Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene

TL;DR

This paper investigates how magnetic fields induce quantum Hall ferromagnetism in weakly coupled graphene, revealing spontaneous symmetry breaking and detailed fermion spectrum characteristics.

Contribution

It demonstrates that in weak coupling, graphene's ground state under magnetic fields is a quantum Hall ferromagnet with exact order parameters, and computes corrections to chiral condensates.

Findings

Quantum Hall ferromagnetism spontaneously breaks U(4) symmetry to U(2)×U(2).

The quantum Hall ferromagnet order parameter is exactly given by leading order perturbation.

The charge neutral state is a bulk insulator with a charge gap and zero Hall conductivity.

Abstract

We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2)XU(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry.