UC Riverside

In quantum materials, the interactions between the bulk lattice, free electrons, and lattice vibrations give rise to interesting phases of matter. In recent years, new materials have been discovered that have nontrivial topological physics, allowing them to host topologically protected surface states. Much work has been done in exploring whether or not such materials can be rendered superconducting via the proximity effect. In this work, I will explore interesting phases of two topological materials: Weyl semimetals and transition metal dichalcogenides. In the first section, I explore the properties of proximity induced superconductivity within these materials. Using a numerical technique known as the spectral method, I determine what, if any, types of superconductivity can be induced within these materials, and whether or not the superconducting state retains their topological properties. Ultimately, I show that, in the absence of a non-trivial tunneling interaction at the interface, no interesting superconducting properties can be induced. In the second section, I will explore the optical absorption properties of a semiconducting materials in the presence of electron-phonon interactions, which typically give rise to phonon side-bands in optical spectra. I demonstrate how, with an appropriate transformation, an expression for the optical spectra to arbitrary phonon side-band order can be calculated for a general interacting system. To demonstrate its validity, I fit the model to the measured optical absorption spectrum of a device consisting of layered transition metal dichalcogenides.