Frequency-dependent conductivity of a pinned Wigner crystal

Abstract

We have evaluated the frequency-dependent conductivity of the electron crystal state which occurs in two-dimensional systems in a strong magnetic field and studied its dependence on the strength of a commensurate pinning potential. We find that, in contrast to the zero-field case, the pinning frequency is linearly proportional to the strength of the pinning potential and point out that, even in the absence of pinning, poles in the frequency-dependent conductivity do not occur at magnetophonon frequencies. Our calculations are based on a time-dependent Hartree-Fock approximation which allows for arbitrarily large anharmonicities in the electron crystal and can be used to justify a “two-fluid” model in which the system consists of a thermally excited gas of interstitial electrons and an essentially classical electron crystal.