Symmetry analysis of transport properties in helical superconductor junctions

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.