Dynamics of disordered quantum Hall crystals

Charge density waves are thought to be common in two-dimensional electron systems in quantizing magnetic ,elds. Such phases are formed by the quasiparticles of the topmost occupied Landau level when it is partially ,lled. One class of charge density wave phases can be described as electron solids. In weak magnetic ,elds (at high Landau levels) solids with many particles per unit cell—bubble phases—predominate. In strong magnetic ,elds (at the lowest Landau level) only crystals with one particle per unit cell—Wigner crystals—can form. Experimental identi,cation of these phases is facilitated by the fact that even a weak disorder in5uences their DC and AC magnetotransport in a very speci,c way. In the AC domain, a range of frequencies appears where the electromagnetic response is dominated by magnetophonon collective modes. The e9ect of disorder is to localize the collective modes and to create an inhomogeneously broadened absorption line, the pinning mode. In recent microwave experiments pinning modes have been discovered both at the lowest and at high Landau levels. We present the theory of the pinning mode for a classical two-dimensional electron crystal collectively pinned by weak impurities. We show that long-range Coulomb interaction causes a dramatic line narrowing, in qualitative agreement with the experiments. ? 2003 Elsevier B.V. All rights reserved. PACS: 74.40.Xy; 71.63.Hk