电子的谷自由度

孙家涛; 孟胜

doi:10.7498/aps.64.187301

摘要

电子在晶格周期性势场影响下的运动遵循布洛赫定理. 布洛赫电子除了具有电荷和自旋两个内禀自由度外, 还有其他内禀自由度. 能带色散曲线上的某些极值点作为谷自由度, 具有独特的电子结构和运动规律. 本文从布洛赫电子的谷自由度出发, 简单介绍传统半导体的谷电子性质研究现状, 并重点介绍新型二维材料体系, 如石墨烯、硅烯、硫族化合物等材料中谷相关的物理特性. 有效利用谷自由度的新奇输运特性, 将其作为信息的载体可以制作出新颖的纳米光电子器件, 并有望造就下一代纳电子器件的新领域, 即谷电子学(valleytronics).

关键词:

Abstract

Under the periodic potential of solid, the movement of an electron obeys the Bloch theorem. In addition to the charge and real spin degree of freedom, Bloch electrons in solids are endowed with valley degree of freedom representing the local energy extrema of the Bloch energy bands. Here we will review the intriguing electronic properties of valley degree of freedom of solid materials ranging from conventional bulk semiconductors to two-dimensional atomic crystals such as graphene, silicene, and transition metal dichalcogenides. The attention is paid to how to break the valley degeneracy via different ways including strain, electric field, optic field, etc. Conventional semiconductors usually have multiple valley degeneracy, which have to be lifted by quantum confinement or magnetic field. This can alleviate the valley degeneracy problem, but lead to simultaneously more complex many-body problems due to the remnant valley interaction in the bulk semiconductor. Two-dimensional materials provide a viable way to cope with the valley degeneracy problem. The inequivalent valley points in it are in analogy with real spin as long as the inversion symmetry is broken. In the presence of electric field, the nonvanishing Berry curvature drives the anomalous transverse velocity, leading to valley Hall effect. The valley degree of freedom can be coupled with other degree of freedom, such as real spin, layer, etc, resulting in rich physics uncovered to date. The effective utilization of valley degree of freedom as information carrier can make novel optoelectronic devices, and cultivate next generation electronics–valleytronics.

Keywords:

作者及机构信息

孙家涛,
孟胜

1.
北京凝聚态物理国家实验室, 中国科学院物理研究所, 北京 100190;

2.
量子物质协同创新中心, 北京 100190

通信作者: 孙家涛, jtsun@iphy.ac.cn;smeng@iphy.ac.cn ; 孟胜, jtsun@iphy.ac.cn;smeng@iphy.ac.cn

基金项目: 国家自然科学基金(批准号: 61306114, 11222431)、国家重点基础研究发展计划(批准号: 2013CBA01600, 2012CB921403)和中国科学院战略性B类先导科技专项 (批准号: XDB07030100)资助的课题.

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

2.
Collaborative Innovation Center for Quantum Matter, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Sun Jia-Tao, jtsun@iphy.ac.cn;smeng@iphy.ac.cn ; Meng Sheng, jtsun@iphy.ac.cn;smeng@iphy.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61306114, 11222431), and the National Basic Research Program of China (Grant Nos. 2013CBA01600, 2012CB921403), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07030100).

