Ergodic vs diffusive decoherence in mesoscopic devices

TL;DR

This paper compares phase coherence lengths in mesoscopic devices using two measurement methods, revealing different temperature dependencies due to ergodic and diffusive electron behaviors.

Contribution

It demonstrates that phase coherence length measurements via weak localization and Aharonov-Bohm oscillations yield different temperature scalings, highlighting the impact of electron trajectory regimes.

Findings

L_phi in wires scales as T^{-1/3}

L_phi in rings scales as T^{-1/2}

Different regimes reflect ergodic vs diffusive electron motion

Abstract

We report on the measurement of phase coherence length in a high mobility two-dimensional electron gas patterned in two different geometries, a wire and a ring. The phase coherence length is extracted both from the weak localization correction in long wires and from the amplitude of the Aharonov-Bohm oscillations in a single ring, in a low temperature regime when decoherence is dominated by electronic interactions. We show that these two measurements lead to different phase coherence lengths, namely $L_{\Phi}^\mathrm{wire}\propto T^{-1/3}$ and $L_{\Phi}^\mathrm{ring}\propto T^{-1/2}$. This difference reflects the fact that the electrons winding around the ring necessarily explore the whole sample (ergodic trajectories), while in a long wire the electrons lose their phase coherence before reaching the edges of the sample (diffusive regime).