Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

TL;DR

This paper develops a theoretical framework for understanding the integer quantum Hall effect in graphene, considering both ferromagnetic and paramagnetic regimes influenced by interactions, disorder, and symmetry-breaking effects.

Contribution

It introduces an interacting continuum Dirac theory for graphene in magnetic fields and analyzes quantum Hall ferromagnetism and paramagnetism at various filling factors, incorporating lattice-scale interactions and disorder effects.

Findings

Ferromagnetic regime may not be realized in current samples due to disorder.

Zeeman splitting and interactions can produce quantum Hall states in paramagnetic graphene at certain fillings.

Predictions for activation energies aid in identifying the nature of quantum Hall states.

Abstract

Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at nu = 0 and nu = \pm 1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at nu = \pm 3, \pm 4, and \pm 5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at nu = 0, \pm 1 and \pm 4, but not at nu = \pm 3 or \pm 5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.