  Charge density waves are thought to be common in two-dimensional electron
systems in quantizing magnetic fields. Such phases are formed by the
quasiparticles of the topmost occupied Landau level when it is partially
filled. One class of charge density wave phases can be described as electron
solids. In weak magnetic fields (at high Landau levels) solids with many
particles per unit cell - bubble phases - predominate. In strong magnetic
fields (at the lowest Landau level) only crystals with one particle per unit
cell - Wigner crystals - can form. Experimental identification of these phases
is facilitated by the fact that even a weak disorder influences their dc and ac
magnetotransport in a very specific way. In the ac domain, a range of
frequencies appears where the electromagnetic response is dominated by
magnetophonon collective modes. The effect 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.
