Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Electron transport properties of order-disorder separated two-dimensional bilayer systems

Lu Yan-Yan Wang Chao Liu Jie Jiang Jin-Yi Zhong Jian-Xin

Citation:

Electron transport properties of order-disorder separated two-dimensional bilayer systems

Lu Yan-Yan, Wang Chao, Liu Jie, Jiang Jin-Yi, Zhong Jian-Xin
PDF
HTML
Get Citation
  • In the framework of the electronic tight-binding model of order-disorder separated (ODS) bilayer square lattice (BSL) and by calculating the density of states (DOS), participation number of eigen-wavefunctions and quantum diffusion, we systematically study the effects of stacking interface structure, strength of interlayer coupling and degree of disorder on the electron transport properties of order-disorder separated two-dimensional bilayer systems. Our results show that for the ODS-BSL of AA-stacking in the regime of weak coupling, the ODS-BSL always possesses a single energy band with localized states in its band tail, and extended states or critical states similar to the extended ones in the band center region with persistent metal-insulator transitions and associated mobility edges under strong disorder. In the regime of strong coupling, weak disorder leads the critical states to exist in its band tails and extended states to occur in the band center regions, while strong disorder results in the formation of a single band due to the overlapping of the coupling-induced two bands with localized states in the band tails and critical states in the band center region with increasing participation numbers as disorder increases. The ODS-BSL of AB-stacking always possesses a single band and supports extended states and critical states in its band center region, regardless of the strengths of interlayer coupling and disorder. In both ODS-BSL systems of AA- and AB- stackings, quantum diffusion undergoes an anomalous transition from weakening to enhancing behaviors as disorder increases. In the AA-stacking ODS-BSL of weak coupling, AA-stacking ODS-BSL of weak disorder and the AB-stacking ODS-BSL, quantum diffusion exhibits super-diffusion due to the contribution of extended states and the critical states similar to extended ones. In the AA-stacking ODS-BSL of strong coupling, quantum diffusion undergoes sub-diffusion under strong disorder due to the existence of critical states. The numerical results also show that the order-disorder separated (ODS) bilayer hexagonal lattice exhibits the same behaviors as those revealed in ODS-BSL systems.
      Corresponding author: Zhong Jian-Xin, jxzhong@xtu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874316, 11474244), the National Basic Research Program of China (Grant No. 2015CB921103), and the International Visiting Faculty Program of Hunan Provincial Government, China.
    [1]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar

    [2]

    Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451Google Scholar

    [3]

    Geim A K, Grigorieva I V 2013 Nature 499 419Google Scholar

    [4]

    Novoselov K S, Mishchenko A, Carvalho A, Neto A C 2016 Science 353 aac9439Google Scholar

    [5]

    Zhu Y, Ji H, Cheng H M, Ruoff R S 2018 Natl. Sci. Rev. 5 90Google Scholar

    [6]

    Bian R, Li C, Liu Q, Cao G, Fu Q, Meng P, Zhou J, Liu F, Liu Z 2021 Natl. Sci. Rev. 0 nwab164Google Scholar

    [7]

    Cao Y, Fa Temi V, Fa Ng S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar

    [8]

    Lu X, Stepanov P, Yang W, Xie M, Efetov D K 2019 Nature 574 653Google Scholar

    [9]

    吕新宇, 李志强 2019 物理学报 68 220303Google Scholar

    Lü X Y, Li Z Q 2019 Acta Phys. Sin. 68 220303Google Scholar

    [10]

    Nimbalkar A, Kim H 2020 Nano-Micro Lett. 12 20Google Scholar

    [11]

    何龙, 宋筠 2013 物理学报 62 057303Google Scholar

    He L, Song Y 2013 Acta Phys. Sin. 62 057303Google Scholar

    [12]

    Rozhkov A V, Sboychakov A O, Rakhmanov A L, Nori F 2016 Phys. Rep. 648 1Google Scholar

