Microwave spectroscopy of Majorana vortex modes

The observation of zero-bias conductance peaks in vortex cores of certain Fe-based superconductors has sparked renewed interest in vortex-bound Majorana states. These materials are believed to be intrinsically topological in their bulk phase, thus avoiding potentially problematic interface physics encountered in superconductor-semiconductor heterostructures. However, progress toward a vortex-based topological qubit is hindered by our inability to measure the topological quantum state of a non-local vortex Majorana state, i.e., the charge of a vortex pair. In this paper, we theoretically propose a microwave-based charge parity readout of the Majorana vortex pair charge. A microwave resonator above the vortices can couple to the charge allowing for a dispersive readout of the Majorana parity. Our technique may also be used in vortices in conventional superconductors and allows one to probe the lifetime of vortex-bound quasiparticles, which is currently beyond existing scanning tunneling microscopy capabilities.