Can non-local conductance spectra conclusively signal Majorana zero modes? -- Insights from von Neumann entropy

The topological origin of the zero bias conductance signatures obtained via conductance spectroscopy in topological superconductor hybrid systems is a much contended issue. Recently, non-local conductance signatures that exploit the non-locality of the zero modes in three terminal hybrid setups have been proposed as means to ascertain the definitive presence of Majorana modes. The topological entanglement entropy, which is based on the von Neumann entropy, is yet another way to gauge the non-locality in connection with the bulk-boundary correspondence of a topological phase. We show that while both the entanglement entropy and the non-local conductance exhibit a clear topological phase transition signature for long enough pristine nanowires, non-local conductance fails to signal a topological phase transition for shorter disordered wires. While recent experiments have indeed shown premature gap-closure signatures in the non-local conductance spectra, we believe that the entanglement entropy can indeed signal a genuine transition, regardless of the constituent non-idealities in an experimental situation. Our results thereby point toward furthering the development of experimental techniques beyond conductance measurements to achieve a conclusive detection of Majorana zero modes.