    [13]

    Conte F, Ninno D, Cantele G 2019 Phys. Rev. B 99 155429Google Scholar

    [14]

    Anderson P W 1958 Phys. Rev. 109 1492Google Scholar

    [15]

    Abrahams E A, Anderson P, Licciardello D, Ramakrishnan T 1979 Phys. Rev. Lett. 42 673Google Scholar

    [16]

    Addou R, Colombo L, Wallace R M 2015 ACS Appl. Mater Interf. 7 11921Google Scholar

    [17]

    Fernández-Serra M, Adessi C, Blase X 2006 Phys. Rev. Lett. 96 166805Google Scholar

    [18]

    Yang K W, Chen X Y, Zheng Z H, Wan J Q, Feng M, Yu Y 2019 J. Mater. Chem. A 7 3863Google Scholar

    [19]

    Xu D, Liu H, Iv V S, Song J, Jiang H, Sun Q F, Xie X C 2013 J. Phys. Condens Matter 25 105303Google Scholar

    [20]

    Bagci V, Krokhin A A 2007 Phys. Rev. B 76 134202Google Scholar

    [21]

    Zhang W, Yang R, Ulloa S E 2009 Phys. Rev. E 80 051901Google Scholar

    [22]

    Markussen T, Rurali R, Brandbyge M, Jauho A P 2006 Phys. Rev. B 74 245313Google Scholar

    [23]

    Akguc G B, Gong J 2009 Phys. Rev. B 81 117402Google Scholar

    [24]

    Menezes M G, Nero J D, Capaz R B, Rego L 2010 Phys. Rev. B 81 117401Google Scholar

    [25]

    Sun L, Li S, Su Y, He D, Zhang Z 2019 Appl. Surf. Sci. 463 474Google Scholar

    [26]

    Abhinav S, Muttalib K A 2019 J. Phys. Communica. 3 105010Google Scholar

    [27]

    Zhong J, Stocks G M 2006 Nano Lett. 6 128Google Scholar

    [28]

    Vogel E 2007 Nature Nanotechnol. 2 25Google Scholar

    [29]

    Xiong, Gang 2007 Phys. Rev. B 76 153303Google Scholar

    [30]

    Wei Z, Rong Y, Yi Z, Duan S, Ping Z, Ulloa S E 2010 Phys. Rev. B 81 214202Google Scholar

    [31]

    Ganguly S, Maiti S K 2020 J. Phys. D: Appl. Phys. 53 025301Google Scholar

    [32]

    Zhong J X, Stocks G M 2007 Phys. Rev. B 75 033410Google Scholar

    [33]

    Patrick A, Lee T, Ramakrishnan V 1985 Rev. Modern Phys. 57 287Google Scholar

    [34]

    Zhong J X, Mosseri R 1995 J. Phys. Condensed Matter 7 8383Google Scholar

    [35]

    Schulz-Baldes H, Bellissard J 1998 Rev. Mathema. Phys. 10 1Google Scholar

  • 图 1  有序-无序双层耦合正方晶格模型图($\varepsilon _i^{\left( 2 \right)}$, $\varepsilon _i^{\left( 1 \right)}$)分别表示上、下层格点能, $ U $h分别表示层间与层内最近邻格点跃迁能) (a) AA堆垛 (上层原子位于下层原子正上方); (b) AB堆垛 (上层原子位于下层正方格子中心正上方)

    Figure 1.  Schematic illustration of the order-disorder coupling system of bilayer square lattices ($\varepsilon _i^{\left( 2 \right)}$, $\varepsilon _i^{\left( 1 \right)}$) are onsite energies of upper and lower layers, $ U $ and h represent the hoping energy of inter-layer and intra-layer respectively): (a) AA stacking (the upper atom is directly above the lower atom); (b) AB stacking (the upper atom is located directly above the center of the lower square).

