Parity dependent Josephson current through a helical Luttinger liquid

TL;DR

This paper investigates how electron-electron interactions influence the 2π- and 4π-periodic Josephson currents in a superconductor-topological insulator-superconductor junction modeled as a helical Luttinger liquid, revealing interaction-dependent effects and phase shifts.

Contribution

It introduces a bosonization approach to analyze parity effects in a helical Luttinger liquid with superconducting contacts, highlighting the impact of interface transparency and magnetic impurities.

Findings

Interaction marginally affects Josephson current with perfect interfaces.

Strong magnetic scatterers significantly alter the current due to Coulomb interactions.

Magnetization direction of impurities can induce phase shifts in the Josephson current.

Abstract

We consider a superconductor-two dimensional topological insulator- superconductor junction (S-2DTI-S) and study how the 2{\pi}- and 4{\pi}-periodic Josephson currents are affected by the electron-electron interaction. In the long-junction limit the supercurrent can by evaluated by modeling the system as a helical Luttinger liquid coupled to superconducting reservoirs. After having introduced bosonization in the presence of the parity constraint we turn to consider the limit of perfect and poor interfaces. For transparent interfaces, where perfect Andreev reflections occur at the boundaries, the Josephson current is marginally affected by the interaction. On the contrary, if strong magnetic scatterers are present in the weak link, the situation changes dramatically. Here Coulomb interaction plays a crucial role both in low and high temperature regimes. Furthermore, a phase-shift of Josephson current can be induced by changing the direction of the magnetization of the impurity.