Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior

TL;DR

This paper investigates how electron interaction-induced dephasing time in disordered mesoscopic rings transitions from diffusive and ergodic regimes to zero-dimensional behavior as temperature decreases below the Thouless energy, providing detailed theoretical derivations.

Contribution

It offers a comprehensive derivation of the dephasing time crossover in mesoscopic rings, including the effects of Pauli blocking, and suggests experimental methods to observe the zero-dimensional regime.

Findings

Dephasing time exhibits distinct temperature dependencies in diffusive, ergodic, and 0D regimes.

The zero-dimensional dephasing regime influences magnetoconductivity and AAS oscillation amplitudes.

Proposes experimental filtering techniques to observe the 0D crossover in ring geometries.

Abstract

We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time $\tPh(T)$ from diffusive or ergodic 1D ($\tPh^{-1} \propto T^{2/3}, T^{1}$) to $0D$ behavior ($\tPh^{-1} \propto T^{2}$) as $T$ drops below the Thouless energy $\ETh$. We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the $0D$ regime on equal footing as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for 3D systems, has so far eluded experimental observation. We will show that for $T \ll \ETh$, $0D$ dephasing governs not only the $T$-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry holds promise of finally observing the crossover to $0D$ experimentally.