Parity protected superconducting diode effect in topological Josephson junctions

Abstract

In bulk superconductors or Josephson junctions formed in materials with spin-orbit interaction, the critical current can depend on the direction of current flow and applied magnetic field, an effect known as the superconducting (SC) diode effect. Here, we consider the SC diode effect in Josephson junctions in nanowire devices. We find that the 4π-periodic contribution of Majorana bound states (MBSs) to the current phase relation (CPR) of single junctions results in a significant enhancement of the SC diode effect when the device enters the topological phase. Crucially, this enhancement of the SC diode effect is independent of the parity of the junction and therefore protected from parity altering events, such as quasiparticle poisoning, which have hampered efforts to directly observe the 4π-periodic CPR of MBSs. We show that this effect can be generalized to SQUIDs and that, in such devices, the parity-protected SC diode effect can provide a highly controllable probe of the topology in a Josephson junction.

Reconstruction-Induced $\varphi_0$ Josephson Effect in Quantum Spin Hall Constrictions

“…Such a temperature dependence is hence a clear cut signature of the constriction. Lastly, we point out that, going beyond the low-transparency assumption, and hence including higher order contributions of δ ĤE in the calculation of the current, would result in a superconducting diode effect [62].…”

Reconstruction-Induced φ0 Josephson Effect in Quantum Spin Hall Constrictions

“…Such a temperature dependence is hence a clear cut signature of the constriction. Lastly, we point out that, going beyond the low-transparency assumption, and hence including higher order contributions of δ ĤE in the calculation of the current, would result in a superconducting diode effect [66]. In order to capture the essential physics underlying the temperature behavior, some expansions of Equation ( 14) are particularly helpful.…”