Symmetry analysis of transport properties in helical superconductor junctions

We study the discrete symmetries satisfied by helical p-wave superconductors with the d-vectors k(x)(x) over cap +/- k(y)(x) over cap or k(y)(x) over cap +/- k(x)(y) over cap and the transformations brought by symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with the transport properties in heterojunctions, including helical superconductors. In particular, the partial symmetries of the Hamiltonian under spin-rotation and gauge-rotation operations are responsible for the novel invariances of the conductance in tunnel junctions and the new selection rules for the lowest current and peculiar phase diagrams in Josephson junctions, which were reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed, and are consistent with the results from the Hamiltonian.