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施引文献

[1]	Tikhonenko F V, Horsell D W, Gorbachev R V, Savchenko A K 2008 Phys. Rev. Lett. 100 056802
[2]	Wu G Y, Lue N Y, Chen Y C 2013 Phys. Rev. B 88 125422
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[4]	Gunlycke D, White C T 2011 Phys. Rev. Lett. 106 136806
[5]	Liu Y, Song J, Li Y, Liu Y, Sun Q F 2013 Phys. Rev. B 87 195445
[6]	Guinea F, Katsnelson M I, Geim A K 2009 Nat. Phys. 6 30
[7]	Jiang Y J, Low T, Chang K, Katsnelson M I, Guinea F 2013 Phys. Rev. Lett. 110 046601
[8]	Prada E, San-Jose P, Schomerus H 2009 Phys. Rev. B 80 245414
[9]	Low T, Jiang Y J, Katsnelson M I, Guinea F 2012 Nano Lett. 12 850
[10]	Wu Z, Zhai F, Peeters F M, Xu H Q, Chang K 2011 Phys. Rev. Lett. 106 176802
[11]	Ezawa M 2014 Phys. Rev. B 89 195413
[12]	Xiao D, Liu G, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802
[13]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489
[14]	Gong Z, Liu G B, Yu H, Xiao D, Cui X, Xu X, Yao W 2013 Nat. Commun. 4 2053
[15]	Zhang L F, Niu Q 2014 arXiv:1502.02573
[16]	Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120
[17]	Friesen M, Rugheimer P, Savage D E, Lagally M G, van der Weide D W, Joynt R, Eriksson M A 2003 Phys. Rev. B 67 121301
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[57]	Ni Z H, Yu T, Lu Y H, Wang Y Y, Feng Y P, Shen Z X 2008 ACS Nano 2 2301
[58]	Ni Z H, Yu T, Lu Y H, Wang Y Y, Feng Y P, Shen Z X 2009 ACS Nano 3 483
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[60]	Zhai F, Zhao X, Chang K, Xu H Q 2010 Phys. Rev. B 82 115442
[61]	Zhai F, Chang K 2012 Phys. Rev. B 85 155415
[62]	Zhai F, Ma Y, Chang K 2011 New J. Phys. 13 083029
[63]	Song Y, Zhai F, Guo Y 2013 Appl. Phys. Lett. 103 183111
[64]	Jiang Y, Low T, Chang K, Katsnelson M I, Guinea F 2013 Phys. Rev. Lett. 110 046601
[65]	Brouwer PW 1998 Phys. Rev. B 58 10135
[66]	Wang J, Chan K W, Lin Z 2014 Appl. Phys. Lett. 104 013105
[67]	Abergel D S L, Chakraborty T 2009 Appl. Phys. Lett. 95 062107
[68]	Golub L E, Tarasenko S A, Entin M V, Magarill L I 2011 Phys. Rev. B 84 195408
[69]	Linnik T L 2014 Phys. Rev. B 90 075406
[70]	Oka T, Aoki H 2009 Phys. Rev. B 79 081406
[71]	Xiao D, Yao Y, Fang Z, Niu Q 2006 Phys. Rev. Lett. 97 026603
[72]	Xiao D, Chang M, Niu Q 2010 Rev. Mod. Phys. 82 1959
[73]	Chang M, Niu Q 1996 Phys. Rev. B 53 7010
[74]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809
[75]	Yao Y, Ye F, Qi X L, Zhang S C, Fang Z Phys. Rev. B 75 041401
[76]	Yao W, Xiao D, Niu Q 2008 Phys. Rev. B 77 235406
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[78]	Cahangirov S, Topsakal M, Akturk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804
[79]	Ezawa M 2013 Phys. Rev. B 87 155415
[80]	Pan H, Li Z, Liu C C, Zhu G, Qiao Z, Yao Y 2014 Phys. Rev. Lett. 112 106802
[81]	Gorbachev R V, Song J C W, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448
[82]	Sui M, Chen G, Ma L, Shan W, Tian D, Watanabe K, Taniguchi T, Jin X, Yao W, Xiao D, Zhang Y 2014 arXiv: 1501.04685
[83]	Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N, Strano M S 2012 Nat. Nano 7 699
[84]	Mak K F, Lee C, Hone J, Shan J, Heinz T F 2010 Phys. Rev. Lett. 105 136805
[85]	Scholes G D, Rumbles G 2006 Nat. Mater. 5 683
[86]	Law M, Goldberger J, Yang P D 2004 Annu. Rev. Mater. Res. 34 83
[87]	Qiu D Y, da Jornada F H, Louie S G 2013 Phys. Rev. Lett. 111 216805
[88]	Ye Z, Cao T, O’Brien K, Zhu H, Yin X, Wang Y, Louie S G, Zhang X 2014 Nature 513 214
[89]	Shi H, Pan H, Zhang Y, Yakobson B I 2013 Phys. Rev. B 87 155304
[90]	Ramasubramaniam A 2012 Phys. Rev. B 86 115409
[91]	Shishkin M, Kresse G 2006 Phys. Rev. B 74 035101
[92]	Shishkin M, Kresse G 2007 Phys. Rev. B 75 235102
[93]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nano 7 490
[94]	Mak K F, He K, Shan J, Heinz T F 2012 Nat. Nano 7 494
[95]	Zhu Z Y, Cheng Y C, Schwingenschlogl U 2011 Phys. Rev. B 84 153402
[96]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343
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