Distinguishing topological Majorana zero modes: non-local conductance versus the von Neumann entropy

The topological origin of the zero bias conductance signatures of Majorana zero modes has been a topic of intense debate. We propose to differentiate between true Majorana bound states and trivial Andreev bound states using the von Neumann entanglement entropy. The topological von Neumann entropy provides a distinct signature of non-local correlations of topological origin. We also establish its connection with recently proposed ideas on the lines of the non-local conductance spectra in a three-terminal normal-topological superconductor-normal hybrid system. We show that both entanglement entropy and non-local conductance exhibit a clear topological phase transition signature for long enough system sizes. However, we observe that the non-local conductance fails to signal a topological phase transition for small system sizes. Moreover, we demonstrate the robustness of entanglement entropy to system parameters as well as its size, establishing it as an ideal metric for distinguishing topological phases.

[1] A. Kejriwal and B. Muralidharan, ArXiv:2112.02235, (2021).