Splitting of critical energies in the $n$=0 Landau level of graphene

Abstract

The lifting of the degeneracy of the states from the graphene $n$=0 Landau level (LL) is investigated through a non-interacting tight-binding model with random hoppings. A disorder-driven splitting of two bands and of two critical energies is observed by means of density of states and participation ratio calculations. The analysis of the probability densities of the states within the $n$=0 LL provides some insights into the interplay of lattice and disorder effects on the splitting process. An uneven spatial distribution of the wave function amplitudes between the two graphene sublattices is found for the states in between the two split peaks. It is shown that as the splitting is increased (linear increasing with disorder and square root increasing with magnetic field), the two split levels also get increasingly broadened, in such a way that the proportion of the overlapped states keeps approximately constant for a wide range of disorder or magnetic field variation.

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• From One Electron to One Hole: Quasiparticle Counting in Graphene Quantum Dots Determined by Electrochemical and Plasma Etching
• Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties
• Polarization of graphene in a strong magnetic field beyond the Dirac cone approximation
• Topological Transition of Graphene from Quantum Hall Metal to Quantum Hall Insulator at $\nu =0$
• Shape of the zeroth Landau level in graphene with non-diagonal disorder