Universal conductance fluctuations in metals: Effects of finite temperature, interactions, and magnetic field

The conductance of any metallic sample has been shown to fluctuate as a function of chemical potential, magnetic field, or impurity configuration by an amount of order $e^2$/h independent of sample size and degree of disorder at zero temperature. We discuss the relationship of these results to other results in the theory of weak and strong localization, and discuss its physical implications. We discuss the physical assumptions underlying the ergodic hypothesis used to relate theory to experiment. We review the zero-temperature theory and provide a detailed discussion of the conductance correlation functions in magnetic field and Fermi energy. We show that the zero-temperature amplitude of the fluctuations is unaffected by electron-electron interactions to lowest order in ($k_f$l${)}^{\mathrm{-}1}$, and at finite temperature interactions only enter insofar as they contribute to the inelastic scattering rate. We calculate the effects of finite temperature on both the amplitude of the fluctuations and their scale. We discuss the conditions for dimensional crossover at finite temperature, and the behavior of different experimental measures of the fluctuation amplitude, in order to facilitate quantitative comparisons of experiment and theory.