Doubled Shapiro Steps in a Topological Josephson Junction

TL;DR

This paper investigates the transport properties of a superconductor-quantum spin Hall insulator-superconductor hybrid system under microwave radiation, revealing unique Shapiro step behaviors and fractional Josephson effects through microscopic calculations.

Contribution

It provides a microscopic Green's function analysis of Shapiro steps in a topological Josephson junction, highlighting novel step structures and fractional effects.

Findings

All Shapiro steps are visible at high frequency.

Odd Shapiro steps are suppressed at low frequency.

The I-V curves show distinct features due to multiple Andreev reflections.

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.