Doubled Shapiro steps in a topological Josephson junction

Abstract

We study the transport properties of a superconductor–quantum spin Hall insulator–superconductor hybrid system in the presence of microwave radiation. Instead of adiabatic analysis or use of the resistively shunted junction model, we start from the microscopic Hamiltonian and calculate the d.c. current directly with the help of the nonequilibrium Green's function method. The numerical results show that (i) the I-V curves of background current due to multiple Andreev reflections exhibit a different structure from those in the conventional junctions, and (ii) all Shapiro steps are visible and appear one by one at high frequencies, while at low frequencies, the steps evolve exactly as the Bessel functions and the odd steps are completely suppressed, implying a fractional Josephson effect.

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