On the relationship between the noise-induced persistent current and dephasing rate

TL;DR

This paper establishes a simple, universal relationship between noise-induced persistent current and dephasing rate in disordered conductors, linking two longstanding puzzles in mesoscopic physics.

Contribution

It demonstrates a direct proportionality between the ensemble-averaged persistent current and the dephasing rate caused by high-frequency AC noise, depending on the symmetry class.

Findings

The flux harmonic and dephasing rate are related by <I> tau_{}=C e.

The constant C varies with symmetry class: diamagnetic for potential disorder, paramagnetic with spin-orbit.

The relationship aligns with experimental observations, suggesting a common solution to persistent current and dephasing puzzles.

Abstract

AC noise in disordered conductors causes both dephasing of the electron wave functions and a DC current around a mesoscopic ring. We demonstrate that the dephasing rate tau_{\phi}^{-1} in long wires and the DC current, induced by the same noise and averaged over an ensemble of small rings are connected. The ensemble-averaged h/2e flux harmonic <I> of the current and the dephasing rate caused by the same uniform in space high frequency AC field are related in a remarkably simple way: <I> tau_{\phi}=C e. Here e is an electron charge, and the constant C depends on the Dyson symmetry class. For a pure potential disorder the current <I> is diamagnetic C = -(4/\pi) and in the presence of strong spin-orbit scattering it is paramagnetic C =(2/\pi). The relationship seems to agree reasonably with experiments. This suggests that the two puzzles: anomalously large persistent current [L.P.Levy et al., Phys.Rev.Lett., v.64, 2074 (1990)] and the low-temperature saturation of the dephasing [P.Mohanty et al., Phys.Rev.Lett., v.78, 3366 (1997)] may have a common solution.