Topological superconductivity in interacting systems

The discussion of topology in condensed matter represents a paradigm shift – when classifying states of matter, one needs to consider both the symmetry and the topology of the system.  In superconductivity this leads to an exciting result – a topological superconductor capable of localizing a Majorana fermion, a peculiar excitation that is its own antiparticle and may be useful for quantum computing.Some encouraging evidence of topological superconductivity has been found experimentally in one dimension when Majorana fermions reside on the edges of the system.  In two dimensions, many theoretical proposals have been found but the 2d topological superconductor has not yet seen conclusively. In this talk I will give an example of a model in which superconductivity arises from interaction and may be topological when spin-orbit coupling is strong enough.  The topological state is induced when a Zeeman field is applied.  I will also discuss the characterization of topological states through their entanglement entropy.