High-frequency conductivity and phonon damping of a two-dimensional Wigner solid on a free surface of liquid He-3

We present results of theoretical studies of the high-frequency conductivity of a two-dimensional Wigner solid (WS) formed on a free surface of liquid He-3. One-phonon processes are taken into account in an exact way, including a self-consistent reconstruction of the phonon spectrum caused by the interaction with surface excitations of the Fermi liquid, Multi-phonon effects are described by means of the incoherent Gaussian approximation. It is shown that the reconstruction of the phonon spectrum can substantially affect the plasmon resonance (PR) linewidth depending on the resonant frequency. If the excitation frequency is away from the bottom spectrum of WS optical modes, or the dimple lattice is disregarded, the conductivity of the WS appears to be surprisingly very close to an AC conductivity of a nondegenerate electron gas even if temperature is much lower than the Wigner-crystal Debye temperature. When the excitation frequency approaches the bottom of the optical modes, the effective collision rate of the WS decreases substantially, which explains recent Pn linewidth data.