Single-electron gap in the spectrum of twisted bilayer graphene

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.

Many-body effects in twisted bilayer graphene at low twist angles

“…Once the interaction is accounted for, the latter relation is replaced by Eq. (47), which describe mathematically the splitting of the spectrum into two band quartets caused by the non-zero ∆ nisσ . The emergence of two separate quartets minimizes the mean-field energy.…”

Twistronics: Manipulating the electronic properties of two-dimensional layered structures through their twist angle

“…In real materials, the difference between an incommensurate and a commensurate twist-angle is less clear, as the presence of imperfections (strain, tears, ripples) may make even a commensurate system sample Ω continuously. The effect of disorder on twisted bilayer graphene's electronic properties has begun to be investigated theoretically 20,21 , but we do not study it here.…”

Externally Controlled Magnetism and Band Gap in Twisted Bilayer Graphene

“…Analysis in the single-particle approximation shows that one can distinguish three qualitatively different types of behavior of the spectrum at low energies. When the twist angle θ is close to commensurate value corresponding to the superstructure with considerably small size of the supercell, the spectrum has a gap at Fermi level [7][8][9][10]. This gap, however, is very sensitive to small variations of the twist angle, and is non-negligible only for a limited number of superstructures [9,10].…”

“…When the twist angle θ is close to commensurate value corresponding to the superstructure with considerably small size of the supercell, the spectrum has a gap at Fermi level [7][8][9][10]. This gap, however, is very sensitive to small variations of the twist angle, and is non-negligible only for a limited number of superstructures [9,10]. With the exception of those values, one can assume that when θ is greater than critical value θ c ∼ 1-2 • , the electron spectrum has a linear dispersion and consists of four Dirac cones inherited from two graphene layers.…”