Fractal Landau-Level Spectra in Twisted Bilayer Graphene

Citation:
Wang, ZF, Liu F, Chou MY.  2012.  Fractal Landau-Level Spectra in Twisted Bilayer Graphene, Jul. Nano Letters. 12:3833-3838., Number 7

Abstract:

The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a specific range of rotational angles twisted bilayer graphene serves as a special system with a fractal energy spectrum under laboratory accessible magnetic field strengths. This unique feature arises from an intriguing electronic structure induced by the interlayer coupling. Using a recursive tight-binding method, we systematically map out the spectra of these Landau levels as a function of the rotational angle. Our results give a complete description of LLs in twisted bilayer graphene for both commensurate and incommensurate rotational angles and provide quantitative predictions of magnetic field strengths for observing the fractal spectra in these graphene systems.

Notes:

ISI Document Delivery No.: 972QYTimes Cited: 5Cited Reference Count: 34Cited References: Albrecht C, 2001, PHYS REV LETT, V86, P147, DOI 10.1103/PhysRevLett.86.147 Bistritzer R, 2011, PHYS REV B, V84, DOI 10.1103/PhysRevB.84.035440 Bistritzer R, 2011, P NATL ACAD SCI USA, V108, P12233, DOI 10.1073/pnas.1108174108 Choi MY, 2011, PHYS REV B, V84, DOI 10.1103/PhysRevB.84.195437 Coraux J, 2008, NANO LETT, V8, P565, DOI 10.1021/nl0728874 de Gail R, 2011, PHYS REV B, V84, DOI 10.1103/PhysRevB.84.045436 Dietl P, 2008, PHYS REV LETT, V100, DOI 10.1103/PhysRevLett.100.236405 dos Santos JMBL, 2007, PHYS REV LETT, V99, DOI 10.1103/PhysRevLett.99.256802 Gusynin VP, 2005, PHYS REV LETT, V95, DOI 10.1103/PhysRevLett.95.146801 Hass J, 2008, PHYS REV LETT, V100, DOI 10.1103/PhysRevLett.100.125504 HOFSTADTER DR, 1976, PHYS REV B, V14, P2239, DOI 10.1103/PhysRevB.14.2239 Kim KS, 2009, NATURE, V457, P706, DOI 10.1038/nature07719 Kindermann M, 2011, PHYS REV B, V84, DOI 10.1103/PhysRevB.84.161406 Kwon SY, 2009, NANO LETT, V9, P3985, DOI 10.1021/nl902140j de Laissardiere GT, 2010, NANO LETT, V10, P804, DOI 10.1021/nl902948m Li GH, 2010, NAT PHYS, V6, P109, DOI 10.1038/NPHYS1463 Li XS, 2009, SCIENCE, V324, P1312, DOI 10.1126/science.1171245 Luican A, 2011, PHYS REV LETT, V106, DOI 10.1103/PhysRevLett.106.126802 Miller DL, 2009, SCIENCE, V324, P924, DOI 10.1126/science.1171810 Miller DL, 2010, NAT PHYS, V6, P811, DOI 10.1038/NPHYS1736 Miller DL, 2010, PHYS REV B, V81, DOI 10.1103/PhysRevB.81.125427 Moon P, 2012, PHYS REV B, V85, DOI 10.1103/PhysRevB.85.195458 Nemec N, 2007, PHYS REV B, V75, DOI 10.1103/PhysRevB.75.201404 Novoselov KS, 2005, NATURE, V438, P197, DOI 10.1038/nature04233 Peeters F. M., 2007, PHYS REV B, V76 Shallcross S, 2008, PHYS REV LETT, V101, DOI 10.1103/PhysRevLett.101.056803 Morell ES, 2010, PHYS REV B, V82, DOI 10.1103/PhysRevB.82.121407 Sutter PW, 2008, NAT MATER, V7, P406, DOI 10.1038/nmat2166 Wang ZF, 2011, NANOSCALE, V3, P4201, DOI 10.1039/c1nr10489f Wang ZF, 2010, ACS NANO, V4, P2459, DOI 10.1021/nn1001722 Wu SD, 2008, PHYS REV B, V77, DOI 10.1103/PhysRevB.77.195411 Xian L, 2011, PHYS REV B, V84, DOI 10.1103/PhysRevB.84.075425 Zhang YB, 2005, NATURE, V438, P201, DOI 10.1038/nature04235 Zhu W, 2009, PHYS REV LETT, V102, DOI 10.1103/PhysRevLett.102.056803Wang, Z. F. Liu, Feng Chou, M. Y.wang, zhengfei/E-8150-2011; Chou, Mei-Yin/D-3898-2012wang, zhengfei/0000-0002-0788-9725;Department of Energy [DE-FG02-97ER45632, DE-FG02-03ER46027]; National Science Foundation [DMR-02-05328]This work is supported by the Department of Energy (Grants DE-FG02-97ER45632 and DE-FG02-03ER46027). We acknowledge interaction with the Georgia Tech MRSEC funded by the National Science Foundation (Grant DMR-02-05328). We thank the NERSC and CHPC at University of Utah for providing the computing resources.5Amer chemical socWashington

Website