Quantum transport in graphene Hall bars: Effects of vacancy disorder

TL;DR

This study explores how vacancy disorder affects quantum transport in graphene Hall bars under magnetic fields, revealing localized states and their dependence on vacancy type, concentration, and magnetic field strength.

Contribution

It provides new insights into vacancy-induced localized states in graphene and their impact on electronic transport, including effects of vacancy type and magnetic field.

Findings

Localized states are observable in bend resistance and DOS.

Vacancy type influences the energy and magnetic field dependence of localized states.

Next nearest neighbor hopping modifies the localized states' properties.

Abstract

Using the tight-binding model, we investigate the influence of vacancy disorder on electrical transport in graphene Hall bars in the presence of quantizing magnetic fields. Disorder, induced by a random distribution of monovacancies, breaks the graphene sublattice symmetry and creates states localized on the vacancies. These states are observable in the bend resistance, as well as in the total DOS. Their energy is proportional to the square root of the magnetic field, while their localization length is proportional to the cyclotron radius. At the energies of these localized states, the electron current flows around the monovacancies and, as we show, it can follow unexpected paths depending on the particular arrangement of vacancies. We study how these localized states change with the vacancy concentration, and what are the effects of including the next nearest neighbor hopping term. Our results are also compared with the situation when double vacancies are present in the system. Double vacancies also induce localized states, but their energy and magnetic field dependences are different. Their localization energy scales linearly with the magnetic field, and their localization length appears not to depend on the field strength.