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

TLDR

Conductance in metallic samples fluctuates with chemical potential, magnetic field, or impurity configuration by an amount of order e²/h, independent of size and disorder at zero temperature. The study examines how universal conductance fluctuations relate to weak and strong localization theories, the ergodic hypothesis, dimensional crossover conditions, and experimental measurement behaviors to enable quantitative theory–experiment comparisons. The authors review zero‑temperature theory and conductance correlation functions, calculate finite‑temperature effects on fluctuation amplitude and scale, and analyze dimensional crossover and experimental measurement behavior. They find that at zero temperature the fluctuation amplitude is unaffected by electron‑electron interactions to lowest order in (k_f l)⁻¹, and at finite temperature interactions influence only through the inelastic scattering rate.

Abstract

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${)}^{\mathrm{\ensuremath{-}}1}$, 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.