Pinned Wigner crystals

We study the effects of weak Gaussian disorder on various physical and dynamical properties of the pinned Wigner crystal. We use the replica based Gaussian variational method to study the problem. The pinned crystal is the quantum analog of the Bragg glass phase seen in vortex lattices. We obtain the full frequency dependence of the dynamical magnetoconductivities. This allows us to extract various features of the pinning peak which can be compared directly with experimentally measured quantities. We also calculate the magnetic field and density dependences of these quantities. We find that the physical properties of the crystal depend crucially on the relative magnitudes of the disorder correlation length and the cyclotron length. This has dramatic experimental consequences. Our results are of extreme relevance to the recent experiments on two dimensional Ga-As quantum Hall samples and Si MOSFETS, where the insulating phase seen at low densities and/or high magnetic fields is expected to be a pinned Wigner crystal