Abstract
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 3 He. 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 o...
Highlights
Since the first observation of the Wigner solid (WS)transition in a two-dimensional (2D) electron system formed on a free surface of liquid 4 He,1, 2) considerable research has been performed on describing the interaction of the electron crystal with a medium.3–7) The reason of these studies is to develop new approaches, avoiding the “divergence” in the mean-square fluctuation of a 2D lattice present in conventional methods
We found that the general conductivity theory based on the memory function formalism, establishing relation between the effective collision frequency and the equilibrium electron DSF, appears to be very fruitful for an analysis of the high-frequency conductivity and phonon damping of a 2D electron solid
Employing different approximations for the electron DSF reveals effects which are of general nature of a 2D electron system, regardless of the actual state of the electron matter, as well as the effects which exist only for the WS state
Summary
Temperature Physics Laboratory, RIKEN, Hirosawa 2-1, Wako-shi 351-0198 for Low Temperature Physics and Engineering, 47 Lenin Avenue, 310164 Kharkov, Ukraine (Received December 4, 2000). We present results of theoretical studies of the high-frequency conductivity of a twodimensional Wigner solid (WS) formed on a free surface of liquid 3 He. 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. It is shown that the reconstruction of the phonon spectrum can substantially affect the plasmon resonance (PR). 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 PR linewidth data
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