Quantum Hall Ferromagnetism in Graphene

TL;DR

This paper investigates the conditions under which electron interactions induce quantum Hall effects in graphene, focusing on the role of symmetry breaking and charge gaps near certain quantized conductance values.

Contribution

It derives a new criterion for the emergence of interaction-driven quantum Hall states in graphene at intermediate conductance levels.

Findings

Interaction-driven quantum Hall effects can occur near specific integer values of conductance.

Charge gaps in broken symmetry states are crucial for these effects.

The criterion helps predict when such states will form in graphene.

Abstract

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected its Landau levels are four-fold degenerate, explaining the $4 e^2/h$ separation between quantized Hall conductivity values seen in recent experiments. In this paper we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of $e^2/h$ due to charge gaps in broken symmetry states.