% {\Omega _A}$ , the resistive wall modes can be completely stabilized without feedback control. And, with the plasma pressure scaling factor ${C_\beta } = 0.7$ and the feedback gain $\left| G \right| = 0.6$ , only plasma rotation with the frequency ${\Omega _{0}} = 0.2\% {\Omega _A}$ can stabilize the resistive wall modes. Therefore, a faster plasma rotation is required to stabilize the resistive wall modes by the plasma flow alone. The synergetic effects of the feedback and the toroidal plasma flow on the stability of the RWM can reduce plasma rotation threshold, which satisfies the requirements for the operation of the advanced tokamaks. The conclusion of this work has a certain reference for the engineering design and the operation of CFETR.">In tokamak plasmas, the resistive wall mode is a very important magnetohydrodynamic instability, and its time scale is on the order of millisecond. For the advanced tokamaks with long-pulse and steady-state operation, the resistive wall mode limits the operating parameter space (the discharge time and the radio of the plasma pressure to the magnetic pressure) of the fusion devices so that it affects the economic benefits. Therefore, it is very important to study the stability of the resistive wall modes in tokamaks. In this work, the influences of the plasma rotations and the feedback controls on the resistive wall modes are studied numerically using MARS code for an ITER 9 MA equilibrium designed for the advanced steady-state scenario. In the equilibrium, the profile of the safety factor has a weak negative magnetic shear in the core region. The safety factor is ${q_0}= 2.44$ on the magnetic axis and ${q_a}= 7.13$ on the plasma boundary. And, the minimum safety factor ${q_{\min }}$ is 1.60. The structure of this kind of weakly negative magnetic shear can generate higher radio of the plasma pressure to the magnetic pressure and it is the important feature of the advanced steady-state scenario. Using MARS code, for two cases: without wall and with ideal wall, the results of growth rates of the external kink modes for different values of ${\beta _{\rm N}}$ are obtained. The limit value of $\beta _{\rm N}^\text{no-wall}$ is 2.49 for the case without wall, and the limit value of $\beta _{\rm N}^\text{ideal-wall}$ is 3.48 for the case with ideal wall. Then, a parameter ${C_\beta } = \left( {{\beta _{\rm{N}}} - \beta _{\rm{N}}^{{\text{no-wall}}}} \right)/\left( {\beta _{\rm{N}}^{{\text{ideal-wall }}} - \beta _{\rm{N}}^{{\text{no-wall }}}} \right)$ is defined. The research results in this work show that with the plasma pressure scaling factor ${C_\beta } = 0.7$ and plasma rotation frequency ${\Omega _{0}} = 1.1\% {\Omega _A}$ , the resistive wall modes can be completely stabilized without feedback control. And, with the plasma pressure scaling factor ${C_\beta } = 0.7$ and the feedback gain $\left| G \right| = 0.6$ , only plasma rotation with the frequency ${\Omega _{0}} = 0.2\% {\Omega _A}$ can stabilize the resistive wall modes. Therefore, a faster plasma rotation is required to stabilize the resistive wall modes by the plasma flow alone. The synergetic effects of the feedback and the toroidal plasma flow on the stability of the RWM can reduce plasma rotation threshold, which satisfies the requirements for the operation of the advanced tokamaks. The conclusion of this work has a certain reference for the engineering design and the operation of CFETR.

## EDITOR'S SUGGESTION

2021, 70 (4): 045202.
doi: 10.7498/aps.70.20201540

Abstract +

High-power pulsed magnetron sputtering (HiPIMS) can produce high density and high adhesion coatings due to the high ionization. However, industrial application of HiPIMS is limited because of the unstable discharge and small deposition rate. A cylindrical cathode, developed on the basis of hollow cathode effect, can improve the discharge stability. With the development of electromagnetic systems, the plasma transport is improved, and thus increasing the deposition rate significantly. However, the introduction of electromagnetic system leads the strong discharge and large etching area on the target to be incompatibly controlled. In this work, the distribution of the tangential and longitudinal magnetic field on the target surface are improved by adding external magnets, and their effects on the plasma discharge are studied. By optimizing the magnets, the tangential magnetic field on the target surface becomes stronger and more uniform. Meanwhile, the peak of the longitudinal magnetic field increases from 73 to 96 mT and the peak location expands to two-sides of the cathode. The simulation result shows that the target etching area described by the proportion of the target area with the tangential magnetic field intensity higher than 40 mT increases from 51% to 67%, and the HiPIMS discharge studied by the particle in cell/Monte Carlo collision (PIC/MCC) method and plasma global model shows that the ion current and spectral intensity are significantly enhanced, exhibiting a doubled Cr density of 2.6 × 10

