Abstract

In this thesis, I study topological topological superconducting phases in condensed matter systems. The search for topological superconductors which support Majorana fermion excitations has been an important topic in condensed matter physics. Here, we propose a new experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on top of a superconductor with Rashba spin-orbit coupling, topological superconducting phases can be achieved without fine-tuning the chemical potential. Moreover, superconductors with different Chern numbers can be obtained by changing the superlattice structure of the organic molecules. I will also discuss the superconductivity induced in flat band systems. I will talk about three features of flat band superconductors: (1) The critical temperatures of flat band supercondutors are very high due to the divergent density of states near Fermi surface. (2) BCS wavefunction is the exact ground state in infinity large size limit. (3) At high temperature the fluctuation effect becomes important and the mean field theory is no longer valid.