Long-wavelength gauge symmetry and translations in a magnetic field for Dirac electrons in graphene

Abstract

In two-dimensional (2D) electron systems in a magnetic field, the Coulomb interaction among charge carriers, under Landau quantization, essentially governs a variety of many-body phenomena while there are also phenomena, such as the (integer) quantum Hall effect, that appear unaffected by the interaction. It is pointed out that the response of 2D electrons to spatially-uniform potentials and fields enjoys a long-wavelength gauge symmetry, associated with cyclotron motion of electrons, that leaves the Coulomb interaction invariant and that thus naturally explains why cyclotron resonance (as implied by Kohn’s theorem) and the quantized Hall conductance appear insensitive to the interaction. It is discussed, in the light of this new long-wavelength gauge symmetry, how Dirac electrons in graphene and conventional 2D electrons differ in cyclotron-resonance characteristics and the quantum Hall effect.