We study relaxation in two-dimensional Coulomb glasses up to macroscopic times. We use a kinetic Monte Carlo algorithm especially designed to escape efficiently from deep valleys around metastable states. We find that, during the relaxation process, the site occupancy follows a Fermi-Dirac distribution with an effective temperature much higher than the real temperature $T$. Long electron-hole excitations are characterized by $T_{\mathrm{eff}}$, while short ones are thermalized at $T$. We argue that the density of states at the Fermi level is proportional to $T_{\mathrm{eff}}$ and is a good thermometer to measure it. $T_{\mathrm{eff}}$ decreases extremely slowly, roughly as the inverse of the logarithm of time, and it should affect hopping conductance in many experimental circumstances.

• Received 24 January 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.056601