Two-dimensional classical electron gas in a periodic field: Delocalization and dielectric-plasma transition

Results are reported of extensive molecular-dynamics simulations of a two-dimensional Coulomb gas made up of finite-size ions held fixed on the sites of a triangular lattice, and of classical electrons moving in the periodic field of the ions. The fixed-ion model maps the dielectric-plasma (or Kosterlitz-Thouless) transition of the Coulomb gas onto a delocalization transition of the electrons. The transition is characterized by a number of static and dynamic ‘‘diagnostics.’’ As the temperature is increased in the dielectric phase, electron self-diffusion and electrical conductivity set in at a density-dependent threshold temperature $T_1$. The breakup of ion-electron pairs is signaled by a sharp peak in the specific heat at a temperature $T_2$>$T_1$. As $T_1$ is approached from above in the plasma phase, the screening length diverges. In the high-temperature plasma, the frequency of the long-wavelength collective charge oscillation (plasmon) mode decreases with T and the mode becomes overdamped by ion-electron recombination well before the threshold $T_1$ is reached. The dispersion ω(k) of the mode exhibits an unexpected oscillatory behavior. The temperatures $T_1$ and $T_2$ increase as the density decreases and there is strong evidence that the low-density limit of the reduced temperatures $T_1^{\mathrm{*}}$=$k_B$T/$e^2$ and $T_2^{\mathrm{*}}$ is 1/2 as compared with the value (1/4 expected for the mobile-ion case.