Some topological aspects of condensed matter physics

The angular momentum paradox in Helium 3 is revisited. The edge currents in an infinite half plane and in a cylinder are calculated using the Bogoliubov de Gennes approximation and are shown to be consistent with the expectation of an unit of angular momentum associated with every Cooper pair. The problem is also studied using an effective Action approach. Edge currents in a quantum spin Hall model in graphene are also studied using similar techniques. A model for the integer quantum Hall effect on a square lattice is presented. Using techniques from algebraic topology, a classification of band insulators with time reversal symmetry in two and three dimensions is presented. The possibility of a three dimensional quantum spin Hall effect is pointed out. A topological classification of lattice superconductors is also derived.