# Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges

## TL;DR

This paper presents a theoretical analysis of a three-terminal conductance setup to probe Andreev bound states, revealing symmetry relations and methods to extract BCS charges, including those of Majorana states.

## Contribution

It introduces a comprehensive theoretical framework for analyzing three-terminal conductance, highlighting symmetry relations and a novel way to determine BCS charges of bound states.

## Key findings

- Local and nonlocal conductance elements have identical antisymmetric parts.
- Nonlocal conductance relates directly to BCS charges of bound states.
- Method to experimentally extract BCS charge of overlapping Majorana states.

## Abstract

Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.