二维三角格点系统中的拓扑陈数

doi:10.19596/j.cnki.1001-246x.7696

计算物理 ›› 2018, Vol. 35 ›› Issue (5): 606-612.DOI: 10.19596/j.cnki.1001-246x.7696

二维三角格点系统中的拓扑陈数

郁华玲, 高雨, 翟章印

淮阴师范学院物理与电子电气工程学院, 淮安 223300

收稿日期:2017-05-15 修回日期:2017-07-20 出版日期:2018-09-25 发布日期:2018-09-25
作者简介:郁华玲(1975-),女,博士,副教授,主要从事凝聚态理论研究,E-mail:hlyu_phys@126.com
基金资助:
江苏省自然科学基金（BK20140450）资助项目

Topological Chern Numbers in a Two-dimensional Triangular-Lattice

YU Hualing, GAO Yu, ZHAI Zhangyin

School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian 223300, China

Received:2017-05-15 Revised:2017-07-20 Online:2018-09-25 Published:2018-09-25

摘要/Abstract

摘要： 利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态，再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布，计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4，5，-1}，t'=-1/2时其对应陈数分布变化为{2，-4，2}，而t'=±1/4时对应的陈数分布都为{2，-1，-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致，并且k空间的能带越平坦，其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐，而该处霍尔电导跳跃就越陡峭.

关键词: 整数量子Hall效应, 拓扑陈数, Hall电导, 态密度, 严格对角化方法

Abstract: We investigate numerically topological Chern number in a two-dimensional triangular-lattice with three bands, considering tight-binding Hamiltonian. Energy spectrum is obtained with Fourier transform and Hall conductance is calculated using Kubo formula. It is found that Chern number of energy band is modulated by next nearest neighbor hopping integral t'.Three bands own Chern numbers in sequence, {-4, 5,-1} at t'=1/2, {2,-4, 2} at t'=-1/2 and {2,-1,-1} at t'=±1/4, which leads to Hall plateaus in sequence, {-4, 1}e²/h, {2,-2}e²/h and {2, 1}e²/h, respectively. Peaks of density of states (DOS) are located at jumps of Hall conductance. Energy gap (DOS=0) gives width of corresponding Hall plateau. If energy band becomes more flat, corresponding peak of DOS becomes higher and sharper, and jump of Hall conductance becomes steeper.

Key words: integer quantum Hall effect, topological Chern number, Hall conductance, density of states, exact diagonalization method

中图分类号:

O469

郁华玲, 高雨, 翟章印. 二维三角格点系统中的拓扑陈数[J]. 计算物理, 2018, 35(5): 606-612.

YU Hualing, GAO Yu, ZHAI Zhangyin. Topological Chern Numbers in a Two-dimensional Triangular-Lattice[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(5): 606-612.

