Josephson-Current Signatures of Unpaired Floquet Majorana Fermions

We theoretically study the transport signatures of unpaired Floquet Majorana fermions in the Josephson current of weakly linked, periodically driven topological superconductors. We obtain analytical expressions for the occupation of the Floquet Majorana fermions in the presence of weak coupling to thermal reservoirs, and show that, similar to undriven topological superconductors, for sufficiently low temperatures and large systems the Josephson current involving Floquet Majorana fermions is 4π-periodic in the phase difference across the junction and depends linearly on the coupling between superconductors. Moreover, unlike the static case, the amplitude of the Josephson current can be tuned by setting the unbiased chemical potential of the driven superconductors at multiple harmonics of the drive frequency. As a result, we uncover a "Josephson Floquet sum rule" for driven superconductors. We confirm our analytical expressions for Josephson current, the occupation of Floquet bands, and a perturbative analysis of the quasienergies with numerically exact results.