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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 five-dimensional space of superconducting phases, crossings of Andreev bands may support the 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 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.
We study the Josephson effect in the multiterminal junction of topological superconductors. We use the symmetry-constrained scattering matrix approach to derive band dispersions of emergent sub-gap Andreev bound states in a multidimensional parameter
Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin $2(hbar/2)$. In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and b
We consider a diffusive S-N-S junction with electrons in the normal layer driven out of equilibrium by external bias. We show that, the non-equilibrium fluctuations of the electron density in the normal layer cause the fluctuations of the phase of th
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 scat
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the norm