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

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Abstract
We show that the recently discovered double-valley splitting of the low-lying Landau level(s) in Quantum Hall Effect in graphene can have the natural explanation as perturbative orbital interaction of intra- and inter-valley microscopic orbital currents with magnetic field. This effect is provided by the gauge-non-invariant terms that are proper to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac Fermions in Quantum Electrodynamics.

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