# Tunable pseudogaps due to non-local coherent transport in voltage-biased three-terminal Josephson junctions

## TL;DR

This paper explores how non-local coherent transport in three-terminal Josephson junctions under voltage bias induces tunable pseudogaps and complex structures in the density of states, revealing new proximity effects beyond two-terminal systems.

## Contribution

It demonstrates the existence of highly tunable pseudogaps caused by non-local processes in three-terminal junctions, a phenomenon absent in two-terminal systems, and analyzes their dependence on various parameters.

## Key findings

- Presence of deep, tunable pseudogaps in the density of states.
- Identification of non-local coherent transport effects absent in two-terminal junctions.
- Similarity of multiple Andreev reflection signatures to two-terminal cases.

## Abstract

We investigate the proximity effect in junctions between $N=3$ superconductors under commensurate voltage bias. The bias is chosen to highlight the role of transport processes that exchange multiple Cooper pairs coherently between more than two superconductors. Such non-local processes can be studied in the dc response, where local transport processes do not contribute. We focus on the proximity-induced normal density of states that we investigate in a wide parameter space. We reveal the presence of deep and highly tunable pseudogaps and other rich structures. These are due to a static proximity effect that is absent for $N=2$ and is sensitive to an emergent superconducting phase associated to non-local coherent transport. In comparison with results for $N=2$, we find similarities in the signature peaks of multiple Andreev reflections. We discuss the effect of electron-hole decoherence and of various types of junction asymmetries. Our predictions can be investigated experimentally using tunneling spectroscopy.