# Symmetry analysis of transport properties in helical superconductor junctions

## TL;DR

This paper analyzes the discrete symmetries of helical p-wave superconductors and their impact on transport properties in heterojunctions, revealing new invariances and selection rules in conductance and Josephson effects.

## Contribution

It provides a detailed symmetry analysis of helical p-wave superconductors and links these symmetries to novel transport phenomena in junctions, including conductance invariances and phase diagram features.

## Key findings

- Symmetries under spin-rotation and gauge-rotation lead to conductance invariances.
- Partial Hamiltonian symmetries determine Josephson junction phase diagrams.
- Constructed free energy symmetries align with Hamiltonian analysis.

## Abstract

We study discrete symmetries satisfied by helical $p$-wave superconductors with d-vectors $k_{x}\hat{x}\pm k_{y}\hat{y}$ or $k_{y}\hat{x}\pm k_{x}\hat{y}$ and transformations brought by the symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with transport properties in heterojunctions including helical superconductor. Especially, the partial symmetries of the Hamiltonian under the spin-rotation and gauge-rotation operations are responsible for novel invariances of the conductance in tunnel junctions and new selection rules of the lowest current and peculiar phase diagrams in Josephson junctions which are reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed which are consistent with the results from Hamiltonian.