^{20}m^{–3}and an increased ionization from 90% to 92.1%. The practical Ar/Cr HiPIMS discharge is carried out separately with the original and optimized cylindrical cathode, and the results reveal that the brightness of plasma glow, the target current and the etching area all increase after the improvement. Furthermore, the ion current and the optical emission spectrum suggest that the flux of ions arriving at the substrate is approximately doubled, which means that an about doubled deposition rate of the optimized cathode is achievable.
2021, 70 (4): 045203.
doi: 10.7498/aps.70.20200957

Abstract +

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

2021, 70 (4): 046201.
doi: 10.7498/aps.70.20200953

Abstract +

Although the one-dimensional non-conjugated alkane chain, which has an important influence on the electron transport process, does not possess the characteristics of electron-rich and electron-deficient, it often exists in single-molecule devices and biological molecules such as peptides and proteins. In order to understand the electron transport characteristics of alkane chain, a one-dimensional linear non-conjugate (CH

_{2})_{n}molecular junction model is designed in this study. Subsequently, we conduct the systematic study of the electronic transport behavior of (CH_{2})_{n}(*n*= 1–12) molecular linear chain coupling to two graphene electrodes, based on the density functional theory and nonequilibrium Green’s function formalism. The results reveal that the structure and conductance of CH_{2}chain are highly sensitive to the odevity of CH_{2}unit. When the value of n is odd, the groups of CH_{2}extend in a zigzag way from the left electrode to the right electrode in the plane of graphene, while the value of n is even, what is different is that the groups of CH_{2}are arranged above and below the electrode plane. For this reason, the odd-even behavior of conductance occurs in the (CH_{2})_{n}(*n*= 1–12) molecular chain. Furthermore,*n*is also an important factor to affect their transport properties (odd or even behavior of conductance). The longer the (CH_{2})_{n}chain, the deeper the suppression in transmission spectrum and the lower the equilibrium conductance. What is more, the conductance decreases exponentially with the increase of molecular length, with a decay constant*β*of 0.67 and 0.60 for odd and even, respectively, which is in good agreement with the experimental research. Additionally, by analyzing their eigenchannels of odd and even (CH_{2})_{n}molecular chain, we find that the coplanar σ electron with graphene electrode makes a major contribution to the electronic transport channel. The current-voltage curve of (CH_{2})_{n}molecular chain exhibits nonlinearity, implying their semiconductor characteristics. The interesting mechanical and electronic transport properties are expected to conduce to further experimental synthesis, design and operation of the single molecular nanodevices.
2021, 70 (4): 046801.
doi: 10.7498/aps.70.20201505

Abstract +

Non-hydrogenated W-doped amorphous diamond-like carbon films with different tungsten content are prepared by pulsed laser deposition through using the W-doped graphite targets. The variation of the tungsten content in the doped diamond-like carbon films has a stable linear relation with tungsten content in the doped targets, which shows the importance of pulsed laser deposition in the field of the refractory metal doping technology. The doped tungsten has no effect on the crystal structure of the diamond-like carbon film according to X-ray diffraction test. In the W-doped diamond-like carbon film, most of the tungsten atoms form the tungsten carbides with the carbon atoms when the tungsten content is relatively low, and inlay in the network of the amorphous carbon, reducing the carbon coordination atoms and local density. In addition, the tungsten oxides formed from the tungsten atoms and oxygen atoms help to reduce the friction coefficient. Therefore, the friction coefficient of the films decreases with the tungsten content increasing, and the lowest friction coefficient is 0.091 at the doping content of 9.67 at.%. However, more and more tungsten clusters form with the tungsten content further increasing according to the results of atomic force microscope, thus increasing the surface roughness of the diamond-like carbon films and resulting dominantly in the increase of the friction coefficient. On the other hand, the increasing of tungsten content reduces the nano-hardness and Yang’s modulus of the doped diamond-like carbon film due to the reduction of the local atomic binding energy in the per unit volume. However, the best wear-resistance is shown in the W-doped diamond-like carbon film with relatively low tungsten content of 6.28 at.%, instead of the pure diamond-like carbon film with the highest hardness of 52.2 GPa. This research offers an experimental base for practical applications of the non-hydrogenated W-doped diamond-like carbon film with low friction coefficient and high hardness grown by pulsed laser deposition. An optimized W-doped diamond-like carbon film has low friction coefficient and high hardness, along with the high heat conduction and resistance, and can be used as protective tribological coatings for the micro- and nano- electron devices to improve their working stability and reduce the sizes.

