Andreev Level Spectroscopy and Josephson Current Switching in a 3-Terminal Josephson Junction

TL;DR

This paper investigates how a normal metal probe can control and spectroscopically analyze the Josephson current in a three-terminal superconductor-insulator-superconductor junction by tuning Andreev energy levels.

Contribution

It introduces a method to control Josephson current via a normal metal probe and provides detailed analysis of Andreev level spectroscopy in three-terminal junctions.

Findings

Josephson current switches abruptly at certain probe voltages.

Spectroscopy of Andreev levels is possible through differential conductance.

Switching behavior varies between short and long junctions.

Abstract

We calculate the electrical currents through a superconductor - insulator - superconductor junction which is also weakly coupled to a normal metal side probe. The voltage $V$ applied to the normal metal terminal controls the occupation of Andreev energy levels $E_n$, and therefore controls the Josephson current flowing through these levels. Whenever the probe voltage crosses an Andreev level, the Josephson current changes abruptly by an amount equal to the current flowing through the Andreev level. The differential conductance along the normal metal terminal permits spectroscopy of the Andreev levels. In a short junction $(L \ll \xi_0)$, the critical current switches abruptly from the Ambegaokar-Baratoff value to zero when the probe voltage is approximately equal to the superconducting energy gap ($|eV| \simeq \Delta$). The magnitude of the Josephson current switching in a long junction $(L \gg \xi_0)$, and the range of probe voltages over which the Josephson current differs from its equilibrium value, are much smaller than for three-terminal ballistic superconductor - normal metal - superconductor junctions.