Unconventional superconductors with spin-orbit interaction

This thesis studies superconductivity and its transport properties in the presence of spin-orbit interaction. Topological materials are now considered as a promising platform to realize unconventional superconductivity since spin-orbit interaction in some topological materials can support spin-triplet pairing state. In this thesis, we have found that exotic spin-orbit interaction in topological Dirac semimetals enhances the nodal spin-triplet state that hosts an exotic Andreev bound state. We have also studied the Josephson effect in Zeeman-split superconductor/ Rashba wire/ Zeeman-split superconductor trilayer junctions. Our calculations have shown that it is possible to manipulate Andreev levels in the Josephson junctions by tuning the strength of the spin-orbit interaction