Electronic structure of twisted bilayer graphene

Wu Jiang-Bin; Zhang Xin; Tan Ping-Heng; Feng Zhi-Hong; Li Jia

doi:10.7498/aps.62.157302

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:

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).

References

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[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
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[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

Cited By

[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 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 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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Vol. 62, Issue 15 - 2013-08-05

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