Fano effect in Aharonov-Bohm ring with topologically superconducting bridge

Taking into account an inner structure of the arms of the Aharonov-Bohm ring (AB ring) we have analyzed the transport features related to the topological phase transition which is induced in a superconducting wire (SC wire) with strong spin-orbit interaction (SOI). The SC wire acts as a bridge connecting the arms. The in-plane magnetic-field dependence of linear-response conductance obtained using the nonequilibrium Green's functions in the tight-binding approximation revealed the Breit-Wigner and Fano resonances (FRs) if the wire is in the nontrivial phase. The effect is explained by the presence of two interacting transport channels in the system. As a result, the FRs are attributed to bound states in continuum (BSCs). The BSC lifetime is determined by both hopping parameters between subsystems and the SC-wire properties. It is established that the FR width and position are extremely sensitive to the type of the lowest-energy excitation in the SC wire, the Majorana or Andreev bound state (MBS or ABS, respectively). Moreover, it is shown that in the specific case of the AB ring, the T-shape geometry, the FR disappears for the transport via the MBS and the conductance is equal to one quantum. It doubles in the local transport regime. On the contrary, in the ABS case the local conductance vanishes. The influence of the mean-field Coulomb interactions and diagonal disorder in the SC wire on the FR is investigated.