Dynamical response of a pinned two-dimensional Wigner crystal

We reexamine a long-standing problem of the finite-frequency conductivity of a weakly pinned two-dimensional classical Wigner crystal. In this system an inhomogeneously broadened absorption line (pinning mode) centered at disorder- and magnetic-field-dependent frequency ω_p is known to appear. We show that the relative linewidth Δω_p/ω_p of the pinning mode is of the order of 1 in weak magnetic fields, exhibits a power-law decrease in intermediate fields, and eventually saturates at a small value in strong magnetic fields. The linewidth narrowing is due to a peculiar mechanism of mixing between the stiffer longitudinal and the softer transverse components of the collective excitations. The width of the high-field resonance proves to be related to the density of states in the low-frequency tail of the zero-field phonon spectrum. We find a qualitative agreement with recent experiments and point out differences from the previous theoretical work on the subject.