    图 2  双层耦合正方周期晶格的能带与DOS (a), (b) 分别为$ U $ = 1和$ U $= 6的AA型耦合系统的能带图; (c) AA型耦合晶格的DOS 随$ U $的变化; (d), (e) 分别为$ U $= 1和$ U $= 6的AB型耦合系统的能带图; (f) AB型耦合晶格的DOS随$ U $的变化

    Figure 2.  Energy spectra and DOS for the periodic coupling system of bilayer square lattices: (a), (b) Energy spectra for the coupling system of AA stacking with $ U $= 1 and $ U $= 6, respectively; (c) variation of DOS with $ U $ for the coupling system of AA stacking; (d), (e) energy spectra for the coupling system of AB stacking with $ U $ = 1 and $ U $ = 6, respectively; (f) the variation of DOS with $ U $ for the coupling system of AB stacking.

    图 3  AA型堆垛有序-无序双层耦合正方晶格电子能谱 (a)—(d) DOS随$ U $$ W $的变化; (e) 产生带隙所对应的$ U $$ W $(空心圆)及其拟合线(虚线); (f) 带隙宽度$ \Delta E $$ U\rm{和}W $的变化, 左图为$ \Delta E $ (空心符号)随$ U $的变化及其拟合线(虚线), 其中$ W $= 1, 3, 5分别对应斜率1.99, 1.96, 1.90; 右图为$ \Delta E $ (空心符号)随$ W $的变化及其拟合线(虚线), 其中$ U $ = 6, 8, 10分别对应斜率–0.40, –0.44, –0.50

    Figure 3.  Energy spectra for the order-disorder bilayer coupling system of square lattices with AA stacking: (a)–(d) Changes of the DOS for different $ U $ and $ W $; (e) the relationship of $ W $ and $ U $ (open circles) for the band-gap opening with the linear fitting (dashed line); (f) the dependence of bandgap width $ \Delta E $ (hollow symbols) on $ U $ and W with the left panel for $ U $ with the linear fitting (dash lines), where $ W $= 1, 3, 5 correspond to the slopes of 1.99, 1.96, 1.90, respectively, and the right panel for $ W $with the linear fitting (dash lines), where $ U $= 6, 8, 10 correspond to the slopes –0.40, –0.44, –0.50, respectively.

    图 4  AB堆垛有序-无序双层耦合正方晶格DOS分布 (a), (b) DOS随无序强度W的变化; (c), (d) DOS随层间耦合能U的变化

    Figure 4.  DOS for order-disorder bilayer coupling system of the square lattices with AB stacking: (a), (b) Changes of the DOS for different $ W $; (c), (d) changes of the DOS for different $ U $.

    图 5  AA型堆垛有序-无序双层耦合正方晶格本征态波函数分布图(其中D-L和O-L分别代表上层无序晶格和下层有序晶格) (a), (b) 分别为弱耦合系统($ U $= 0.5)在弱无序($ W $= 1)和强无序($ W $= 10)时的带中态(E = 0.140, 0.016)和带尾态(E = 4.60, 11.46)的波函数$ {\left|\boldsymbol{\varPhi }\left(E\right)\right|}^{2} $分布; (c), (d) 分别为强耦合系统($ U $= 4)在弱无序($ W $= 1)和强无序($ W $= 10)时的带中态(E = 3.86, –0.17)和带尾态(E = 8.08, 12.96)的波函数$ {\left|\boldsymbol{\varPhi }\left(E\right)\right|}^{2} $分布; 黑色表示概率大于 0.005

    Figure 5.  Eigen-wavefunctions $ {\left|\boldsymbol{\varPhi }\left(E\right)\right|}^{2} $ for the bilayer coupling system of square lattices with AA stacking, where D-L and O-Lrepresent the upper disordered layer and the lower ordered layer respectively: (a), (b) Eigen-wavefunctions of the eigen-states (E = 0.140, 0.016) in the spectral central region and the eigen-states (E = 4.60, 11.46) in the tail region for the weak coupling system of $ U $= 0.5 with small disorder of $ W $= 1 and strong disorder of $ W $= 10, respectively; (c), (d) the eigen-wavefunctions of the eigen-states (E = 3.86, –0.17) in the spectral central region and the eigen-states (E = 8.08, 12.96) in tail region for the strong coupling system of $ U $= 4 with small disorder of $ W $= 1 and strong disorder of $ W $= 10, respectively. The black color means that the values are larger than 0.005.

