# Landauer Formula for a Superconducting Quantum Point Contact

## TL;DR

This paper extends the Landauer formula to account for dissipative electron transport in superconducting quantum point contacts, providing a unified framework that also applies to hybrid structures and normal contacts.

## Contribution

The authors derive a generalized Landauer formula incorporating phase- and energy-dependent scattering matrices for superconducting point contacts, unifying various transport regimes.

## Key findings

- The formula accurately describes finite-temperature, linear-in-bias conductance.
- It reduces to known limits for Andreev reflection and normal conductance.
- Applicable to hybrid superconducting-normal structures.

## Abstract

We generalize the Landauer formula to describe the dissipative electron transport through a superconducting point contact. The finite-temperature, linear-in-bias, dissipative DC conductance is expressed in terms of the phase- and energy-dependent scattering matrix of the Bogoliubov quasiparticles in the quantum point contact. The derived formula is also applicable to hybrid superconducting-normal structures and normal contacts, where it agrees with the known limits of Andreev reflection and normal-state conductance, respectively.