Modeling transport in the Coulomb blockade regime in realistic Majorana nanowires

The ability to distinguish Andreev bound states and disorder-induced zero-bias peaks is a crucial step towards the demonstration of topological quantum computation using Majorana modes. Coulomb blockade (CB) transport that has been measured in Majorana nanowires is a probe that effectively probes both ends of the wire simultaneously. Here we theoretically study the Coulomb-blockaded Majorana nanowire with all the prominent realistic effects (self-energy, quantum dot, Zeeman-field-varying superconducting gap, SC states, metallic continuum states) included. Instead of using the computationally-demanding master equation approach due to its exponentially large space of many-body probabilities, we utilize a generalization of the Meir-Wingreen formalism to calculate the conductance. We will derive the generalized Meir-Wingreen formula from the rate equations in this work. Specifically, we will focus on the strong CB limit and discuss the transport from the few-electron process, two-level case, one-level case analytically. To explain the experimental phenomena from the past experimental works, we numerically demonstrate bright-dark-bright pattern, decreasing oscillations of conductance peak spacing, and suppressed normal CB peak relative to Andreev bound states/MBSs.