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

TL;DR

This paper investigates how disorder causes the splitting of critical energies in the $n$=0 Landau level of graphene using a tight-binding model, revealing band splitting, wave function distribution differences, and broadening effects.

Contribution

It demonstrates disorder-driven splitting of critical energies in graphene's Landau level and analyzes the interplay of lattice and disorder effects on this process.

Findings

Disorder causes splitting of the $n$=0 Landau level into two bands.

Wave functions show uneven sublattice distribution between split peaks.

Splitting increases linearly with disorder and with the square root of magnetic field.

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.