Effect of topological length on bound state signatures in a topological nanowire

Majorana bound states (MBSs) at the end of nanowires have been proposed as one of the most important candidates for topological qubits. However, similar tunneling conductance features for both the MBSs and Andreev bound states have turned out to be a major obstacle in the verification of the presence of MBSs in semiconductor-superconductor heterostructures. In this article, we use a protocol to probe properties specific to the MBSs and use it to distinguish the topological zero-bias peak (ZBP) from a trivial one. For a scenario involving a quantized ZBP in the nanowire, we propose a scheme wherein the length of the topological region in the wire is altered. The tunneling conductance signatures can then be utilized to gauge the impact on the energy of the low-energy states. We show that the topological and trivial ZBPs behave differently under our protocol; in particular, the topological ZBP remains robust at zero bias throughout the protocol, while the trivial ZBP splits into two peaks at finite bias. This protocol probes the protection of near-zero-energy states due to their separable nature, allowing us to distinguish between topological and trivial ZBP.