Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Ribbed moraines and subglacial geomorphological signatures of interior-sector palaeo-ice sheet dynamics

Transverse, subglacial bedforms (ribbed moraines) occur frequently in southern Keewatin, Nunavut, Canada, where they record a complex glacial history, including shifting centers of ice dispersal and fluctuating basal thermal regimes. Comprehensive mapping and quantitative morphometric analysis of the subglacial bedform archive in this sector reveals that ribbed moraines are spatially clustered by size and assume a broad range of visually distinct forms. Results suggest that end-member morphologies are consistent with a dichotomous polygenetic origin, and that a continuum of forms emerged through subsequent reshaping processes of variable intensity and duration. Translocation of mobile, immobile and quasi-mobile beds throughout the last glacial cycle conditioned the development of a subglacial deforming bed mosaic, and is likely responsible for the patchy zonation of palimpsest and inherited landscape signatures within this former core region of the Laurentide Ice Sheet. Comparison against field evidence collected from central Norway suggests that bedforming processes can be locally mediated by pre-existing topography.