Detecting Majorana modes through Josephson junction ring-quantum dot hybrid architectures

Unequivocal signatures of Majorana zero energy modes in condensed matter systems and manipulation of the associated electron parity states are highly sought after for fundamental reasons as well as for the prospect of topological quantum computing. In this Letter, we demonstrate that a ring of Josephson coupled topological superconducting islands threaded by magnetic flux and attached to a quantum dot acts as an excellent parity-controlled probe of Majorana mode physics. As a function of flux threading through the ring, standard Josephson coupling yields a ${\mathrm{\Phi }}_0=h\mathrm{/}(2e)$ periodic features corresponding to $2\pi$ phase difference periodicity. In contrast, Majorana mode assisted tunneling provides additional features with $2{\mathrm{\Phi }}_0$ ($4\pi$ phase difference) periodicity, associated with single electron processes. We find that increasing the number of islands in the ring enhances the visibility of the desired $4\pi$ periodic components in the groundstate energy. Moreover as a unique characterization tool, tuning the occupation energy of the quantum dot allows controlled groundstate parity changes in the ring, enabling a toggling between ${\mathrm{\Phi }}_0$ and $2{\mathrm{\Phi }}_0$ periodicity.