转角双层石墨烯在应变下的光电导率

蔡潇潇; 罗国语; 李志强; 贺言

doi:10.7498/aps.70.20210110

摘要

理论研究了转角双层石墨烯在施加不同单轴应变下的能带结构和光电导率, 用连续模型分别计算了转角为1.05°和1.47°的转角双层石墨烯在应变下的能带、态密度以及光电导率, 发现这些量随应变的变化是连续且显著的. 通过对能带的分析以及光电导率的测量能够获得应变对平带产生的实际影响, 这为今后实验对应变与平带的研究打下基础; 此外样品往往受到具有空间不均匀性的应变作用, 测量其局域的光电导率便能够估计应变的空间分布大小; 同时应变对能带的调制为原位调控转角双层石墨烯的强关联、拓扑以及量子效应提供了思路.

关键词:

Abstract

Twisted bilayer graphene (TBG) is a two-dimensional material composed of two layers stacked at a certain angle. When the twisted angle decreases, the lattice mismatch between two layers produces moiré pattern at a long wavelength which significantly modifies the low-energy band structure. In particular, when the twisted angle is close to the so-called “magic angle”, two moiré flat bands are formed near a charge neutral point due to the strong interlayer coupling. These flat bands with high density of states are essential in realizing superconductivity and correlated insulating states. More recently, the magic angle TBG combining an hBN system has exhibited spin-valley polarization when 3/4 of flat bands are filled, thereby providing an ideal platform to achieve quantum anomalous Hall states. Whether it is TBG system or TBG-hBN system, the flat band becomes a crucial condition for discovering so rich physical connotations. Besides the twisted angle, the strain gives an alternative way to modulate flat bands. It has been reported that applying heterostrain in magic angle TBG can makes flat moiré band tunable; strain can also generate flat bands in non-magic angle TBG. Moreover, the reconstruction of TBG due to the strain gives rise to a serial of novel physical phenomena such as topological protected soliton and photonic crystal. Another reason for studying strain effect is that the strain is ubiquitous in the fabrication progress. The strain can also be controlled via piezoelectric substrate which makes possible the in situ modulation of correlated states, topology and quantum effect. Our work is to study the heterostrain effect in TBG band structure and optical conductivity by using a continuum model. Although the resulting conduction band and valence bands keep connected through Dirac points protected by the C₂ symmetry, their separation increases significantly when heterostrain is applied while the Dirac point is also shifted. The optical conductivity is characterized by a series of peaks associated with van Hove singularities, and the peak energies are systematically shifted with the strain amplitude. These changes show that the heterostrain exerts a great influence on electron property of TBG.

Keywords:

作者及机构信息

四川大学物理学院, 成都　610065

通信作者: 贺言, heyan_ctp@scu.edu.cn

基金项目: 国家自然科学基金(批准号: 11874271)资助的课题

Authors and contacts

College of Physics, Sichuan University, Chengdu 610065, China

Corresponding author: He Yan, heyan_ctp@scu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874271)

文章全文 : translate this paragraph

参考文献

[1]	卢晓波, 张广宇 2015 64 077305 Google Scholar Lu X B, Zhang G Y 2015 Acta Phys. Sin. 64 077305 Google Scholar
[2]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E 2018 Nature 556 80 Google Scholar
[3]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[4]	Xia L, Kennes D M, Tancogne-Dejean N, Altarelli M, Rubio A 2019 Nano Lett. 19 4934 Google Scholar
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[8]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[9]	Huder L, Artaud A, Quang T L, Laissardière G T D, Jansen A G M, Lapertot G, Chapelier C, Renard V T 2018 Phys. Rev. Lett. 120 156405 Google Scholar
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施引文献

图 1 TBG在转角为5°时的结构示意图, 其莫尔周期结构清晰可见

Fig. 1. Schematic of TBG structure at θ = 5°, the resulted moiré pattern can be clearly seen.

下载: 全尺寸图片幻灯片

图 2 (a) TBG莫尔布里渊区示意图: 两个大正六边形代表上下两层单层石墨烯的第一布里渊区, 小正六边形为转角形成的莫尔布里渊区; (b) 偏移后的狄拉克点附近能带: 红色和蓝色曲线分别代表图(a)中莫尔布里渊区同色虚线路径的能带, 虚线路径中的黑点代表狄拉克点的位置

Fig. 2. (a) Schematic of TBG moiré Brillouin zone: The two large regular hexagons represent the first Brillouin zone of the upper and lower graphene layers, the small regular hexagons refer to the moiré Brillouin zone. (b) The band structures near the shifted Dirac points: Red and blue curve lines represent the band structures follow the same colored dashed lines path in the panel (a) respectively, the Dirac points are marked by the black dots in dash lines.

下载: 全尺寸图片幻灯片

图 3 TBG的能带　(a)—(c) TBG在转角为1.05°, 应变大小分别为0%, 3%和6%时的能带; (d)—(f) TBG在转角为1.47°, 应变大小分别为0%, 3%和6%时的能带

Fig. 3. Band structures of TBG: (a)−(c) The band structures with 0%, 0.3%, 0.6% uniaxial heterostrain at twisted angle θ = 1.05°, respectively; (d)−(f) the band structures with 0%, 0.3%, 0.6% uniaxial heterostrain of at twisted angle θ = 1.47°, respectively.

