In this thesis I study superconductivity and topological phases in condensed matter systems. First I briefly introduce some concepts of topological phases as well as BCS theory of superconductivity. Then I will show a new experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on the 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. Next I will show that giant spin currents can be induced by using nodal topological superconductors due to selective eq...[ Read more ]

In this thesis I study superconductivity and topological phases in condensed matter systems. First I briefly introduce some concepts of topological phases as well as BCS theory of superconductivity. Then I will show a new experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on the 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. Next I will show that giant spin currents can be induced by using nodal topological superconductors due to selective equal spin Andreev reflection (SESAR). SESAR is related to spin-triplet correlations at the edge of nodal topological superconductors. Superconductivity induced in flat band systems is also discussed. Flat band superconductors have two important features: (1) The critical temperatures of flat band supercondutors are very high due to the divergent density of states near Fermi surface. (2) At high temperature the fluctuation effect becomes important and the mean field theory is no longer valid.