    图 6  AB型堆垛有序-无序双层耦合正方晶格的带中态和带尾态波函数分布图 (a), (b)分别为层间弱耦合(U = 0.5)时弱无序(W = 1)及强无序(W = 12)体系中带中态(E = 0.34, 0.89)及带尾态(E = 6.07, 13.50)波函数的分布; (c), (d) 分别为层间强耦合(U = 4)时弱无序(W = 1)及强无序(W = 12)体系中带中态(E = –1.98, –0.67)及带尾态(E = 20.01, 23.05)波函数的分布; 黑色表示概率大于 0.005

    Figure 6.  Eigen-wavefunctions of the eigen-states in the spectral central and tail regions for the order-disorder bilayer couplingsystem of square lattices with AB stacking: (a), (b) Eigen-wavefunctions of the eigen-states (E = 0.34, 0.89) in the spectral central region and the eigen-states (E = 6.07, 13.50) in the tail region for the weak coupling system of $ U $= 0.5 with small disorder of $ W $ = 1 and strong disorder of $ W $= 12, respectively; (c), (d) the eigen-wavefunctions of the eigen-states (E = –1.98, –0.67) in the spectral central region and the eigen-states (E = 20.01, 23.05) in tail region for the strong coupling system of $ U $ = 4 with small disorder of $ W $ = 1 and strong disorder of $ W $= 12, respectively. The black color means that the values are larger than 0.005.

    图 7  AA型堆垛有序-无序双层耦合正方晶格波函数的格点占据数$ P\left(E\right) $$ W $的变化情况 (a) 弱耦合系统$ U $= 0.5; (b), (c) 强耦合系统$ U $= 4.0

    Figure 7.  Variation of participation number $ P\left(E\right) $ with $ W $ for the order-disorder bilayer coupling system with AA stacking: (a) Weak coupling system of $ U $= 0.5; (b), (c) strong coupling system of $ U $= 4.0.

    图 8  AA型堆垛有序-无序双层耦合正方晶格的格点占据数$ P(E) $随体系尺寸大小N的变化 (a), (b) 弱耦合系统$ U $= 0.5;(c), (d) 强耦合系统$ U $= 4.0.

    Figure 8.  Variation of participation number P(E) with system size N for order-disorder bilayer coupling system with AA stacking. (a), (b) Weak coupling system of $ U $= 0.5; (c), (d) strong coupling system of $ U $= 4.0

    图 9  (a)—(d) AA型堆垛有序-无序双层耦合正方晶格系统的带尾态和带中态中典型能量处的P(E)随N的变化, 符号对应计算结果, 虚线为对${\text{log}}P\sim \gamma {\text{log}}N$的拟合线; (e), (f) 拟合指数$ \gamma $随能量的分布

    Figure 9.  (a)–(d) Variation of P(E) with N for the order-disorder bilayer coupling system with AA stacking at typical energy values in the spectral tail and central regions, where symbols are the calculation results, dashed lines are the fitting results to $ \text{log}P\sim \gamma \text{log}N $; (e), (f) distribution of fitting exponent $ \gamma $ with energy.

