Theory on superconducting chiral crystal and its applications

Chiral crystals are shown to have nontrivial band topology: at the time reversal invariant momenta, Kramers Weyl points and multi-fold Weyl points can emerge due to the chiral lattice symmetry. In the normal metallic state, the chiral lattice symmetry along with the band topology introduces the magnetoelectric effect and circular photogalvanic effect to modify the electromagnetic properties in the mateirals. However, how does the chiral lattice symmetry and the associated band topology affect the superconducting phase in chiral crystals remains unknown. In this work, we classify the possible pairing phases resulted from chiral lattice symmetry and find various topological superconducting phases. We propose the candidate topological superconducting chiral crystal and study its unique superconducting properties.