Luttinger Liquid at the Edge of a Graphene Vacuum

TL;DR

This paper shows that undoped graphene in the quantum Hall regime can host a non-chiral Luttinger liquid at its edge, characterized by unique dispersion, domain wall structures, and a quantum phase transition to a metallic state.

Contribution

It reveals the existence of a non-chiral Luttinger liquid at graphene edges in the quantum Hall regime, highlighting the role of band crossing and domain wall formations.

Findings

Supports gapless charged excitations with power-law tunneling.

Demonstrates a quantum phase transition at the edge.

Identifies the conditions for Luttinger liquid stability.

Abstract

We demonstrate that an undoped two-dimensional carbon plane (graphene) whose bulk is in the integer quantum Hall regime supports a non-chiral Luttinger liquid at an armchair edge. This behavior arises due to the unusual dispersion of the non-interacting edges states, causing a crossing of bands with different valley and spin indices at the edge. We demonstrate that this stabilizes a domain wall structure with a spontaneously ordered phase degree of freedom. This coherent domain wall supports gapless charged excitations, and has a power law tunneling $I-V$ with a non-integral exponent. In proximity to a bulk lead, the edge may undergo a quantum phase transition between the Luttinger liquid phase and a metallic state when the edge confinement is sufficiently strong relative to the interaction energy scale.