Transport properties of Majorana bound state networks in the Coulomb blockade regime

Topologically protected qubits based on nanostructures hosting Majorana bound states (MBSs) hold great promise for fault-tolerant quantum computing. We study the transport properties of nanowire networks hosting MBSs with a focus on the effects of the charging energy and the overlap between neighboring MBSs in short mesoscopic samples. In particular, we investigate structures hosting four MBSs such as T-junctions and Majorana boxes. Using a Markovian master equation, we discuss the leading transport processes mediated by the MBSs. Single-electron tunneling and a processes involving creation and annihilation of Cooper pairs dominate in the sequential tunneling limit. In the cotunneling regime, Andreev processes are suppressed due to the charging energy and transport is dominated by transitions via virtual intermediate states. Our results show that four-terminal measurements in the T-junction and Majorana box geometries can be useful tools for the characterization of the properties of MBSs with finite overlaps and charging energy.