Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase

• Published in: arXiv.org
• Main Authors: Rodríguez Ruiz, Gabriel F, Rampp, Michael A, Aligia, A A, Schmalian, Joerg, Arrachea, Liliana
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.11.2022
• Subjects: Hamiltonian functions; Invariants; Josephson junctions; Physics - Mesoscale and Nanoscale Physics; Physics - Superconductivity; Spin-orbit interactions; Topological superconductors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2205.14993

We determine the current-phase relation (CPR) of two-terminal configurations of Josephson junctions containing two-dimensional (2D) time-reversal invariant topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as junctions between topological and non-topological superconductors (TRITOPS-S). We focus on long junctions for which several channels intervene in the tunneling coupling through the junction. We present a description of the topological edge modes for different TRITOPS models including \(p\)-wave pairing and the combination of \(s\)-wave pairing with spin-orbit coupling. We derive effective low-energy Hamiltonians to describe the Josephson junction, which can be solved analytically to explain the contribution of the edge states to the Josephson current as a function of the phase bias. We find that edge-modes yield singular corrections to the CPR for both junction types. The primary effects occur for the response of the Majorana zero-modes at half-flux quantum phase \(\phi\approx \pi\) in TRITOPS-TRITOPS junctions and for integer flux quantum phase \(\phi \approx 0\) for TRITOPS-S junctions, respectively. The former effect is particularly strong two-component nematic superconductors. The latter effect leads to a spontaneously broken time-reversal symmetry in the TRITOPS-S junction and to a breakdown of the bulk-boundary correspondence.