# Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires

## TL;DR

This paper provides a comprehensive catalog of Andreev spectra and Josephson effects in various configurations of topological superconductor wires, revealing novel phenomena like anomalous periodicity and phase jumps.

## Contribution

It introduces effective Hamiltonians to explain diverse Josephson behaviors in topological superconductor junctions, including effects with quantum dots.

## Key findings

- Identification of 0-π transition behaviors
- Observation of anomalous Josephson periodicity
- Finite Josephson current without magnetic flux

## Abstract

We study all the possible different two terminal configurations of Josephson junctions containing wires of time-reversal invariant topological superconductors (TRITOPS) and ordinary superconductors, including combinations with an interacting quantum dot between both wires in the junction. We introduce simple effective Hamiltonians which explain the different qualitative behaviors obtained. We analyze a wide range of phenomena, including occurrence and quenching of the so called $0-\pi$ transition, anomalous periodicity and jumps of the Josephson current as a function of the phase difference, and finite Josephson current in the absence of magnetic flux.