Dephasing by coupling with the environment, application to Coulomb electron-electron interactions in metals

Abstract

A general formulation will be given of the loss of phase coherence between two partial waves, leading to the dephasing of their interference. This is due to inelastic scattering from the 'environment' (which is a different set of degrees of freedom that the waves are coupled with). For a conduction electron, the other electrons ('Fermi sea') are often the dominant environment of this type. Coulomb interactions with the latter are, especially at lower dimensions, the most important dephasing mechanism. It will be shown how this picture yields rather straightforwardly the very non-trivial results of Altshuler, Aronov and Khmelnitskii in one and two dimensions, in the diffusive case. Subtleties associated with divergences that have to be subtracted will be discussed. These results are known to agree well with experiments. As a new application of the above ideas, the dephasing in a zero-dimensional quantum dot will be briefly considered. This will lead to stringent conditions for observing the discrete spectrum of such a dot, in agreement with recent experiments. The crossover at low temperatures in small wires from one- to zero-dimensional behaviour will be shown to 'rescue' the Landau Fermi-liquid theory from being violated because of the T^2/3 behaviour of the 1D dephasing rate. After clarifying the relationship between the e-e scattering rate and the dephasing rate, the connection with the former will be made, including the ballistic regime.