Collective modes of the superconducting condensate

When a continuous symmetry is spontaneously broken, collective modes emerge. Usually, their spectrum is dominated by the low-energy physics of massless Goldstone modes. Superconductors, that break U(1) symmetry, are different. Here, the Goldstone boson is gapped out due to the Anderson-Higgs mechanism. The superconducting condensate can therefore host a zoo of massive collective excitations that are stable for lack of a gapless decay channel. The most prominent of them is the Higgs mode. Spectroscopy of collective modes can serve as a probe to reveal the nature of the superconducting state. In this thesis, we study the signatures of collective modes in nonlinear optical experiments. We explore the theoretical description of a new spectroscopic excitation scheme. We show how impurity scattering significantly enhances the optical Higgs mode response. We apply group theoretical methods to multi-order-parameter theories and investigate microscopic signatures of coupled modes in third harmonic generation experiments. We study the phenomenology and collective mode spectrum of an exotic system of twisted cuprate bilayers that supports topological superconductivity. Finally, we propose a novel device implementation of the superconducting diode effect. These results contribute to the emerging field of collective mode spectroscopy.Science, Faculty ofPhysics and Astronomy, Department ofGraduat