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

2021, 70 (4): 047101.
doi: 10.7498/aps.70.20201237

Abstract +

MnBi

_{2}Te_{4}as an intrinsic magnetic topological insulator has attracted lots of attention. Since the electronic structure of MnBi_{2}Te_{4}is quite sensitive to the change of lattice constant, here in this work, we use a first-principles method based on density functional theory to implement the isometric strain control of the electronic structure of MnBi_{2}Te_{4}antiferromagnetic bulk. The so-called isometric strain is to change the lattice constant under the premise that the volume of the crystal remains unchanged. Our results show that the energy band structure of the system changes sensitively under the action of isometric tension and compression strains of the material, and the system has an insulator-metal phase transition. In particular, when a certain strain is applied, the conduction band and the valence band cross at Γ, and the system presents a zero band gap state. Under this strain, the band inversion can still be observed, showing non-trivial energy band topological properties. According to the charge density and local charge density maps under different strains, it is found that the isometric strain will affect the interlayer spacing of the system's seven-fold layers. The isometric compression and tensile strain can increase and reduce the Te atomic layer spacing respectively, indicating that isometric compression is beneficial to reducing the antiferromagnetic interlayer coupling. Through the control of isometric pressure and strain, we can master the change law of the electronic structure of MnBi_{2}Te_{4}, which has important guiding significance for the research of physical properties and experimental preparation of the intrinsic magnetic topological insulator MnBi_{2}Te_{4}.
2021, 70 (4): 047302.
doi: 10.7498/aps.70.20201399

Abstract +

${E_{\rm fm}} \approx 2{E_{\rm em}}$ . It is found that the J-aggregate has a higher rate of annihilation than the H-aggregate because its coherent energy transfer time is shorter than H-aggregate’s. The high-intensity external field makes high exciton-exciton annihilation rate. The dipole configuration and the decay rate of higher excited state of molecules have strong effects on the annihilation, so one can adjust these factors to control the exciton-exciton annihilation in molecular aggregations.">It is of ongoing interest to uncover energy and charge transfer processes in molecular systems, which are essentially important for photovoltaic cells or light emitting diodes. The exciton-exciton annihilation is one of the important aspects in excitation energy transfer in molecular aggregations, so it is important to study its dynamics of exciton-exciton annihilation, and to compare the theoretical parameters with the related transient absorption signal. Upon the excitation of laser pulses, multiple excitons can be produced in molecular aggregations, and its annihilation process is composed of two steps. The first step is that two excitations existing in the first excited state of the molecules move together so that their excitation energy can be used to create a high excited state in one molecule, called exciton fussion. The second step is that an ultrafast internal conversion process brings the molecule which is in the higher excited state back to the first excited state. This paper uses the scheme of classical rate equation in the approximation of weak coupling among molecules to describe the dynamics of exciton-exciton annihilation. With the parameters of squaraine, the effects of external or internal parameters such as the intensity of external field, the dipole configuration in aggregations, the decay rate of molecules on the annihilation process are studied. The relationship between the relaxation time of exciton in the first excited state and the high excited state, between their times of coherent charge transfer, and between their times of exciton and annihilation are studied. These conclusions are suitable to the aggregations with their single molecule having an energy level of ${E_{\rm fm}} \approx 2{E_{\rm em}}$ . It is found that the J-aggregate has a higher rate of annihilation than the H-aggregate because its coherent energy transfer time is shorter than H-aggregate’s. The high-intensity external field makes high exciton-exciton annihilation rate. The dipole configuration and the decay rate of higher excited state of molecules have strong effects on the annihilation, so one can adjust these factors to control the exciton-exciton annihilation in molecular aggregations.

## COVER ARTICLE

2021, 70 (4): 047401.
doi: 10.7498/aps.70.20201213

Abstract +

Based on the proximity effect, the exchange interaction at the interface between a ferromagnetic insulator (FI) and a superconductor (S) could enhance the Zeeman splitting of the superconducting quasiparticle density of states. The superconducting electrons feel the exchange field on the surface of the S layer. Therefore, tuning the internal exchange field at the FI/S interface could switch the superconductor from a superconducting state to a normal state, leading to an infinite magnetoresistance in FI/S heterostructure. Here in this work, we fabricate the EuS/Ta heterojunction by the pulsed laser deposition, and perform the magnetotransport measurements. In the EuS/Ta heterojunction, Ta film as a typical BSC supercenter exhibits the superconducting transition under 3.6 K, and the EuS film is ferromagnetic under 20 K. The magnetization of EuS is suppressed by superconductivity of Ta at 0.01 T below 3 K. In addition, the butterfly-type hysteresis loop is observed at 2 K. And the decrease of the saturation magnetization of EuS/Ta heterostructure is observed by comparing with the EuS single layer. It is caused by a reconstruction of homogeneous ferromagnetic order in the EuS ferromagnetic layer due to the proximity effect with the Ta superconducting layer. The above measurement results show that the competition between the ferromagnetism of EuS film and superconductivity of Ta film below T

