The energy and temperature dependence of the electron-electron scattering rate in a one-dimensional surface superlattice

Increased interest in one-dimensional surface superlattices has motivated us to study the electron-electron scattering rate in these structures. Using a single-miniband model, we show a rich dependence of the scattering rate on the position of the Fermi level. This is particularly interesting from an experimental point of view, since the Fermi level can be externally controlled. When the Fermi level lies below the top of the miniband, the scattering rate is αΔ² ln(εf/Δ) (Δ is the temperature, or the electron's excess energy above the Fermi level, whichever is larger). This behaviour is similar to that of a uniform two-dimensional electron system. Near the top of the miniband, the Van Hove singularity in the energy spectrum strongly affects the scattering rate, which is αΔ. Above the top of the miniband, the non-trivial shape of the Fermi surface leads to a rich dependence of the scattering rate on the wave vector of the scattered electron. This causes the scattering rate averaged over states near the Fermi surface to be αΔ² ln²(εf/Δ). The method described here for calculating the scattering rate can be applied to any two-dimensional electron system with an arbitrary energy spectrum.