参考文献

[1] KLITZING K V,DORDA G,PEPPER M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance[J]. Phys Rev Lett,1980,45:494-497.
[2] TSUI D C, STORMER H L, GOSSARD A C. Two-dimensional magnetotransport in the extreme quantum limit[J]. Phys Rev Lett,1982,48:1559-1562.
[3] LAUGHLIN R B. Quantized Hall conductivity in two dimensions[J]. Phys Rev B, 1981, 23:5632.
[4] HALPERIN B I. Quantized Hall conductance, current-carrying edge states,and the existence of extended states in a two-dimensional disordered potential[J]. Phys Rev B, 1982, 25:2185-2190.
[5] THOULESS D J, KOHMOTO M, NIGHTINGATE M P,et al. Quantized Hall conductance in a two-dimensional periodic potential[J]. Phys Rev Lett, 1982, 49:405-408.
[6] NIU Q, THOULESS D J, WU Y S. Quantized Hall conductance as a topological invariant[J]. Phys Rev B, 1985,31:3372-3377.
[7] HATSUGAI Y. Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function[J].Phys Rev B, 1993,48:11851-11862.
[8] HATSUGAI Y. Chern number and edge states in the integer quantum Hall effect[J]. Phys Rev Lett, 1993,71:3697-3700.
[9] HOFSTADTER D R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields[J]. Phys Rev B, 1976, 14:2239-2249.
[10] SHENG D N, WENG Z Y. Disappearance of integer quantum Hall effect[J]. Phys Rev Lett, 1997,78:318-321.
[11] DUTTA P, MAITI S K, KARMAKAR S N. Integer quantum Hall effect in a lattice model revisited:Kubo formalism[J]. J Appl Phys, 2012,112:044306.
[12] SHENG D N, WENG Z Y. New universality of the metal-insulator transition in an integer quantum Hall effect system[J]. Phys Rev Lett, 1998, 80:580-583.
[13] SHENG D N, WENG Z Y, WEN X G. Float-up picture of extended levels in the integer quantum Hall effect:A numerical study[J]. Phys Rev B, 2001,64:165317-165321.
[14] SHENG D N, SHENG L, WENG Z Y. Quantum Hall effect in graphene:Disorder effect and phase diagram[J]. Phys Rev B, 2006, 73:233406-233409.
[15] WANG Y F, GONG C D. Redistributing Chern numbers of Landau subbands:Tight-binding electrons under staggered modulated magnetic fields[J]. Phys Rev Lett, 2007,98:096802-096805.
[16] PRIEST J, LIM S P, SHENG D N. Scaling behavior of the insulator-to-plateau transition in a topological band model[J]. Phys Rev B, 2014,89:165422-165428.
[17] MAITI S K, DEY M, KARMAKAR S N. Integer quantum Hall effect in a square lattice revisited[J]. Phys Lett A,2012, 376:1366-1370.
[18] NAUMIS G G. Integer quantum Hall effect in a square lattice revisited[J]. Phys Lett A,2016,380:1772-1780.
[19] KEIL R, POLI C, HEINRICH M, et al. Universal sign control of coupling in tight-binding lattices[J]. Phys Rev Lett, 2016, 116:213901-213905.
[20] MEI F, ZHANG D W, ZHU S L. Graphene-like physics in optical lattices[J]. Chinese Phys B, 2013,22:116106-116116.
[21] YANG Y, LI X L. Theoretical analysis of transcranial Hall-effect stimulation based on passive cable model[J]. Chinese Phys B,2015, 24:124302-124307.
[22] ZHANG Y, VISHWANATH A. Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modular S-matrix[J]. Phys Rev B, 2013,87:161113-161117.
[23] UDAGWA M, BERGHOLTZ E J. Correlations and entanglement in flat band models with variable Chern numbers[J].J Stat Mech, 2014,10:10012-10028.
[24] MA R, SHENG L, SHEN R, LIU M, et al. Quantum Hall effect in bilayer graphene:Disorder effect and quantum phase transition[J]. Phys Rev B, 2009, 80:205101-205105.
[25] NITÃ M, OSTAHIE B, ALDEA A. Spectral and transport properties of the two-dimensional Lieb lattice[J]. Phys Rev B, 2013,87:125428-125440.
[26] WANG Y F, YAO H, GONG C D, et al. Fractional quantum Hall effect in topological flat bands with Chern number two[J]. Phys Rev B, 2012, 86:201101-201104.
[27] LI J, WANG Y F, GONG C D. Tight-binding electrons on triangular and Kagome lattices under staggered modulated magnetic fields:Quantum Hall effects and Hofstadter butterflies[J]. J Phys Condens Matter, 2011,23:156002-156010.
[28] WANG W, GAO J, ZHANG T, et al. Performance of asymmetric linear doping triple-material-gate GNRFETs[J]. Chinese Journal of Computational Physics, 2015, 32:115-126.
[29] ZOU J H, YE Z Q, CAO B Y. Effects of potential models on thermal properties of graphene in molecular dynamics simulations[J]. Chinese Journal of Computational Physics,2017, 34:221-229.

二维三角格点系统中的拓扑陈数

Topological Chern Numbers in a Two-dimensional Triangular-Lattice

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