Quench dynamics of the Josephson current in a topological Josephson junction

Abstract

The 4π-periodic Josephson Effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. In this work, we study the transient transport properties in a topological Josephson junction numerically. We show that the 4π Josephson current can be sustained under nonequilibrium conditions. The properties of the Josephson current are analyzed for different conditions, and three main regimes are identified: First, when both the superconducting wires of the Josephson junction lie in the topologically nontrivial region, a 4π Josephson current can appear upon suddenly applying a DC voltage. Second, when one superconducting wire lies in the trivial region, while the other wire lies in the non-trivial region, the Josephson current is 2π periodic but the component of the higher order Josephson current increases. Third, when both wires lie in the trivial region, a stable 2π Josephson current is observed. Most importantly, the fractional Josephson Effect is fragile in the presence of disorder. Hence, experiments should be designed carefully to eliminate the effect of disorder. These results could be helpful to optimize fine-tuning of the experimental parameters to observe the 4π-periodic Josephson current in a topological Josephson junction.

Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions

“…It is possible to calculate, at a microscopic level, the Andreev spectrum of a topological Josephson junctions in the zero bias equilibrium situation under various assumptions [2,17,15,16]. However, it is much more difficult to compute at the same elementary level the time-dependent response to a bias voltage or current, that emerges from the non-linear Josephson equations [76,77], especially in the currentbias situation that is experimentally most relevant. To simulate the response of our devices, we turn to the RSJ model [78,79,73], in which we incorporate both 2πand 4π-periodic supercurrents [33,52,57,80].…”

Minimal setup for non-Abelian braiding of Majorana zero modes

“…. We calculate the wavefunction evolution during the braiding as |ψ ± j (t) = U (t)|ψ ± j (0) , where U (t) = T exp[i t 0 dτ H s (τ )] is the time-evolution operator and T is the time-ordering operator [46][47][48]. The results confirm that ψ + j evolves into ψ − j after adiabatically swapping γ 2 and γ 3 twice in succession [Fig.…”

Non-Hermiticity stabilized Majorana zero modes in semiconductor-superconductor nanowires

“…3(a). It is well known that the MZMs may induce fractional Josephson effect, but the effect is vulnerable to the finite size effect of the nanowire [73]. In Fig.…”