_{c}of Ta film. If the exchange field of the FI is sufficiently strong, it tries to align the spins of the electrons of a Cooper pair in S layer parallel to each other, thus destroying the superconductivity. Meanwhile, the superconductivity in S layer will be recovered when the exchange field of the FI is weak. The resistance at a specific value of the magnetic field (1 T) steeply drops to zero, and clear hysteresis behavior is observed in EuS/Ta heterostructure, resulting in an infinite magnetoresistance up to 144000%, by tuning the internal exchange field at EuS/Ta interface. Meanwhile, the anomalous Hall effect with hysteresis behavior is observed at 2 K, indicating that the electron in Ta film is spin polarized due to the magnetic proximity effect near the EuS/Ta interface. Our results show that the EuS/Ta heterostructure with infinite magnetoresistance could be a good candidate for spintronic devices.
2021, 70 (4): 047801.
doi: 10.7498/aps.70.20201324

Abstract +

_{0.25}As

_{0.1}S

_{0.65}glass possesses the highest laser damage threshold.

_{0.25}As

_{0.1}S

_{0.65}glass therefore is chosen as a core material of the designed fiber, while a compatible Ge

_{0.26}As

_{0.08}S

_{0.66}glass is selected as a cladding material. A step-index nonlinear fiber with a core diameter of 15 μm is fabricated by the traditional rod-in-tube method. The numerical aperture and the background loss of the fabricated Ge

_{0.25}As

_{0.1}S

_{0.65}/Ge

_{0.26}As

_{0.08}S

_{0.66}fiber are ~0.24 and < 2 dB/m, respectively.

2021, 70 (4): 047802.
doi: 10.7498/aps.70.20201512

Abstract +

In recent years, the polymers represented by macromolecular materials have attracted widespread attention due to their higher flexibility and viscoelastic, compared with other materials used for light absorption (such as semiconductor materials, carbon-based materials and noble metal nanomaterials). Although the polymers have shown potential applications in the photothermal field, compared with other light-absorbing materials, the polymer substrates have a low light absorption rate and a narrow absorption bandwidth concentrated in the visible light band. Therefore, it is necessary to prepare a structure on the polymer material layer for absorbing light, thereby improving the ability of the polymer to absorb light. In addition, since the existing preparation processes of polymer absorption structures require the use of templates and the processes are relatively complicated, there is an urgent need for a simple and easy process to prepare the absorption structures on the polymer material layer. In this article, composite nanoforests are prepared on polymer substrates based on a plasma repolymerization technology and magnetron sputtering process; due to the metallic nanoparticles existing, multi-hybrid plasmonic effect is achieved, thus the average light absorption rate of the polymer in a wavelength range of 380–2500 nm is increased from 23.34% to 74.56%. Such polymer composite nanoforests have high absorption characteristics in a wide spectral range. The method of preparing the structure is quite simple, and can be applied to preparing different polymer materials. Besides, by changing the plasma bombardment time, the morphology of the nanoforests can be adjusted; by increasing the size of the metallic nanoparticles, the absorption of the composite nanoforests can be increased. It is foreseeable that the polymer composite nanoforests will have applications in various optical devices.

