Dynamical response of a pinned two-dimensional Wigner crystal

Abstract

We re-examine a long-standing problem of a 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 ${\omega }_p$ is known to appear. We show that the relative linewidth $\Delta {\omega }_p/{\omega }_p$ of the pinning mode is of the order of one 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.

19 pages, 11 figures. Supersedes cond-mat/9904245

References in corpus (6)

• Smectic Liquid Crystals in Random Environments
• Absence of Two-Dimensional Bragg Glasses
• Density of states in the non-hermitian Lloyd model
• Disordered XY models and Coulomb gases: renormalization via traveling waves
• Melting of two dimensional solids on disordered substrate
• Electromagnetic absorption of a pinned Wigner crystal at finite temperatures

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