    图 10  (a)—(d) AB型堆垛有序-无序双层耦合正方晶格的带尾态和带中态中典型能量处的$ P\left(E\right) $N的变化, 符号对应计算结果, 虚线为对$ {\rm{log}}P \sim \gamma{ \rm{log}}N $的线性拟合线; (e), (f) 拟合指数$ \gamma $随能量的分布

    Figure 10.  (a)–(d) Variation of P(E) with N for the order-disorder bilayer coupling system with AB stacking at typical energy values in the spectral tail and central regions, where symbols are the calculation results, dashed lines are the fitting results to ${ \rm{log}}P \sim $$ \gamma {\rm{log}}N$; (e), (f) distribution of fitting exponent $ \gamma $ with energy.

    图 11  AA堆垛有序-无序双层耦合正方晶格中量子扩散的均方位移$ d\left(t\right) $(符号)及对$ d\left(t\right)\sim{t}^{b} $的拟合结果(虚线) (a) 弱耦合系统$ U $= 0.5; (b) 强耦合系统$ U $= 4; (c) 拟合指数b随无序度$ W $的变化

    Figure 11.  Mean-square displacement $ d\left(t\right) $ (symbols) of the quantum diffusion for the order-disorder bilayer coupling system of the square lattices with AA stacking and theirfitting results to $ d\left(t\right)\sim{t}^{b} $ (dash line): (a) Weak coupling system of U = 0.5; (b) strong coupling system of U = 4; (c) variation of the fitting results of b with the degree of disorder W.

    图 12  AB堆垛有序-无序双层耦合正方晶格中量子扩散的均方位移$ d\left(t\right) $(符号)及对$d\left(t\right)\sim{t}^{b}$拟合结果(虚线) (a) 弱耦合系统$ U $= 1; (b) 强耦合系统$ U $= 4; (c) 拟合指数$ b $随无序度$ W $的变化

    Figure 12.  Mean-square displacement d(t) (symbols) of the quantum diffusion for the order-disorder bilayer coupling system of the square lattices with AB stacking and their fitting results to $ d\left(t\right)\sim {t}^{b} $ (dash line): (a) Weak coupling system of $ U $= 1; (b) strong coupling system of $ U $= 4; (c) variation of the fitting results of b with the degree of disorder W.

    图 13  有序-无序双层六角晶格耦合体系模型图, 上层原子位于下层原子正上方

    Figure 13.  Schematic illustration of the order-disorder coupling system of bilayer hexagonal lattices, the upper atom is directly above the lower atom.

    图 14  双层耦合六角周期晶格的能带与DOS (a) $ U $=1的能带图; (b) $ U $= 4的能带图; (c) DOS 随$ U $的变化

    Figure 14.  Energy spectra and density of states for the periodic coupling system of bilayer hexagonal lattices: (a) Energy spectra with U = 1; (b) energy spectra with U = 4; (c) variation of DOS with U.

    图 15  有序-无序双层耦合六角晶格电子能谱 (a), (b) DOS随W的变化; (c), (d) DOS随U的变化

    Figure 15.  Energy spectra for the order-disorder bilayer coupling system of bilayer hexagonal lattices: (a), (b) Changes of the DOS for different W; (c), (d) changes of the DOS for different U.

    图 16  有序-无序双层耦合六角晶格结构中对不同能量处${ \rm{l}\rm{o}\rm{g}}P\sim\gamma {\rm{l}\rm{o}\rm{g}}N$的拟合结果 (a) 弱耦合体系(U = 0.5)中不同W下拟合指数$ \gamma $随能量的分布; (b) 强耦合体系(U = 4.0)中不同W下拟合指数$ \gamma $随能量的分布

    Figure 16.  Fitting results to ${\rm{l}\rm{o}\rm{g}}P\sim\gamma {\rm{l}\rm{o}\rm{g}}N$ for the order-disorder bilayer coupling system of bilayer hexagonal lattices at different energy: (a) Changes of the distribution of fitting exponent $ \gamma $ with energy for different W for weak coupling system of $ U $= 0.5; (b) changes of the distribution of fitting exponent $ \gamma $ with energy for different W for strong coupling system of $ U $= 4.0.

