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