Disconnected entanglement entropy and fermion parity noise for the conclusive electrical detection of Majorana zero modes

Rashba nanowire-superconductor hybrids are under intense scrutiny with respect to the conclusive sighting of Majorana zero modes (MZM). Protocols for their conclusive detection based on local and non-local conductance signatures have been subject to intense scrutiny and altercations [1]. We extend the idea of topological entanglement entropy [2,3] to faithfully distinguish between true MZMs and trivial Quasi-MZMs in a Rashba nanowire setup. We demonstrate that the disconnected entanglement entropy, derived from the von Neumann entanglement entropy, provides a distinct and robust signature of the topological phase transition which is immune to system parameters, size and disorders. In order to understand the entanglement entropy of the Rashba nanowire system, we establish its connection to a model of interacting spinfull Kitaev chains. Moreover, we relate the entanglement entropy to a physical observable of the system — the fermion parity noise [4], and show that it behaves concordantly with entanglement entropy, hence nominating it as a suitable metric for the detection of MZMs. We comment on possible transport signatures beyond the conductance spectra for possibly connecting this construct to actual measurements.

[1] H. Pan and S. Das Sarma, Phys. Rev. Research 2, 013377 (2020).

[2] A. Kejriwal and B. Muralidharan, Phys. Rev. B 105, L161403 (2022).

[3] S. Ryu and Y. Hatsugai, Phys. Rev. B 73, 245115 (2006).

[4] K. Pöyhönen, A. Moghaddam, and T. Ojanen, Phys. Rev. Research 4, 023200 (2022).