    图 17  有序-无序双层耦合六角晶格结构中对$ d\left(t\right) \sim {t}^{b} $的拟合参数$ b $随无序度$ W $的变化情况

    Figure 17.  Variation of the fitting parameter of b of the fitting function $ d\left(t\right)\sim{t}^{b} $ with the degree of disorder $ W $ for the order-disorder bilayer coupling system of bilayer hexagonal lattices.

  • [1]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar

    [2]

    Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451Google Scholar

    [3]

    Geim A K, Grigorieva I V 2013 Nature 499 419Google Scholar

    [4]

    Novoselov K S, Mishchenko A, Carvalho A, Neto A C 2016 Science 353 aac9439Google Scholar

    [5]

    Zhu Y, Ji H, Cheng H M, Ruoff R S 2018 Natl. Sci. Rev. 5 90Google Scholar

    [6]

    Bian R, Li C, Liu Q, Cao G, Fu Q, Meng P, Zhou J, Liu F, Liu Z 2021 Natl. Sci. Rev. 0 nwab164Google Scholar

    [7]

    Cao Y, Fa Temi V, Fa Ng S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar

    [8]

    Lu X, Stepanov P, Yang W, Xie M, Efetov D K 2019 Nature 574 653Google Scholar

    [9]

    吕新宇, 李志强 2019 物理学报 68 220303Google Scholar

    Lü X Y, Li Z Q 2019 Acta Phys. Sin. 68 220303Google Scholar

    [10]

    Nimbalkar A, Kim H 2020 Nano-Micro Lett. 12 20Google Scholar

    [11]

    何龙, 宋筠 2013 物理学报 62 057303Google Scholar

    He L, Song Y 2013 Acta Phys. Sin. 62 057303Google Scholar

    [12]

    Rozhkov A V, Sboychakov A O, Rakhmanov A L, Nori F 2016 Phys. Rep. 648 1Google Scholar

    [13]

    Conte F, Ninno D, Cantele G 2019 Phys. Rev. B 99 155429Google Scholar

    [14]

    Anderson P W 1958 Phys. Rev. 109 1492Google Scholar

    [15]

    Abrahams E A, Anderson P, Licciardello D, Ramakrishnan T 1979 Phys. Rev. Lett. 42 673Google Scholar

    [16]

    Addou R, Colombo L, Wallace R M 2015 ACS Appl. Mater Interf. 7 11921Google Scholar

    [17]

    Fernández-Serra M, Adessi C, Blase X 2006 Phys. Rev. Lett. 96 166805Google Scholar

    [18]

    Yang K W, Chen X Y, Zheng Z H, Wan J Q, Feng M, Yu Y 2019 J. Mater. Chem. A 7 3863Google Scholar

    [19]

    Xu D, Liu H, Iv V S, Song J, Jiang H, Sun Q F, Xie X C 2013 J. Phys. Condens Matter 25 105303Google Scholar

    [20]

    Bagci V, Krokhin A A 2007 Phys. Rev. B 76 134202Google Scholar

    [21]

    Zhang W, Yang R, Ulloa S E 2009 Phys. Rev. E 80 051901Google Scholar

    [22]

    Markussen T, Rurali R, Brandbyge M, Jauho A P 2006 Phys. Rev. B 74 245313Google Scholar

    [23]

    Akguc G B, Gong J 2009 Phys. Rev. B 81 117402Google Scholar

    [24]

    Menezes M G, Nero J D, Capaz R B, Rego L 2010 Phys. Rev. B 81 117401Google Scholar

    [25]

    Sun L, Li S, Su Y, He D, Zhang Z 2019 Appl. Surf. Sci. 463 474Google Scholar

    [26]

    Abhinav S, Muttalib K A 2019 J. Phys. Communica. 3 105010Google Scholar

    [27]

    Zhong J, Stocks G M 2006 Nano Lett. 6 128Google Scholar

    [28]

    Vogel E 2007 Nature Nanotechnol. 2 25Google Scholar

    [29]

