Replica study of pinned bubble crystals -: art. no. 115344

In higher Landau levels (N>1), the ground state of the two-dimensional electron gas in a strong perpendicular magnetic field evolves from a Wigner crystal for small filling nu of the partially filled Landau level, into a succession of bubble states with an increasing number of guiding centers per bubble as nu increases, to a modulated stripe state near nu=0.5. In this work, we compute the frequency-dependent longitudinal conductivity sigma(xx)(omega) of the Wigner and bubble crystal states in the presence of disorder. We apply an elastic theory to the crystal states that is characterized by a shear and a bulk modulus. We obtain both moduli from the microscopic time-dependent Hartree-Fock approximation. We then use the replica and Gaussian variational methods to handle the effects of disorder. Within the semiclassical approximation we get the dynamical conductivity as well as the pinning frequency as functions of the Landau level filling factor and compare our results with recent microwave experiments.