Detecting fractional Josephson effect through 4π phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe the fractional DC Josephson effect of a semiconductor nanowire-based topological Josephson junction through 4π phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting in a resonant tunneling with 4π phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4π phase slip could overwhelm the topological trivial 2π phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.