Nonequilibrium mesoscopic conductance fluctuations

TL;DR

This paper studies how mesoscopic conductance fluctuations in a metallic wire vary with bias voltage, revealing a crossover from universal behavior to a high-voltage regime influenced by electron interactions and dephasing effects.

Contribution

It provides a detailed analysis of conductance fluctuation behavior at arbitrary voltages, including the effects of electron-electron interactions and dephasing, extending previous theoretical predictions.

Findings

Variance increases with voltage, approaching a large-V asymptote.

Crossover regime occurs at V/V_c  30, with a threefold increase in fluctuations.

Electron-electron interactions cause the fluctuations to decrease as 1/V at high voltages.

Abstract

We investigate the amplitude of mesoscopic fluctuations of the differential conductance of a metallic wire at arbitrary bias voltage V. For non-interacting electrons, the variance <delta g^2> increases with V. The asymptotic large-V behavior is <delta g^2> \sim V/V_c (where eV_c=D/L^2 is the Thouless energy), in agreement with the earlier prediction by Larkin and Khmelnitskii. We find, however, that this asymptotics has a very small numerical prefactor and sets in at very large V/V_c only, which strongly complicates its experimental observation. This high-voltage behavior is preceded by a crossover regime, V/V_c \lesssim 30, where the conductance variance increases by a factor \sim 3 as compared to its value in the regime of universal conductance fluctuations (i.e., at V->0). We further analyze the effect of dephasing due to the electron-electron scattering on <delta g^2> at high voltages. With the Coulomb interaction taken into account, the amplitude of conductance fluctuations becomes a non-monotonic function of V. Specifically, <delta g^2> drops as 1/V for voltages V >> gV_c, where g is the dimensionless conductance. In this regime, the conductance fluctuations are dominated by quantum-coherent regions of the wire adjacent to the reservoirs.