Intrinsic contributions to the anomalous Hall conductivity in multiband chiral superconductors

Abstract

The anomalous Hall conductivity is a material property that can quantify time-reversal symmetry breaking in bulk materials. It is closely related to the polar Kerr effect, which is used as an experimental probe of such states, including in unconventional superconductors such as Sr2RuO4 and UPt3. In such materials there is controversy as to the origin of the effect: is it due to an extrinsic mechanism such as scattering, or is the underlying mechanism intrinsic to the clean superconductor. Previous work in single-band models has indicated that an intrinsic contribution to the anomalous Hall conductivity is vanishing, and much of the theoretical literature has focussed on extrinsic contributions. However, recent work has shown that an intrinsic contribution is possible in multi- band superconductors. This thesis builds on previous work to develop an understanding as to the general conditions under which a two-band Hamiltonian will exhibit an anomalous Hall conductivity. Our results can be applied to explain experiments in order to gain insight into the pairing states of various unconventional superconductors. Substantial attention is paid towards strontium ruthenate as an illustrative model.