Electronic Properties of Twisted Bilayer Graphene in the Presence of a Magnetic Field

Abstract

In AA-stacked twisted bilayer graphene, the lower energy bands become completely flat when the twist angle passes through certain specific values: the so-called “magic angles”. The Dirac peak appears at zero energy due to the flattening of these bands when the twist angle is sufficiently small [1-3]. When a constant perpendicular magnetic field is applied, Landau levels start appearing as expected [5]. We used the Kernel Polynomial Method (KPM) [6] as implemented in KITE [7] to study the optical and electronic properties of these systems. The aim of this work is to analyze how the features of these quantities change with the twist angle in the presence of an uniform magnetic field.

Excitonic condensation and metal-semiconductor transition in AA bilayer graphene in the external magnetic field

“…(37) (see in the next section) and by putting the obtained values of the physical parameters µ, δn, ∆ ↑ and ∆ ↓ in Eq. (38). For U = 3 eV, the absolute value of the total splitting between E ↑ and…”

“…The effect of the magnetic field on the electronic and transport properties in the AA-BLG has been studied in a series of theoretical works [30][31][32][33][34][35][36][37][38][39][40][41]. The magnetic filed dependence of thermal properties in the doped AA-BLG has been considered theoretically in [31,35], where the presence of both electron and hole type contributions in transport properties has been shown in AA-BLG.…”

“…To achieve the CN in such construction a huge number of internal and external physical parameters should be properly considered and tuned [37]. This requires also an important experimental setup and efforts to calibrate the BLG system at the CN [38]. The electronic and transport properties at the CN and away of it have been discussed in a number of works [42][43][44][45][46][47].…”

Magnetic response of twisted bilayer graphene

“…While this is the first mathematical work to study twisted bilayer graphene in a magnetic field, we want to mention that the dependence of Landau levels on the twisting angle have been studied for a simplified model in [CHK11] and numerically in [MGJ20] for a tight-binding model. We will show in this article that many of the effects that have been identified in these works can be derived from an asymptotic expansion of the DOS in the continuum model with external magentic field.…”

“…The quantum Hall effect for twisted bilayer graphene has been theoretically analyzed in [MGJ20]. It has been predicted that the Hall conductivity would show both features resembling monolayer graphene [MK12] with Landau levels of higher degeneracy compared to monolayer graphene close to zero energy and a more smeared out behaviour at higher energies.…”