TRANSPORT IN A NEARLY PERIODIC POTENTIAL WITH A MAGNETIC-FIELD

A two-dimensional gas of non-interacting quasiparticles in a nearly pe riodic potential and a perpendicular magnetic field is studied. The po tential is a superposition of a periodic potential, induced, for examp le, by a charge-density wave or a vortex lattice of a type-II supercon ductor, and a weak random potential due to impurities. Approximating t his model by Dirac fermions with random mass, random energy, and rando m vector potential, we evaluate the density of states and the Hall con ductivity using a self-consistent approximation. We obtain a singular average density of states rho(E) approximate to rho(o) + \E\, where al pha decreases with the strength of the randomness. The Hall conductivi ty has a plateau which is destroyed for strong tunnelling through the saddle points of the nearly periodic potential.