Chiral symmetry of microscopic currents in the quantum Hall effect

Abstract

The spatial distribution of microscopic currents in two-dimensional electron gas devices is investigated exploiting the nonequilibrium Keldysh Green's function formalism, within the tight-binding framework. First, we establish a criterion at any selected energy for the occurrence of chiral symmetry, i.e., for the spatial separation of carriers with opposite direction of propagation, in the presence of magnetic fields. Then, in the chiral regime, we show that an exact identity links transport current conductance and persistent current conductance, naturally giving rise to the integer quantum Hall effect. Several profiles of current distributions in quantum wires are examined numerically to illustrate the chiral link between local currents and conductance quantization.