Circuit theory of crossed Andreev reflection

TL;DR

This paper analyzes nonlocal conductance in a three-terminal mesoscopic device using circuit theory, focusing on the roles of crossed Andreev reflection and electron cotunneling, and how they depend on system parameters like resistance and Thouless energy.

Contribution

It provides a detailed theoretical framework for separating and quantifying crossed Andreev reflection and electron cotunneling contributions in mesoscopic superconducting devices.

Findings

Nonlocal conductance vanishes without resistance between device and superconductor.

Electron cotunneling dominates when resistance is finite.

Conductance depends strongly on the Thouless energy.

Abstract

We consider transport in a three terminal device attached to one superconducting and two normal metal terminals, using the circuit theory of mesoscopic superconductivity. We compute the nonlocal conductance of the current out of the first normal metal terminal in response to a bias voltage between the second normal metal terminal and the superconducting terminal. The nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance between the superconducting terminal and the device, in agreement with previous theoretical work. Electron cotunneling dominates when there is a finite resistance between the device and the superconducting reservoir. Decoherence is taken into account, and the characteristic timescale is the particle dwell time. This gives rise to an effective Thouless energy. Both the conductance due to crossed Andreev reflection and electron cotunneling depend strongly on the Thouless energy. We suggest to experimentally determine independently the conductance due to crossed Andreev reflection and electron cotunneling in measurement of both energy and charge flow into one normal metal terminal in response to a bias voltage between the other normal metal terminal and the superconductor.