# Andreev rectifier: a nonlocal conductance signature of topological phase transitions

## TL;DR

This paper demonstrates how nonlocal conductance measurements can reliably identify topological phase transitions and Majorana modes in superconductor-semiconductor systems, providing a robust tool against local defects and inhomogeneities.

## Contribution

It introduces a method using nonlocal conductance to distinguish topological Majorana modes from trivial zero-energy states and identifies the odd bias dependence as a signature of topological transitions.

## Key findings

- Nonlocal conductance probes bulk and induced gaps effectively.
- Nonlocal conductance distinguishes Majorana modes from trivial states.
- The odd bias dependence signals the topological phase transition.

## Abstract

The proximity effect in hybrid superconductor-semiconductor structures, crucial for realizing Majorana edge modes, is complicated to control due to its dependence on many unknown microscopic parameters. In addition, defects can spoil the induced superconductivity locally in the proximitised system which complicates measuring global properties with a local probe. We show how to use the nonlocal conductance between two spatially separated leads to probe three global properties of a proximitised system: the bulk superconducting gap, the induced gap, and the induced coherence length. Unlike local conductance spectroscopy, nonlocal conductance measurements distinguish between non-topological zero-energy modes localized around potential inhomogeneities, and true Majorana edge modes that emerge in the topological phase. In addition, we find that the nonlocal conductance is an odd function of bias at the topological phase transition, acting as a current rectifier in the low-bias limit. More generally, we identify conditions for crossed Andreev reflection to dominate the nonlocal conductance and show how to design a Cooper pair splitter in the open regime.