Single-electron gap in the spectrum of twisted bilayer graphene

TL;DR

This paper studies how the electronic gap in twisted bilayer graphene varies with twist angle and disorder, highlighting the importance of finite-size effects and sample purity for experimental observations.

Contribution

It introduces a numerical approach to analyze finite clusters, revealing the crossover between gapped and gapless regimes due to twist angle variations and disorder effects.

Findings

Finite clusters show a crossover between gapless and gapped states.

Disorder can induce a similar crossover as finite size.

Accurate twist angle tuning and high sample purity are essential for observing the gap.

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.