Fractionalized superconductors and topological orders

Mehdi Kargarian

​​​​​​​Integer quantum Hall effect, Chern insulators, topological insulators, and  topological superconductors are famous examples of topological phases in noninteracting or weakly correlated electron systems. In these states  the ground state is nondegenerate and the excitations carry the original quantum  numbers. Fractional quantum Hall effect (FQHE) and spin liquids, on the other hand, arise in strongly correlated electron systems and exhibit exotic properties such as  ground state degeneracy and fractionalized excitations, dubbed as topologically ordered states, with potential applications in quantum computations. While there are many material candidates for noninteracting topological phases of matter, the topological orders usually arise in texteme conditions such as strong magnetic fields and low temperatures, e.g., in FQHE, and in spin liquids, usually the extra interactions between spins spoil the realization of true topological orders.  Here, we ask the following question: Can we design the topological orders in  more conventional systems by properly coupling the degrees of freedom together? we try to present an understanding of one of the simplest topological orders, the Wen plaquette model, in a superconducting lattice model. Then, we discuss how one may obtain more exotic topological orders.