Electronic transport studies of architectures supporting Majorana fermions

Majorana zero modes that exist in hybrid semiconductor-superconductor systems in the presence of magnetic field and spin-orbit coupling have been proposed as building blocks of topological qubits. The existence of these zero modes has been confirmed by zero-bias conductance peaks on electronic transport measurements on these systems. The next goal is to realistically observe the fusion and braiding of these Majorana zero modes and look for transport characteristics of these phenomena. Here, we develop a recursive Green’s function-based technique to study electronic transport using the realistic tight-binding models of systems holding Majorana fermions. The method supports multiple orbitals, magnetic field, and spin-orbit coupling, as well as superconductivity in both leads and the system. We also study transport in a T-junction with multiple leads to understand the signatures of the exchange of the Majorana zero modes that reside in either the same or different topological regions.