Gali, Virginia2024-07-242024-07-242024-05https://hdl.handle.net/11299/264305University of Minnesota Ph.D. dissertation. May 2024. Major: Physics. Advisor: Rafael Fernandes. 1 computer file (PDF); xii, 152 pages.Strongly correlated electron systems display phase diagrams with a rich variety of symmetry breaking states, such as unconventional superconducting phases. To advance our understanding of the fundamental mechanisms that lead to unconventional superconductivity, it is necessary to go beyond Bardeen–Cooper–Schrieffer theory. One way is to consider superconductors with multi-component order parameters, a framework that allows for a wide range of pairing symmetries and the description of more complex symmetry breaking superconducting states. In this thesis, we present two research projects that shed light on the properties and mechanisms of multi-component superconductors. First, we discuss layered unconventional superconductors on the hexagonal and tetragonal lattices in the presence of electromagnetic fluctuations. We showed that these fluctuations play a crucial role in the selection of the symmetry of the superconducting ground state, and generally favor a nematic superconductivity. Our results may be applied to nematic superconductivity observed in twisted bilayer graphene and other layered materials. Secondly, we discuss recent theoretical work that has shown that Bogoliubov quasiparticles can form Fermi surfaces in time-reversal symmetry-breaking superconductors. In the search for experimental signatures to identify these novel states unambiguously, we used symmetry arguments to construct an effective low-energy model. We used it to derive the low-temperature behavior of the superfluid density and the specific heat, identifying the key fingerprints of the quasiparticle Fermi surfaces. Another correlated electronic phase of interest is the electronic nematic, with increasing experimental evidence in two-dimensional materials. Motivated by this, we analyzed the effects that phase fluctuations of the nematic order parameter have on the electronic spectrum. Crystallographic restrictions constrain nematicity to display critical behaviors which are dominated by amplitude fluctuations. We circumvented this by considering a $30^{\circ}$-twisted hexagonal bilayer which has a critical phase at non-zero temperatures, dominated by phase fluctuations of a $Z_{6}$ nematic order parameter. The phase fluctuations of the quasi-long-range nematic order dominate and produce a thermal pseudogap-like behavior in the electronic spectrum, whose properties depend on the anomalous critical exponent. We also show that an out-of-plane magnetic field induces nematic phase fluctuations that suppress the critical region and give rise to a putative nematic quantum critical point with emergent continuous symmetry.enBogoliubov Fermi surfaceselectronic nematicityLandau-Ginzburg theorymulti-component superconductorstwisted heterostructuresunconventional superconductivityThesis or Dissertation