Single-electron gap in the spectrum of twisted bilayer graphene

A. V. Rozhkov, A. O. Sboychakov, A. L. Rakhmanov, and Franco Nori
Phys. Rev. B 95, 045119 – Published 13 January 2017

Abstract

We investigate the gap in the single-electron spectrum of twisted bilayer graphene. In a perfect infinite lattice of a twisted bilayer, the gap varies exponentially in response to weak changes of the twist angle. Such a large sensitivity makes theoretical predictions of the gap nearly impossible, since experimentally the twist angle is always known with finite accuracy. To address this issue, we numerically study finite clusters of twisted bilayer graphene. For finite systems, changing the twist angle causes a gradual crossover between gapless and gapped regimes. The crossover occurs when the finite-size quantization energy becomes comparable to the matrix elements responsible for the generation of the gap. We further argue that disorder scattering can induce similar crossover, in which the mean-free path plays the same role as the system size for the finite clusters. It is demonstrated that to observe the gap experimentally, it is necessary to have a sample of suitable purity and to possess the ability to tune the twist angle accurately.

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  • Received 7 October 2016

DOI:https://doi.org/10.1103/PhysRevB.95.045119

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. V. Rozhkov1,2,3, A. O. Sboychakov1,2, A. L. Rakhmanov1,2,3,4, and Franco Nori1,5

  • 1CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
  • 2Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow 125412, Russia
  • 3Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
  • 4All-Russia Research Institute of Automatics, Moscow 127055, Russia
  • 5Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

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Issue

Vol. 95, Iss. 4 — 15 January 2017

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