Current aspects of topological superconductivity

Recent experiments have provided mounting evidence for the existence of Majorana
bound states (MBSs) in condensed-matter systems. Until the long-term goal of braiding MBSs is
achieved, one is prompted to ask: what is the next step in the study of topological
superconductivity and MBSs? In my talk I will discuss two topics relating to this question. In the
first part I will examine the possibility of, not only detecting the Majoranas, but also witnessing
some of their exotic properties. In particular their non-local nature, or in other words, the fact that
the MBS is half a fermion whose occupation is encoded in a nonlocal way. I will show that current
cross correlations in a T-junction with a single MBS exhibit universal features, related to the
Majorana nonlocality. This will be contrasted with the case of an accidental low-energy Andreev
bound state. In the second part I will discuss the possibility of realizing a different topological
phase hosting MBSs in currently available experimental platforms. This will be a topological
superconducting phase which is protected by time-reversal symmetry, and which is characterized
by having a Kramers’ pair of MBSs at each end. As I will discuss, repulsive interactions are a
necessary ingredient for the realization of this phase. I will present a mechanism, based on the
interplay between repulsive interactions and proximity to a conventional superconductor, which
drives the system into the topological phase. The effect of interactions is studied analytically using
both a mean-field approach and the renormalization group. We corroborate our conclusions
numerically using DMRG.