Ergodic versus diffusive decoherence in mesoscopic devices

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 ${L}_{\ensuremath{\Phi}}^{\mathrm{wire}}\ensuremath{\propto}{T}^{\ensuremath{-}1/3}$ and ${L}_{\ensuremath{\Phi}}^{\mathrm{ring}}\ensuremath{\propto}{T}^{\ensuremath{-}1/2}$. 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).