# Supercurrent Interference in Semiconductor Nanowire Josephson Junctions

## TL;DR

This paper models quantum transport in semiconductor nanowire Josephson junctions, revealing that critical current oscillations are interference effects of transverse sub-bands, influenced by disorder and phase-breaking processes, aligning with experimental observations.

## Contribution

It introduces a detailed theoretical model of III-V semiconductor nanowire Josephson junctions, incorporating disorder and dephasing to explain critical current oscillations observed experimentally.

## Key findings

- Critical current oscillations are interference effects of transverse sub-bands.
- Disorder and gate voltage significantly affect oscillation patterns.
- Phase-breaking processes are essential to match experimental data.

## Abstract

Semiconductor-superconductor hybrid systems provide a promising platform for hosting unpaired Majorana fermions towards the realisation of fault-tolerant topological quantum computing. In this study, we employ the Keldysh Non-Equilibrium Green's function formalism to model quantum transport in normal-superconductor junctions. We analyze III-V semiconductor nanowire Josephson junctions (InAs/Nb) using a three-dimensional discrete lattice model described by the Bogolubov-de Gennes Hamiltonian in the tight-binding approximation, and compute the Andreev bound state spectrum and current-phase relations. Recent experiments [Zuo et al., Phys. Rev. Lett. 119,187704 (2017)] and [Gharavi et al., arXiv:1405.7455v2 (2014)] reveal critical current oscillations in these devices, and our simulations confirm these to be an interference effect of the transverse sub-bands in the nanowire. We add disorder to model coherent scattering and study its effect on the critical current oscillations, with an aim to gain a thorough understanding of the experiments. The oscillations in the disordered junction are highly sensitive to the particular realisation of the random disorder potential, and to the gate voltage. A macroscopic current measurement thus gives us information about the microscopic profile of the junction. Finally, we study dephasing in the channel by including elastic phase-breaking interactions. The oscillations thus obtained are in good qualitative agreement with the experimental data, and this signifies the essential role of phase-breaking processes in III-V semiconductor nanowire Josephson junctions.