Look-alike Landau levels in locally biased twisted bilayer graphene

Abstract

Large lattice constant of Moire superlattice formed in twisted bilayer graphene enables observing Landau levels splitting into Hofstadter butterflies. This is expected for homogeneous bias conditions but its robustness against spatial potential fluctuations is left open question. We study the energy structure of twisted bilayer system in dependence of both, homogeneous magnetic field and bias voltage applied in its central region. Although translational symmetry is broken, the energy states localized outside the biased region still form Landau levels revealing self-similarity feature. Moreover, besides generic Landau levels appearing when both layers are biased with the same voltage, the second look-alike energy branch can be developed by states largely localized in central biased region. Otherwise, for counter-biasing of layers, only generic branch exists but with lowest Landau levels flanked by either, hole-like and electron-like states localized at the top or at the bottom layer of central biased part of twisted bilayer system.