Current oscillations in a metallic ring threaded by a time-dependent magnetic flux

TL;DR

This paper investigates the non-equilibrium electronic dynamics in a mesoscopic metallic ring with a linearly time-varying magnetic flux, revealing regimes of stationary behavior and Bloch oscillations with measurable tunneling currents.

Contribution

It introduces a real-space Green function method for non-equilibrium analysis and identifies conditions for different dynamical regimes in the ring.

Findings

Identification of stationary and oscillatory regimes based on flux rate

Prediction of a measurable tunneling current oscillating with flux variation

Analysis of inelastic scattering effects on transport properties

Abstract

We study a mesoscopic metallic ring threaded by a magnetic flux which varies linearly in time PhiM(t)=Phi t with a formalism based in Baym-Kadanoff-Keldysh non-equilibrium Green functions. We propose a method to calculate the Green functions in real space and we consider an experimental setup to investigate the dynamics of the ring by recourse to a transport experiment. This consists in a single lead connecting the ring to a particle reservoir. We show that different dynamical regimes are attained depending on the ratio hbar Phi/Phi0 W, being Phi0=h c/e and W, the bandwidth of the ring. For moderate lengths of the ring, a stationary regime is achieved for hbar Phi/Phi0 >W. In the opposite case with hbar Phi/Phi0 < W, the effect of Bloch oscillations driven by the induced electric field manifests itself in the transport properties of the system. In particular, we show that in this time-dependent regime a tunneling current oscillating in time with a period tau=2piPhi0/Phi can be measured in the lead. We also analyze the resistive effect introduced by inelastic scattering due to the coupling to the external reservoir.