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

We present results of theoretical studies of the high-frequency conductivit y 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, includi ng a self-consistent reconstruction of the phonon spectrum caused by the in teraction with surface excitations of the Fermi liquid, Multi-phonon effect s are described by means of the incoherent Gaussian approximation. It is sh own 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 app ears to be surprisingly very close to an AC conductivity of a nondegenerate electron gas even if temperature is much lower than the Wigner-crystal Deb ye temperature. When the excitation frequency approaches the bottom of the optical modes, the effective collision rate of the WS decreases substantial ly, which explains recent Pn linewidth data.