Abstract
The phenomenon of superconductivity has been puzzling scientists for over a century. It is a quantum
state of matter, usually realised at low temperature, where a material loses all electrical resistance.
Despite being discovered in 1911, it was not until the late 1950s that a microscopic theory of
superconductivity was developed by Bardeen, Cooper, and Schrieffer. This BCS theory described
pairing of electrons into so-called Cooper pairs via coupling to lattice vibrations, and these pairs
condensing into a spin-singlet, isotropic ground state.
Since then, however, swathes of materials whose superconductivity could not be described by BCS
theory have been discovered. These materials, dubbed unconventional superconductors, are now
studied with a generalised BCS theory which is agnostic to the pairing mechanism. Considerations
of crystal symmetries can provide a framework for constructing the possible superconducting states,
the most stable of which can be determined in a number of ways.
Unconventional superconductors can host states which sometimes are multi-component or in close
competition with another order such as magnetic ordering or a different superconducting state.
This gives rise to some interesting physics and strong dependence on internal and external factors.
Specifically, the class of locally noncentrosymmetric superconductors have been predicted to host
topological superconductivity, singlet-triplet mixed states, and to have high magnetic field resistance
and field-induced transitions between different superconducting states. The latter two of these
features have been tentatively observed in CeRh2 As2 , to which there are many references herein.
On the whole, this thesis explores the physics of locally noncentrosymmetric superconductors as a
class. The first three chapters investigate the physics of a strongly coupled system with multiple
different possible states, the competition between them, and identify possible factors which stabilise
exotic states. The main goal of this investigation is to uncover how superconducting state stability
depends on internal and external parameters, those being spin-orbit coupling strength, level of
doping, interlayer hopping, and an externally applied magnetic field. Rich phase diagrams in these
parameter spaces were uncovered, with regions in which unconventional layer-odd states were found
to be stabilised. Possible causes for this are also considered.
Chapters 5 onwards explores single component singlet superconducting states in the weak coupling
limit, in the presence of a variety of impurities. Considering the possibility of a conventional layer-
even pairing and its odd counterpart, the dependence of the gap distributions on impurity type
and concentration, and an external magnetic field were determined. It was seen that the field-
mediated transition between even and odd states can depend heavily on time reversal symmetry
breaking disorder, and that there may be significant coexistence of the gaps in the regime between
even singlet dominated and odd singlet dominated superconductivity. A simple Ginzburg-Landau
analysis was used to investigate the relationship between the gaps and the transition between them.