旋转双层石墨烯的电子结构

吴江滨; 张昕; 谭平恒; 冯志红; 李佳

doi:10.7498/aps.62.157302

摘要

本文将第一性原理和紧束缚方法结合起来, 研究了层间不同旋转角度对双层石墨烯的电子能带结构和态密度的影响. 分析发现, 旋转双层石墨烯具有线性的电子能量色散关系, 但其费米速度随着旋转角度的减小而降低. 进一步研究其电子能带结构发现, 不同旋转角度的双层石墨烯在M点可能会出现大小不同的的带隙, 而这些能隙会增强双层石墨烯的拉曼模强度, 并由拉曼光谱实验所证实. 通过对比双层石墨烯的晶体结构和电子态密度, 发现M点处带隙来自于晶体结构中的类AB堆垛区.

关键词:

Abstract

This paper uses the first-principles and the tight-binding methods to study the electronic structures of twisted bilayer graphene for different angles. The band structures and density of states of twisted bilayer graphene in different angles are calculated. Our analysis points out that there is a linear dispersion relation in a twisted bilayer graphene, which is similar to a monolayer graphene, and the Fermi velocity of twisted graphene is lower and lower with reducing angle. Furthermore, gaps appearing at M point of certain angles, in which the width of gap depends on the twist angle, this gap would strengthen the Raman mode intensity of twisted bilayer graphene, as was confirmed by experiment. The comparison of moire patterns and the location of density of states both certify that AB region of moire patterns is the reason of gap at M point.

Keywords:

作者及机构信息

1.
中国科学院半导体研究所, 半导体超晶格国家重点实验室, 北京 100083;

2.
河北半导体研究所, 专用集成电路重点实验室, 石家庄 050051

基金项目: 国家重点基础研究发展计划 (批准号: 2009CB929301)和国家自然科学基金 (批准号: 11225421, 10934007)资助的课题.

Authors and contacts

1.
The State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China;

2.
Science and Technology on ASIC Lab., Hebei Semiconductor Research Institute, Shijiazhuang 050051, China

Funds: Project Supported by the Special Funds for Major State Basic Research of China (Grant No. 2009CB929301), and the National Natural Science Foundation of China (Grant Nos. 11225421, 10934007).

参考文献

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施引文献

[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 306 666
[2]	Tan P H, Han W P, Zhao W J, Wu Z H, Chang K, Wang H, Wang Y F, Bonini N, Marzari N, Savini G, Lombardo A, Ferrari A C 2012 Nat. Mater. 11 294
[3]	Berger C, Song Z, Li T 2004 J. Phys. Chem. B 108 19912
[4]	Novoselov K S, Geim A K, Morozov V 2005 Nature (London) 438 197
[5]	Luk’yanchuk I A, Kopelevich Y 2004 Phys. Rev. Lett. 93 166402
[6]	McCann E, Fal’ko V I 2006 Phys. Rev. Lett. 96 086805
[7]	Castro E V, Novoselov K S, Morozov V, Peres N M R, Lopes dos Santos J M B, Nilsson J, Guinea F, Geim A K, Castro Neto A H 2007 Phys. Rev. Lett. 99 216802
[8]	McCann E 2006 Phys. Rev. B 74 161403
[9]	Yin W H, Han Q, Yang X H 2012 Acta Phys. Sin. 61 248502 (in Chinese) [尹伟红, 韩勤, 杨晓红 2012 物理学报 61 248502]
[10]	Qin J R, Chen S M, Zhang C, Chen J J, Liang B, Liu B W 2012 Acta Phys. Sin. 61 023102 (in Chinese) [秦军瑞, 陈书明, 张超, 陈建军, 梁斌, 刘必慰 2012 物理学报 61 023102]
[11]	Gorbachev R V, Tikhonenko F V, Mayorov A S, Horsell D W, Savchenko A K 2007 Phys. Rev. Lett. 98 176805
[12]	Kechedzhi K, Fal’ko V I, McCann E 2007 Phys. Rev. Lett. 98 176806
[13]	Hass J, Feng R, Li T 2006 Appl. Phys. Lett. 89 143106
[14]	Guinea F, Castro Neto A H, Peres N M R E 2006 Phys. Rev. B 73 245426
[15]	Latil S, Henrard L 2006 Phys. Rev. Lett. 97 036803
[16]	Schmidt H, Ldtke T, Barthold P 2008 Appl. Phys. Lett. 93 172108
[17]	Berger C, Song Z, Li X 2006 Science 312 1191
[18]	Hicks J, Sprinkle M, Shepperd K 2011 Phys. Rev. B 83 205403
[19]	Li G, Luican A, Lopes dos Santos J M B 2010 Nature Phys. 6 109
[20]	Luican A, Li G, Reina A, Kong J, Nair R R, Novoselov K S, Geim A K 2011 Phys. Rev. Lett. 106 126802
[21]	Lopes dos Santos J M B, Peres N M R, Castro Neto A H 2007 Phys. Rev. Lett. 99 256802
[22]	Mele E J 2010 Phys. Rev. B 81 161405
[23]	Trambly de Laissardiere G, Mayou D, Magaud L 2010 Nano Lett. 10 804
[24]	Elstner M, Frauenheim T, Kaxiras E 2000 Phys. Stat. Sol. B 217 357
[25]	Kohn W, Sham L J 1965 Phys. Rev. 137 A1697
[26]	Perdew J P, Zunger A 1981 Phys. Rev. B 23 5048
[27]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864
[28]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133
[29]	Portal D S, Ordejón P, Artacho E 1997 J. Quantum. Chem. 65 453
[30]	Hass J, Varchon F, Milla’n-Otoya J E, Sprinkle M, Sharma N, de Heer W A, Berger C, First P N, Magaud L, Conrad E H 2008 Phys. Rev. Lett. 100 125504
[31]	de Heer W A, arXiv:0704.0285
[32]	Ni Z, Wang Y, Yu T, You Y, Shen Z 2008 Phys. Rev. B 77 235403
[33]	Bistritzer R, MacDonald A H 2011 PNAS 108 12233
[34]	Kim K, Coh S, Tan L Z, Regan W, Yuk J M, Chatterjee E, Crommie M F, Cohen M L, Louie S G, Zettl A 2012 Phys. Rev. Lett. 108 246103
[35]	Zhao W J, Tan P H, Liu J, Ferrari A C 2011 J. Am. Chem. Soc. 113 5941
[36]	Zhao W J, Tan P H, Zhang J, Liu J 2010 Phys. Rev. B 82 245423

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