Spin-resoloved chiral condensate as a spin-unpolarized \nu=0 quantum Hall state in graphene

TL;DR

This paper theoretically demonstrates that the spin-unpolarized  quantum Hall state in graphene is a spin-resolved chiral condensate with a charge gap increasing linearly with magnetic field, aligning with recent experimental observations.

Contribution

It introduces a new theoretical model showing the ground state as a doubly-degenerate spin-resolved chiral condensate in graphene at  quantum Hall regime.

Findings

Charge gap grows linearly with magnetic field.

Ground state is a doubly-degenerate spin-resolved chiral condensate.

Model aligns with recent experimental results.

Abstract

Motivated by the recent experiments indicating a spin-unpolarized \nu=0 quantum Hall state in graphene, we theoretically investigate the ground state based on the many-body problem projected onto the n=0 Landau level. For an effective model with the on-site Coulomb repulsion and antiferromagnetic exchange couplings, we show that the ground state is a doubly-degenerate spin-resolved chiral condensate in which all the zero-energy states with up spin are condensed into one chirality, while those with down spin to the other. This can be exactly shown for an Ising-type exchange interaction. The charge gap due to the on-site repulsion in the ground state is shown to grow linearly with the magnetic field, in qualitative agreement with the experiments.