EXAMPLES OF TOPOLOGICAL SUPERCONDUCTIVITY IN CONDENSED MATTER PHYSICS

Abstract

In this thesis, we theoretically propose several examples to realize topological superconductivity. In Chapter 2, we study twisted bilayer graphene from weak coupling limit. We develop a patch random phase approximation method and the pairing symmetry is found to be topological chiral d+id. In Chapter 3, we study twisted bilayer graphene from strong coupling limit. We find spin fluctuations can mediate attractive interaction between electrons and mean field analysis shows that the superconducting phase has d+id symmetry. In Chapter 4 we propose the possibility to realize time reversal invariant topological superconductivity in 111 surface of SnTe. At mean field level, we find a sign change topological superconductivity phase. Renormalization group calculation shows that particle hole fluctuations can enhance the topological superconducting phase. Finally, in Chapter 5, we find different topological phases by tuning parameters of a coupled Rashba system. It is a good platform to realize different topological superconducting phases.