Time-dependent Andreev reflection

TL;DR

This paper generalizes Andreev reflection theory to include arbitrary time-dependent voltages, revealing how the current responds to short voltage pulses with oscillations at characteristic frequencies.

Contribution

It introduces a causal Fourier transform-based framework for analyzing time-dependent Andreev reflection in normal metal/superconductor junctions.

Findings

Current oscillates at the gap frequency Δ/ħ.

Current varies with the pulse area, showing quantum flux periodicity.

The theory describes coherent superpositions of quasiparticle states.

Abstract

We extend the basic theory of Andreev reflection (AR) in a normal metal/superconductor junction to the situation with an arbitrary time-dependent bias voltage $V(t)$ across the junction. The central element of the theory is the fact that the Fourier transform of the AR amplitude has a casual structure. As an example, the theory is used to describe the current response to short pulses of the bias voltage, which create coherent superposition of quasiparticle states with different energies. The current oscillates in time, with the gap frequency $\Delta/\hbar$, and also as a function of the pulse area $\int V(t)dt$, with the period of the single-electron flux quantum $e/h$.