Phase Relaxation of Electrons in Disordered Conductors

Conduction electrons in disordered metals and heavily doped semiconductors at low temperatures preserve their phase coherence for a long time: phase relaxation time $\tau_\phi$ can be orders of magnitude longer than the momentum relaxation time. The large difference in these time scales gives rise to well known effects of weak localization, such as anomalous magnetoresistance. Among other interesting characteristics, study of these effects provide quantitative information on the dephasing rate $1/\tau_\phi$. This parameter is of fundamental interest: the relation between $\hbar/\tau_\phi$ and the temperature $T$ (a typical energy scale of an electron) determines how well a single electron state is defined. We will discuss the basic physical meaning of $1/\tau_\phi$ in different situations and its difference from the energy relaxation rate. At low temperatures, the phase relaxation rate is governed by collisions between electrons. We will review existing theories of dephasing by these collisions or (which is the same) by electric noise inside the sample. We also discuss recent experiments on the magnetoresistance of 1D systems: some of them show saturation of $1/\tau_\phi$ at low temperatures, the other do not. To resolve this contradiction we discuss dephasing by an external microwave field and by nonequilibrium electric noise.