Microwave spectroscopy of Majorana vortex modes

Majorana zero modes have been predicted to be hosted by vortices of certain iron-based topological superconductors. Recent observations of zero-bias conductance peaks in vortex cores of such superconductors have sparked renewed interest in vortex-bound Majorana states. 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. We study the coupling between electrons in the iron-based superconductor and the photons from a microwave resonator above the such superconductor. The frequency-dependent transmission of the resonator allows 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.