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

2021, 70 (4): 048401.
doi: 10.7498/aps.70.20201465

Abstract +

Fractional calculus is widely used in the analysis and description of various nonlinear and non-integer dimensional physical phenomena and processes in nature, and it gradually becomes a research hotspot. The order value of fractional-order system is more flexible, and fractional-order system is more accurate for analysis of non-integer dimensional physical phenomena and processes. In recent years, various negative half-order fractance approximation circuits and rational approximation algorithms for negative half-order fractional operators have been proposed and aroused people's research interest. The scaling extension of classic negative half-order fractance approximation circuits can facilitate the design of fractance approximation circuits with arbitrary-order fractional operators, but the operational constancy is sacrificed. The typical arbitrary-order fractance approximation circuits have operational oscillating phenomena in frequency domain, both the order-frequency characteristic curves and the phase-frequency characteristic curves have obvious oscillating waveforms. The operational oscillating phenomena will inevitably affect the fractional operator operational performance of the fractance approximation circuits, and result in errors in physical application. In this paper, the negative half-order Carlson fractal-lattice fractance approximation circuit with constant operational performance is analyzed from perspective of circuit network, the symmetry for equivalent two-port network of Carlson fractal-lattice fractance approximate circuit is analyzed. The equivalent two-port network of scaling fractal-lattice fractance approximation circuit is explored, Operational validity for the right port of scaling lattice cascaded two-port network is studied. A symmetrical lattice cascaded passive two-port network after scaling extension is designed through cascade of the ports on both sides of two-port network, and an arbitrary-order scaling fractal-lattice fractance approximation circuit with high-operation constancy is designed. By studying the zero-pole distribution and localization characteristics of the negative real zero-pole pair elemental unit, the physical nature of operational oscillating phenomenon for scaling fractal-lattice fractance approximation circuit with the operational performance of arbitrary-order fractional operator is explained theoretically, the methods and ideas to effectively suppress frequency-domain operational oscillating phenomenon are theoretically analyzed. The physical nature of operational oscillating amplitude reduction is explained by contrastively analyzing the pole-zero distributions of scaling fractal-lattice fractance approximation circuit and symmetrical lattice cascaded two-port network. According to the optimization principle of arbitrary-order fractance approximation circuits, the symmetrical resistor-capacitor T-section circuit optimization methods are used to optimize the frequency-domain approximation performance of any real-order symmetrical lattice cascaded two-port network, and it contributes to obtain any real-order scaling fractal-lattice fractance approximation circuit with high benefit of approximation. Arbitrary-order symmetrical lattice cascaded two-port network provides methods and ideas for the design of fractance approximation circuits with high-operation constancy.

2021, 70 (4): 048502.
doi: 10.7498/aps.70.20201379

Abstract +

Appreciable progress of organometal halide perovskite materials has been achieved in recent years due to their controllable synthesis and excellent optoelectronic properties. And the potential uses of these perovskites in photovoltaics, light-emitting diodes (LEDs), photodetectors and lasers have been successfully demonstrated. Although organometal halide perovskites appear as emitters with extremely high color purity and low cost, the device performance is significantly limited by poor morphology of the perovskite layer. The addition of the polymer into the perovskite layer is a convenient and effective method to improve the homogeneity of the spin-coated perovskite film. In this work, we fabricate green perovskite light emitting diodes (PeLEDs) with poly(styrenesulfonate) (PSS)-modified poly(3,4-ethylenedioxythiophene):PSS (PEDOT:PSS) as the hole injection layer (HIL) and a single spin coating composite film consisting of methylammonium lead tribromide (MAPbBr

_{3}) and poly(ethylene oxide) (PEO) as the emissive layer. The PSS doping increases the work function of PEDOT:PSS and reduces the injection barrier between PEDOT:PSS HIL and MAPbBr_{3}perovskite, thus balancing the carriers within the PeLEDs. The PEO doping enables the MAPbBr_{3}to become a dense and uniform perovskite film with a ~100% coverage. With the above approaches, highly efficient PeLEDs with maximum luminance and current efficiency of 2476 cd·m^{–2}and 7.6 cd·A^{–1}are eventually acquired. This work provides a method of fabricating the high-coverage and high-efficiency PeLEDs.
2021, 70 (4): 048701.
doi: 10.7498/aps.70.20201548

Abstract +

Biosensor has received increasing attention in recent years due to the demand for detecting biological and chemical substances in liquid. In particular, the detection methods based on refractive index have advantages in detection sensitivity. Colorimetric biosensor can transform the change in refractive index of target into the change in color, which has advantages in simple operation, low cost and real-time detection with naked human eyes. In this work, a Fabry-Pérot cavity colorimetric biosensor based on α-MoO

_{3}integrating microfluidic channel is proposed. The α-MoO_{3}is an emerging natural two-dimensional van der Waals material with anisotropic optical properties due to its unique crystal structure. Theoretical analysis of the feasibility of BK7/Ag/SiO_{2}as the reflective layers is carried out. And the transmittance spectra of the proposed colorimetric biosensor are calculated by the transfer-matrix method. The obvious color changes can be observed when the microfluidic channel filled with NaCl solutions with different concentrations. The proposed colorimetric biosensor achieves a high detection sensitivity of 600 nm/RIU, which can detect a concentration change of NaCl solution as low as 9‰. The proposed colorimetric biosensor can tune the operating wavelength by simply rotating the device due to the anisotropic optical properties of α-MoO_{3}to satisfy the color vision of human eyes. Moreover, by tuning the thickness of microfluidic channel, the operating wavelength of colorimetric biosensor can be further shifted. Our approach offers a new direction for developing tunable biosensors with low cost and real-time detection.