Superconductivity is a field with a great many branches and applications. In this dissertation, we focus on two specific processes in superconductors -- light-induced enhancement and hybridization of collective modes -- in two types of quasi-two dimensional materials -- either the loosely coupled planes of a layered superconductor or a superconducting thin film.
Motivated by experiments in the cuprates that have seen evidence of a transient superconducting state upon optical excitation
we study the effects of inter-plane tunneling on the competition between superconductivity and charge order. We find that an optical pump can suppress the charge order and simultaneously enhance superconductivity, due to the inherent competition between the two. Taking into account that the charge order empirically shows a broad peak in c-axis momentum, we consider a model of randomly oriented charge ordering domains and study how interlayer coupling affects the competition of this order with superconductivity.
Also in the cuprates, several groups have reported observations of collective modes of the charge order present in underdoped cuprates. Motivated by these experiments, we study theoretically the oscillations of the order parameters, both in the case of pure charge order, and for charge order coexisting with superconductivity. Using a hot-spot approximation we find in the coexistence regime two Higgs modes arising from hybridization of the amplitude oscillations of the different order parameters. We explore the damping channels of these hybrid modes.
As another means of enhancing superconductivity we consider coupling a two-dimensional superconducting film to the quantized electromagnetic modes of a microwave resonator cavity. We find that when the photon and quasiparticle systems are out of thermal equilibrium, a redistribution of quasiparticles into a more favorable non-equilibrium steady-state occurs, thereby enhancing superconductivity in the sample, a fluctuation analog of a phenomenon known as the Eliashberg effect.
Finally, following the recent success of realizing exciton-polariton condensates in cavities, we examine the hybridization of cavity photons with two types of collective modes in superconductors. Enabled by the recently predicted and observed supercurrent-induced linear coupling between these excitations and light, we find that significant hybridization between the superconductor's collective modes and resonant cavity photons can occur