下载: 全尺寸图片幻灯片

图 4 TBG在转角为1.05°、施加0.6%大小的应变时的能带(a)、态密度(b)以及光电导(c), 图(c)中绿色、红色与蓝色箭头对应的吸收峰分别对应于图(a)中的同色箭头代表的带间跃迁

Fig. 4. (a) Band structure, (b) density of states and (c) corresponding optical conductivity of TBG with 0.6% uniaxial heterostrain at 1.05°. The green, red and blue arrows in panel (c) correspond to the interband transition marked with arrows of the same color in panel (a).

下载: 全尺寸图片幻灯片

图 5 TBG的态密度　(a) TBG在转角为1.05°, 应变大小分别为0% (黑色), 0.3% (蓝色), 0.6% (红色)时的态密度; (b) TBG在转角为1.47°, 应变大小分别为0% (黑色), 0.3% (蓝色), 0.6% (红色)时的态密度; 蓝色虚线表示正文中所讨论的①, ②区域的边界

Fig. 5. (a) Density of states (DOS) of TBG with 0% (black curve), 0.3% (blue curve) and 0.6% (red curve) uniaxial heterostrain at 1.05°; (b) DOS of TBG with 0% (black curve), 0.3% (blue curve) and 0.6% (red curve) uniaxial heterostrain at 1.47°. Blue dash lines in panel (a) and (b) represent the boundary of ①, ② region, respectively.

下载: 全尺寸图片幻灯片

图 6 TBG的光电导　(a) TBG在转角为1.05°, 应变大小分别为0% (黑色), 0.3% (蓝色), 0.6% (红色)时的光电导; (b) TBG在转角为1.47°, 应变大小分别为0% (黑色), 0.3% (蓝色), 0.6% (红色)时的光电导; 蓝色虚线表示正文中所讨论的①, ②区域的边界

Fig. 6. (a) Optical conductivity of TBG with 0% (black curve), 0.3% (blue curve) and 0.6% (red curve) uniaxial heterostrain at 1.05°; (b) optical conductivity of TBG with 0% (black curve), 0.3% (blue curve) and 0.6% (red curve) uniaxial heterostrain at 1.47°. Blue dash lines in panel (a) and (b) represent the boundary of ①, ② region, respectively.

下载: 全尺寸图片幻灯片

map

[1]	卢晓波, 张广宇 2015 64 077305 Google Scholar Lu X B, Zhang G Y 2015 Acta Phys. Sin. 64 077305 Google Scholar
[2]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E 2018 Nature 556 80 Google Scholar
[3]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[4]	Xia L, Kennes D M, Tancogne-Dejean N, Altarelli M, Rubio A 2019 Nano Lett. 19 4934 Google Scholar
[5]	Zhang Y H, Mao D, Cao Y, Jarillo-Herrero P, Senthil T 2019 Phys. Rev. B 99 075127 Google Scholar
[6]	Zhang Y H, Mao M, Senthil T 2019 Phys. Rev. Research 1 033126 Google Scholar
[7]	Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605 Google Scholar
[8]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[9]	Huder L, Artaud A, Quang T L, Laissardière G T D, Jansen A G M, Lapertot G, Chapelier C, Renard V T 2018 Phys. Rev. Lett. 120 156405 Google Scholar
[10]	Bi Z, Yuan N F Q, Fu L 2019 Phys. Rev. B 100 035448 Google Scholar
[11]	Alden J S, Tsen A W, Huang P Y, Hovden R, Brown L, Park J, Muller D A, McEuen P L 2013 PNAS 110 11256 Google Scholar
[12]	Sunku S S, Ni G X, Jiang B Y, Yoo H, Sternbach A, McLeod A S, Stauber T, Xiong L, Taniguchi T, Watanabe K, Kim P, M. Fogler M M, Basov D N 2018 Science 362 1153 Google Scholar
[13]	Wen L, Li Z Q, He Y 2021 Chin. Phys. B 30 017303 Google Scholar
[14]	Kerelsky A, McGilly L, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C 2019 Nature 572 95 Google Scholar
[15]	Lopes dos Santos J M B, Peres N M R, Castro Neto A H 2007 Phys. Rev. Lett. 99 256802 Google Scholar
[16]	Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K, Fu L 2018 Phys. Rev. X 8 031087
[17]	McCann E, Koshino M 2013 Rep. Prog. Phys. 76 056503 Google Scholar
[18]	Moon P, Koshino M 2013 Phys. Rev. B 87 205404 Google Scholar
[19]	Po H C, Zou L J, Vishwanath A, Senthil T 2018 Phys. Rev. X 8 031089
[20]	吕新宇, 李志强 2019 68 220303 Google Scholar Lü X Y, Li Z Q 2019 Acta Phys. Sin. 68 220303 Google Scholar

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转角双层石墨烯在应变下的光电导率