Parity dependent Josephson current through a helical Luttinger liquid

Abstract

We consider a superconductor-two dimensional topological insulator- superconductor junction (S-2DTI-S) and study how the 2π- and 4π-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.

References in corpus (15)

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Cited by in corpus (9)

• Revealing topological superconductivity in extended quantum spin Hall Josephson junctions
• Nonlocal Thermoelectricity in a S-TI-S Junction in Contact with a N-Metal Probe: Evidence for Helical Edge States
• Evidence for Majorana bound states in transport properties of hybrid structures based on helical liquids
• Signatures of topological phase transitions in Josephson current-phase discontinuities
• Fractional Josephson Effect in Number-Conserving Systems
• Magnetic AC control of the spin textures in a helical Luttinger liquid
• Signatures of Jackiw-Rebbi resonance in the thermal conductance of topological Josephson junctions with magnetic islands
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Local Density of States in a Helical Tomonaga-Luttinger Liquid of Loop and Josephson Junction Geometries