Electrical detection of topological quantum phase transitions in disordered Majorana nanowires

Abstract

We study a disordered superconducting nanowire, with broken time-reversal and spin-rotational symmetry, which can be driven into a topological phase with end Majorana bound states by an externally applied magnetic field. As a function of disorder strength, it is known that the Majorana nanowire has a delocalization quantum phase transition from a topologically nontrivial phase, which supports Majorana bound states, to a nontopological insulating phase without them. On both sides of the transition, the system is localized at zero energy albeit with very different topological properties. We exploit this deep connection between topology and localization properties to propose an electrical transport measurement to detect the localization-delocalization transition occurring in the bulk of the nanowire. The basic idea consists of measuring the difference of conductance at one end of the wire obtained at different values of the coupling to the opposite lead. We show that this measurement reveals the nonlocal correlations emergent only at the topological transition. Hence, while the proposed experiment does not directly probe the end Majorana bound states, it can provide direct evidence for the bulk topological quantum phase transition itself.