Semiconductor nanowire-superconductor hybrid systems provide a promising platform for hosting Majorana zero modes. However, the conclusive experimental detection of these exotic modes is a much debated and contentious issue. In this talk, we will describe conductance spectroscopy measurements and the current experimental status on their detection. Starting from the basics of quantum transport theory, we will demonstrate how to adapt the Keldysh non-equilibrium Green’s function (NEGF) technique to model experimentally relevant and current device structures [1-3]. We will then describe various “false positives” associated with conductance spectroscopy on realistic device structures, and how we could capture these effects using quantum transport theory. Moving on, we will describe the non-locality of true Majorana modes can be described via the concept of topological entanglement entropy , which connects directly with the bulk-boundary correspondence of a topological phase . While recent experiments have indeed shown several false positives in the conductance spectra, we demonstrate that the entanglement entropy can indeed signal a genuine transition, regardless of the constituent non-idealities in an experimental situation. Our results point toward furthering the development of experimental techniques beyond conductance measurements to achieve a conclusive sighting of Majorana zero modes.
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