Physical interpretation of weak localization: A time-of-flight experiment with conduction electrons

Abstract

The resistance of two-dimensional electron systems such as thin disordered films shows deviations from Boltzmann theory, which are caused by quantum corrections and are called "weak localization." Theoretically, weak localization is originated by the Langer-Neal graph in the Kubo formalism. In the present paper this graph is translated into a transparent physical picture. It represents an interference experiment with conduction electrons split into pairs of waves interfering in the backscattering direction. The intensity of the interference (integrated over the time) can be easily measured by the resistance of the film. A simple derivation for this quantum correction to the resistance is given. A magnetic field introduces a magnetic phase shift in the electronic wave function and suppresses the interference after a "flight" time proportional to $\frac{1}{H}$. Therefore, the application of a magnetic field allows observation of the fate of the electron as a function of time. Spin-orbit coupling rotates the spin of the electrons and yields an observable destructive interference, thereby demonstrating the change of sign of the electron-spin function by rotation. Magnetic impurities destroy the coherence of the phase. Therefore, with magnetoresistance measurements one can determine the inelastic lifetime, the spin-orbit coupling time, and the magnetic scattering time of the conduction electrons.