Interplay of disorder and interaction in 1D topological superconductors
It is well known that both disorder and interaction have non-perturbative effects on the physical properties of one-dimensional conductors. Separate treatments of these two effects do not capture the physics in many situations, and the interplay between disorder and interaction often leads to a number of novel features. In this seminar, I will talk about our recent work on topological 1D superconductors, where we address the combined effects of interaction and disorder, considering them on the same footing. We show that the topological phase hosting Majorana is stable against weak disorder and interactions. We obtain the phase diagram of the system and compute the phase boundary between topological SC phase and the competing pinned charge density wave. Our analytical results provide concrete information about the regime of parameters where a 1D topological superconductor is expected to survive the detrimental effects of interaction and disorder, and is relevant to realistic semiconductor/superconductor heterostructures, where zero-energy Majorana states are being intensively investigated.