Thermodynamic fluctuations of site energies and occupation numbers in the two-dimensional Coulomb glass

The equilibrium thermodynamic fluctuations of site energies and site occupation numbers in a disordered two-dimensional system of localized classical interacting electrons, known as the Coulomb glass, are studied. Using computer simulations, it is shown that the configuration of occupied sites within the Coulomb gap persistently changes with time, even at temperatures much lower than the Coulomb gap width. A related effect is the fluctuations in the site energies, which are much larger than the temperature, and are of the order of the Coulomb gap width. Numerical arguments are presented that no thermodynamic glass phase transition occurs above $T=0,$ so that at long enough timescales the system will always be in thermal equilibrium. The strong fluctuations in the occupation numbers and site energies are interpreted in terms of a drift of the system within the complex structure of phase space, which is characteristic of glassy systems. Such a drift could provide a new mechanism of electron diffusion, as long as the equilibration time of the system is short enough. However, in realistic systems with tunneling between sites there may be two different regimes. In the first regime the system is effectively frozen in one of the minima of phase space and the regular Efros-Shklovskii hopping is responsible for transport. Our results are applicable to the second regime where the localization length is $\xi \gg 1/T.$ This may shine light on the issue of a possible metal-insulator transition in 2D systems.