# Cross-correlated shot noise in three-terminal superconducting hybrid nanostructures

## TL;DR

This paper develops a unified theory for non-local electron transport and cross-correlated shot noise in three-terminal NSN nanostructures, revealing complex behaviors including positive and negative correlations depending on bias voltages.

## Contribution

It provides a comprehensive theoretical framework for understanding shot noise and non-local transport in NSN structures, including diffusive contacts and bias-dependent correlations.

## Key findings

- Non-local shot noise can be positive or negative depending on bias.
- Derived an analytical expression for cross-correlated noise with accessible parameters.
- Demonstrated complex behavior of shot noise in diffusive NS contacts.

## Abstract

We work out a unified theory describing both non-local electron transport and cross-correlated shot noise in a three-terminal normal-superconducting-normal (NSN) hybrid nanostructure. We describe noise cross correlations both for subgap and overgap bias voltages and for arbitrary distribution of channel transmissions in NS contacts. We specifically address a physically important situation of diffusive contacts and demonstrate a non-trivial behavior of non-local shot noise exhibiting both positive and negative cross correlations depending on the bias voltages. For this case, we derive a relatively simple analytical expression for cross-correlated noise power which contains only experimentally accessible parameters.