| The superconducting state can be conveniently thought of as a condensate of electron pairs. The excitations of this system, the quasiparticles, are obtained by breaking these pairs, while the condensate can support topological defects like vortices. The interaction of quasiparticles with such defects, especially in cases of unconventional pairing, is of much interest and is the subject of this thesis.; We begin by reviewing several results in quasiparticle physics, some of which are well known and established, as well as more recent, exotic developments. Then, we introduce a semiclassical approximation for quasiparticles that gives some insight into their unusual behaviour, as well as a simple derivation of many of the results reviewed.; Next, we consider the problem of d-wave quasiparticles in the vortex lattice state, and inquire about the fate of the low lying Dirac excitations in this phase. We find that in most circumstances, symmetry considerations protect the Dirac like structure down to a low energy scale, below which the system is gapped. The magnitude of this scale is derived. A quantized thermal Hall effect is predicted for temperatures below this scale, which should be observable in some of the cuprate superconductors.; Finally, we study a situation where quasiparticle interactions have a dramatic effect on the behaviour of the system. We first recognize that in relatively strong fields, a degenerate gas of quasiparticles bound to a vortex-line can be realized. Interactions in this one dimensional system would lead to Luttinger liquid behaviour and experimental tests for this as well as for a vortex analog of the Peierls effect, are proposed. |
