Lattice-Induced Double-Valley Degeneracy Lifting in Magnetic Field in Graphene

TL;DR

This paper explains the double-valley splitting of Landau levels in graphene's Quantum Hall Effect as a result of orbital interactions induced by lattice symmetry, highlighting effects absent in relativistic Dirac theory.

Contribution

It introduces a lattice-induced mechanism for valley degeneracy lifting in graphene under magnetic fields, contrasting with relativistic models.

Findings

Double-valley splitting explained by orbital interactions.

Lattice symmetry causes effects not present in Dirac theory.

Reinterpretation of recent experimental data.

Abstract

We show that the recently discovered double-valley splitting of the low-lying Landau level(s) in the Quantum Hall Effect in graphene can be explained as perturbative orbital interaction of intra- and inter-valley microscopic orbital currents with a magnetic field. This effect is provided by the translational-non-invariant terms corresponding to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac Fermions in Quantum Electrodynamics. We discuss recent data in view of these results.