Zero Field Hall Effect in (2+1)-dimensional QED

Abstract

In quantum electrodynamics of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be given by an integer, the Chern number. In our field-free situation, however, the conductivity is ±1/2 in natural units. We fit this half-integral result into the topological setting and give a geometric explanation reconciling the points of view of quantum field theory (QFT) and solid state physics. For quasiperiodic boundary conditions, we calculate the finite size correction to the Hall conductivity. Applications to graphene and similar materials are discussed.