Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances and supercurrents

TL;DR

This paper explores the topological properties of Andreev spectra in four-terminal Josephson junctions, revealing Weyl nodes, Chern numbers, and quantized conductance, with implications for experimental control of supercurrents.

Contribution

It provides an analytical framework for identifying Weyl nodes and topological features in multiterminal Josephson junctions, linking them to measurable conductance and supercurrent behaviors.

Findings

Weyl nodes act as monopoles of Berry curvature in Andreev spectra.

Chern numbers determine quantized nonlocal conductance.

Supercurrent phase relationships show nonanalytic behavior near Weyl points.

Abstract

We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The corresponding fluxes are quantified by Chern numbers that translate into a quantized nonlocal conductance that we compute explicitly for the time-reversal-symmetric scattering matrix. The topological regime can be also identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.