Quantum diffusion of massive Dirac fermions induced by symmetry breaking

Abstract

We show that when a two-dimensional $(2\mathrm{D})$ Dirac fermion moves in disordered environments, the weak time-reversal symmetry breaking by a small mass gives rise to the diffusive wave propagation, i.e., that the wave-packet spread obeys the diffusive law of Einstein, up to a---practically inaccessible---exponentially large length. Strikingly, the diffusion constant is larger than that given by the Boltzmann kinetic theory, and grows unboundedly as the energy-to-mass ratio increases. This diffusive phenomenon is of quantum nature and different from weak antilocalization. It implies a new type of transport in topological insulators at zero temperature.