Signatures of a 4π -periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions

We investigate theoretical aspects of the detection of Majorana bound states in Josephson junctions using the semiclassical resistively capacitively shunted junction (RCSJ) model of junction dynamics. The influence of a 4π-periodic supercurrent contribution can be detected through its effect on the width of the Shapiro steps and the Fourier spectrum of the voltage signal. We explain how the inclusion of a capacitance term results in a strong quenching of the first step when the junction is underdamped, while the higher odd steps are less affected. Remarkably, this feature has been observed experimentally. We examine the emission spectrum of phase-locked solutions, showing that the presence of period doubling may make the measurement of the 4π-periodic contribution from the Fourier spectrum difficult. Finally, we study the voltage response in the quasiperiodic regime and indicate how the Fourier spectra and the first-return maps in this regime reflect the change of periodicity in the supercurrent in the presence of Majorana bound states.This work was supported by the Spanish Ministry of Economy and Competitiveness via Grant No. MAT2014- 58241-P and the Youth European Initiative together with the Community of Madrid, Exp. PEJ15/IND/AI-0444. F.D. acknowledges financial support from the DFG via Grant No. SFB 1170 “ToCoTronics,” the Land of Bavaria (Institute for Topological Insulators and the Elitenetzwerk Bayern), the German Research Foundation DFG (Grant No. SPP 1666)