Measuring the nonlocality of different types of Majorana bound states in a topological superconducting wire

Abstract

According to the degree of topological protection, Majorana bound states (MBSs) can be divided into three types: ideal zero-energy MBSs (IZMs), finite-energy MBSs (FEMs) and zero-energy MBSs at parity crossing points (PZMs). Herein, we investigate the nonlocality of these three types of MBSs by comparing the conductance spectra of a normal lead–topological superconducting wire–normal lead (NSN) junction and an NS junction. We find that for the FEM-related tunnelling process, the decrease in the nonlocal processes is trivially accompanied by an increase in the local processes, whereas for the IZM-related tunnelling process, the left and right tunnelling processes are completely independent. Remarkably, PZMs induce a nonlocal electron-blocking effect in which incoming electrons from the left lead cannot participate in local Andreev reflection unless the right lead is present, even though no nonlocal tunnelling processes occur in the right lead of an NSN junction. We show that this PZM-mediated nonlocal electron-blocking effect is due to the nonlocal coupling of the left lead to the more distant PZM and that the phase difference between the two end PZMs is . Our findings provide an experimentally accessible method for characterizing MBSs by probing their different nonlocal signatures.