  In this work we present a detailed theoretical analysis for the spectral
properties of Andreev bound states in the multiterminal Josephson junctions by
employing a symmetry-constrained scattering matrix approach. We find that in
the synthetic multidimensional space of superconducting phases, crossings of
Andreev bands may support non-Abelian SU(2) monopoles with a topological charge
characterized by the second class Chern number. We propose that these
topological defects can be detected via a nonlinear response measurement of the
current autocorrelations. In addition, multiterminal Josephson junction devices
can be tested as a hardware platform for realizing holonomic quantum
computation.
