Non-Abelian monopoles in the multiterminal Josephson effect

In this Letter 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.