Master equation approach for transport through Majorana zero modes

Abstract

Based on an exact formulation, we present a master equation approach to transport through Majorana zero modes (MZMs). Within the master equation treatment, the occupation dynamics of the regular fermion associated with the MZMs holds a quite different picture from the Bogoliubov–de Gennes (BdG) S-matrix scattering process, in which the ‘positive’ and ‘negative’ energy states are employed, while the master equation treatment does not involve them at all. Via careful analysis for the structure of the rates and the rate processes governed by the master equation, we reveal the intrinsic connection between both approaches. This connection enables us to better understand the confusing issue of teleportation when the Majorana coupling vanishes. We illustrate the behaviors of transient rates, occupation dynamics and currents. Through the bias voltage dependence, we also show the Markovian condition for the rates, which can extremely simplify the applications in practice. As future perspective, the master equation approach developed in this work can be applied to study important time-dependent phenomena such as photon-assisted tunneling through the MZMs and modulation effect of the Majorana coupling energy.