Combinatorics

Physics

Topology (electrical circuits)

Symmetry (geometry)

Mathematics

Matrix (chemical analysis)

Josephson effect

Composite material

Berry connection and curvature

Mesoscopic physics

Andreev reflection

Scattering

Materials science

Geometry

Condensed matter physics

Superconductivity

Quantum mechanics

Quantum

Physical review. B./Physical review. B

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 the 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 also be identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.

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