Due to their nonlocality, Majorana bound states have been proposed to induce current-current correlations (CCCs) that are completely different from those induced by low-energy fermionic Andreev bound states. Such characteristics can be used as a sign
ature to detect Majorana bound states. Herein, we studied the Majorana and fermionic Andreev bound states in a two-dimensional topological insulator system. We found that nonlocality occurs for both types of bound states and that their coupling strengths depend on system parameters in the same pattern. Majorana and fermionic Andreev bound states show the same differential CCCs characteristics, thereby indicating a universal behavior for both types of bound states. The maximal cross differential CCCs are robust to the structural asymmetry of the system.
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 superconductor
s, 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.
