Transport properties of a quantum dot-mediated fractional Josephson junction

We consider a model of a Josephson junction mediated by a quantum dot. An additional normal electrode coupled to the dot allows its density of states to be probed. The junction is made out of two topological superconducting wires with Majorana end states. The two of them, on each side and in the proximity of the junction, convert into a Dirac fermion inside the dot. It is shown that both the density of states of the dot and the phase-biased current through the junction can exhibit [Formula: see text] periodicity in the superconducting phase difference, when the particle-hole symmetry of the junction is broken. It is realized by detuning of the dot level from the Fermi level by the gate voltage. The width of zero-bias peak in differential conductance, produced by an unpaired Majorana state, also possesses [Formula: see text] periodicity under this condition.