Single-electron gap in the spectrum of twisted bilayer graphene

A. V. Rozhkov, A. O. Sboychakov, A. L. Rakhmanov, Franco Nori

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


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.

Original languageEnglish
Article number045119
JournalPhysical Review B
Issue number4
Publication statusPublished - 13 Jan 2017
Externally publishedYes


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