Universal transport signatures of the topological phase transition in Majorana wires

Detecting the predicted magnetic-field-driven topological phase transition in proximitized nanowires is a key problem in the ongoing quest for unambiguous signatures of Majorana zero modes. We investigate the transport properties of a junction between a Luttinger liquid lead and a proximitized nanowire held at the topological phase transition. Upon fine-tuning a single parameter at the interface, the junction can realize a novel nontrivial fixed point at which electrons in the lead split into two propagating Majorana fermions, one that perfectly transmits into the critical nanowire and one that reflects. We introduce a bosonized framework for this fixed point and extract universal conductance signatures of the topological phase transition. We also comment on applications to tunneling into the edge of a two-dimensional topological superconductor.