Doubled Shapiro Steps in a Topological Josephson Junction

Abstract

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

5 pages, 3 figures

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• Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions
• Anomalous photon-assisted tunneling in periodically driven Majorana nanowires and BCS Charge Measurement
• Edge supercurrent in Josephson junctions based on topological materials
• A particle conserving approach to AC-DC driven interacting quantum dots with superconducting leads
• Transport theory for topological Josephson junctions with a Majorana qubit
• Numerical analysis of Josephson junction arrays for multi-order quantum voltage steps
• Ubiquitous missing first Shapiro step in Al-InSb nanosheet Josephson junctions
• Josephson effects in the spin-triplet superconductor/altermagnet/spin-triplet superconductor junctions: the detection of the intrinsic $\mathbf{d}$-vector
• Fractional spin Josephson effect in topological spin superconductors