Current noises in a topological Josephson junction

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor Josephson junction both in the absence and in the presence of a DC bias voltage. As the system is predicted to host Majorana fermions at its interfaces,the Andreev bond states are supposed to exhibit a distinct 4π periodicity in the superconducting phase difference, namely the fractional Josephson effect. Using the non-equilibrium Green's function method, we calculate the current and the related current noise based on a tight-binding Hamiltonian. Our direct results show that the fractional Josephson effect can not be seen in equilibrium junctions. While in non-equilibrium junctions, this effect can be confirmed by the multiple Andreev reflections induced peaks of the non-equilibrium noise, which appear at discrete frequencies ω = ne V with n being an integer number.