  A topological theory of d-wave superconductors is derived in this thesis.
Ginzburg-Landau theory describes superconductivity by defining a complex order
parameter and applying Landau's theory for phase transitions. However, there is
no local, gauge invariant order parameter for a superconductor and classical
order is no appropriate description. Topological order has proven to be a
powerful tool for describing the Quantum Hall effect and it gives also an
appropriate description of s-wave superconductors. For d-wave superconductors
there are gapless excitations at four points on the Fermi surface. The
topological theory for superconductors exhibits a similar structure for the
ground state as found in the s-wave case. However, the gapless excitations
destroy the topological degeneracy of the ground state and introduce an
additional degeneracy in one of the flux sectors. In search for regularities
which reflect the topological order, I include a magnetic point impurity and
focus on the effects it has on the Casimir energy. Indeed, it is shown that the
energy shift reflects the topology to some extend. However, this is work in
progress and further computations will be done.