    Xiong, Gang 2007 Phys. Rev. B 76 153303Google Scholar

    [30]

    Wei Z, Rong Y, Yi Z, Duan S, Ping Z, Ulloa S E 2010 Phys. Rev. B 81 214202Google Scholar

    [31]

    Ganguly S, Maiti S K 2020 J. Phys. D: Appl. Phys. 53 025301Google Scholar

    [32]

    Zhong J X, Stocks G M 2007 Phys. Rev. B 75 033410Google Scholar

    [33]

    Patrick A, Lee T, Ramakrishnan V 1985 Rev. Modern Phys. 57 287Google Scholar

    [34]

    Zhong J X, Mosseri R 1995 J. Phys. Condensed Matter 7 8383Google Scholar

    [35]

    Schulz-Baldes H, Bellissard J 1998 Rev. Mathema. Phys. 10 1Google Scholar

  • [1] Jiang Yong-Lin, He Chang-Chun, Yang Xiao-Bao. Theoretical prediction of solution in ScxY1–x Fe2 and order-disorder transitions in V2x Fe2(1–x)Zr. Acta Physica Sinica, 2021, 70(21): 213601. doi: 10.7498/aps.70.20210998
    [2] Cheng Tai-Min, Ge Chong-Yuan, Sun Shu-Sheng, Jia Wei-Ye, Li Lin, Zhu Lin, Ma Yan-Ming. Properties and order-disorder competition of spin-1/2 XY model in the ferrimagnetic diamond chain. Acta Physica Sinica, 2012, 61(18): 187502. doi: 10.7498/aps.61.187502
    [3] Li Xiao-Chun, Gao Jun-Li, Liu Shao-E, Zhou Ke-Chao, Huang Bo-Yun. Disorder effect on the focus image of phononic crystal panel with negative refraction. Acta Physica Sinica, 2010, 59(1): 376-380. doi: 10.7498/aps.59.376
    [4] Zhao Zhi-Gang, Xu Zi-Wei, Li Bin, Liu Mei. Magnetic-field-induced phase transition of vortex glass states in disordered Josephson junction arrays. Acta Physica Sinica, 2009, 58(8): 5750-5756. doi: 10.7498/aps.58.5750
    [5] Ma Ming-Ming, Chen Hong-Bo, Ding Jian-Wen, Xu Ning. Effects of gradient disorder on persistent currents in two-dimensional mesoscopic rings. Acta Physica Sinica, 2009, 58(4): 2726-2730. doi: 10.7498/aps.58.2726
    [6] Wang Ke-Jia, Zhang Qing-Quan, Lü Jian-Tao, Du Ze-Ming, Liu Jin-Song. Dependence of spectral width of TM-polarization lasing modes on pumping intensity in two-dimensional random media. Acta Physica Sinica, 2008, 57(5): 2941-2945. doi: 10.7498/aps.57.2941
    [7] Pan Jiang-Ling, Ni Jun. Order-disorder phase transitions in the surface layers of fcc (001) AB alloy thin films. Acta Physica Sinica, 2006, 55(1): 413-418. doi: 10.7498/aps.55.413
    [8] Liu Xiao-Liang, Xu Hui, Ma Song-Shan, Song Zhao-Quan, Deng Chao-Sheng. The electronic structure of quasi-two-dimensional disordered systems. Acta Physica Sinica, 2006, 55(5): 2492-2497. doi: 10.7498/aps.55.2492
    [9] Wang Jin, Zhao Zhi-Gang, Liu Mei, Xing Ding-Yu. Order-disorder transitions and inverse melting in vortex lattices. Acta Physica Sinica, 2003, 52(12): 3162-3167. doi: 10.7498/aps.52.3162
