The nature of localization in graphene under quantum Hall conditions

TL;DR

This study investigates how electron localization occurs in graphene under quantum Hall conditions, revealing that Coulomb interactions and disorder potential interplay, differing from traditional high mobility systems.

Contribution

It provides the first microscopic imaging of localized states in disordered graphene, highlighting the dominant role of Coulomb interactions over single particle effects.

Findings

Localization in graphene is influenced more by Coulomb interactions than disorder.

Despite strong disorder, localization is not purely single particle driven.

Screening effects significantly impact the localized state spectrum.

Abstract

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.