Quantum Hall effect in polycrystalline graphene: The role of grain boundaries

TL;DR

This paper uses numerical simulations to explore how grain boundaries in polycrystalline graphene affect quantum Hall effects, revealing unusual localization and transport phenomena caused by structural defects.

Contribution

It demonstrates how grain boundaries alter Landau level formation and localization, leading to breakdown of quantum Hall effects in polycrystalline graphene.

Findings

Landau levels are restricted by grain size and magnetic length.

Localized states dominate at Landau level centers, including zero-energy states.

Extended states percolate along grain boundaries, disrupting quantized conductance.

Abstract

We use numerical simulations to predict peculiar magnetotransport fingerprints in polycrystalline graphene, driven by the presence of grain boundaries of varying size and orientation. The formation of Landau levels is shown to be restricted by the polycrystalline morphology, requiring the magnetic length to be smaller than the average grain radius. The nature of localization is also found to be unusual, with strongly localized states at the center of Landau levels (including the usually highly robust zero-energy state) and extended electronic states lying between Landau levels. These extended states percolate along the network of grain boundaries, resulting in a finite value for the bulk dissipative conductivity and suppression of the quantized Hall conductance. Such breakdown of the quantum Hall regime provoked by extended structural defects is also illustrated through two-terminal Landauer-B\"uttiker conductance calculations, indicating how a single grain boundary induces cross-linking between edge states lying at opposite sides of a ribbon geometry.