Luttinger Liquid at the Edge of a Graphene Vacuum

Details Luttinger Liquid at the Edge of a Graphene Vacuum Luttinger Liquid at the Edge of a Graphene Vacuum

2006-04-10

arxiv.org/abs/cond-mat/0604260v1

Phys. Rev. Lett. 97, 116805 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures

Scientific paper

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.

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