# Transport properties of an electron-hole bilayer/superconductor hybrid junction

## TL;DR

This paper studies how electron-hole bilayer systems in contact with superconductors conduct electricity, revealing a conductance minimum at voltages related to the excitonic gap, indicating the presence of an exciton condensate.

## Contribution

It introduces a model for transport in electron-hole bilayer/superconductor hybrids, highlighting the role of Andreev and crossed reflections and identifying conductance signatures of exciton condensation.

## Key findings

- Differential conductance shows a minimum at voltages around the excitonic gap.
- Transport is governed by Andreev and coherent crossed reflections.
- The conductance minimum indicates the presence of an exciton condensate.

## Abstract

We investigate the transport properties of a junction consisting of an electron-hole bilayer in contact with normal and superconducting leads. The electron-hole bilayer is considered as a semi-metal with two electronic bands. We assume that in the region between the contacts the system hosts an exciton condensate described by a BCS-like model with a gap $\Gamma$ in the quasiparticle density of states. We first discuss how the subgap electronic transport through the junction is mainly governed by the interplay between two kinds of reflection processes at the interfaces: The standard Andreev reflection at the interface between the superconductor and the exciton condensate, and a coherent crossed reflection at the semi-metal/exciton-condensate interface that converts electrons from one layer into the other. We show that the differential conductance of the junction shows a minimum at voltages of the order of $\Gamma/e$. Such a minimum can be seen as a direct hallmark of the existence of the gapped excitonic state.