    [10] SHI HONG-TING, NI JUN, GU BING-LIN. KINETICS OF ORDERING FOR AN ALLOY SYSTEM IN A TWO DIMENSIONAL LATTICE. Acta Physica Sinica, 2001, 50(10): 1970-1978. doi: 10.7498/aps.50.1970
    [11] CAO WAN-QIANG, CHENG YUAN-FA, LIU JUN-DIAO, XING GUO-KUEN. ORIENTATIONAL POPULATION AND RELAXATION BEHAVIOR OF C60 MOLECULES BET WEEN ORDER-DISORDER PHASE TRANSITION AND GLASSY TRANSITION. Acta Physica Sinica, 2000, 49(10): 2001-2006. doi: 10.7498/aps.49.2001
    [12] YANG YONG-HONG, XING DING-YU, GONG CHANG-DE. EFFECT OF INTERSUBBAND IMPURITY SCATTERING IN TWO DIMENSIONAL DISORDERED ELECTRON SYSTEMS. Acta Physica Sinica, 1993, 42(1): 106-113. doi: 10.7498/aps.42.106
    [13] WANG QIANG, GU BING-LIN, ZHANG XIAO-WEN. A STUDY ON THE ORDER-DISORDER TRANSITION IN A+2(B1/31B2/32)O3 PEROVSKITES. Acta Physica Sinica, 1990, 39(2): 325-336. doi: 10.7498/aps.39.325
    [14] WANG QIANG, GU BING-LIN, ZHU JIA-LIN, ZHANG XIAO-WEN. THEORETICAL STUDY ON THE FORMATION OF AN AMORPHOUS PHASE IN FexCu1-x BINARY ALLOY SYSTEM. Acta Physica Sinica, 1989, 38(2): 273-279. doi: 10.7498/aps.38.273
    [15] LI TING, QIN ZI-KAI. GREEN'S FUNCTION THEORY OF PHASE TRANSITION IN ORDER-DISORDER TYPE FERROELECTRICS AND ANTIFERROELECTRICS. Acta Physica Sinica, 1988, 37(9): 1406-1414. doi: 10.7498/aps.37.1406
    [16] ZHAO LI-HUA, FENG KE-AN, WU NAI-JUAN. RENORMALIZATION GROUP STUDY OF ORDER-DISORDER TRANSITIONS IN THE W(112)p(2×l)-O SYSTEM. Acta Physica Sinica, 1986, 35(1): 104-109. doi: 10.7498/aps.35.104
    [17] XIONG SHI-JIE, CAI JIAN-HUA. SCALING THEORY OF ANDERSON LOCALIZATION IN DISORDERED SYSTEMS WITH SPACE MODULATIONS A REAL SPACE RENORMALIZATION GROUP APPROACH. Acta Physica Sinica, 1985, 34(12): 1530-1538. doi: 10.7498/aps.34.1530
    [18] DU YI-JING, CHEN LI-RONG, YAN ZU-TONG. THE THERMODYNAMIC PROPERTIES OF TWO-DIMENSIONAL SYSTEM. Acta Physica Sinica, 1982, 31(7): 939-944. doi: 10.7498/aps.31.939
    [19] Cheng Kai-jia;Li Zhong-zheng. A GENERAL THERMODYNAMICAL THEORY OF INTERNAL FRICTION (II) INTERNAL FRICTION IN ORDERED ANO DISORDERED STATES. Acta Physica Sinica, 1956, 12(4): 281-297. doi: 10.7498/aps.12.281
    [20] SZE SHIH-YUAN, CHANG KOU-HWAN. ON THE RELAXATION TIME OF ISOTHERMAL ORDERING PROCESS IN AuCu3. Acta Physica Sinica, 1956, 12(1): 80-82. doi: 10.7498/aps.12.80
Metrics
  • Abstract views:  2298
  • PDF Downloads:  69
  • Cited By: 0
Publishing process
  • Received Date:  27 May 2022
  • Accepted Date:  26 August 2022
  • Available Online:  10 December 2022
  • Published Online:  24 December 2022

/

返回文章
返回