Transport in a Nearly Periodic Potential with a Magnetic Field

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential and a perpendicular magnetic field is studied. The potential is a superposition of a periodic potential, induced e.g. by a charge density wave or a vortex lattice of a type--II superconductor, and a weak random potential due to impurities. Approximating this model by Dirac fermions with random mass, random energy, and random vector potential, we evaluate the density of states and the Hall conductivity using a self-consistent approximation. We obtain a singular average density of states $\rho(E)\approx\rho_0 +|E|^\alpha$, where $\alpha$ decreases with the strength of randomness. The Hall conductivity has a plateau which is destroyed for strong tunneling through the saddle points of the nearly periodic potential.