Closing the proximity gap in a metallic Josephson junction between three superconductors

TL;DR

This paper investigates the proximity effect in a three-superconductor metallic junction, revealing how Andreev bound state crossings lead to a gap closing, with implications for tunneling spectroscopy and junction transparency.

Contribution

It provides a detailed analysis of the proximity-induced gap closing in a three-terminal superconducting junction, including analytical expressions and numerical results for various parameters.

Findings

The gap closes within a specific phase difference region.

The size of the gap-closing area depends on junction transparency and asymmetry.

Zero-energy density of states remains unaffected by electron-hole decoherence.

Abstract

We describe the proximity effect in a short disordered metallic junction between three superconducting leads. Andreev bound states in the multi-terminal junction may cross the Fermi level. We reveal that for a quasi-continuous metallic density of states, crossings at the Fermi level manifest as closing of the proximity-induced gap. We calculate the local density of states for a wide range of transport parameters using quantum circuit theory. The gap closes inside an area of the space spanned by the superconducting phase differences. We derive an approximate analytic expression for the boundary of the area and compare it to the full numerical solution. The size of the area increases with the transparency of the junction and is sensitive to asymmetry. The finite density of states at zero energy is unaffected by electron-hole decoherence present in the junction, although decoherence is important at higher energies. Our predictions can be tested using tunneling transport spectroscopy. To encourage experiments, we calculate the current-voltage characteristic in a typical measurement setup. We show how the structure of the local density of states can be mapped out from the measurement.