Executive Summary : | This research project aims to explore the nature of transport in topological semimetals, specifically the superconductivity due to the Cooper-pairing of the Weyl monopoles, the Josephson effect across junctions of topological semimetals, and the non-perturbative limit of periodically driven Weyl semimetals in the context of Floquet theory. The project will examine these effects in time reversal symmetry broken and inversion symmetry broken lattice models of tilted multi-Weyl semimetals, nodal line semimetals, and other exotic materials that host Berry curvature singularities in their spectra. The project will employ various techniques, including BdG formulation, linear response theory, Bloch theory, Floquet theory, Group theory, and numerical methods, including integration and eigenvalue solvers. The research will use software like python, C++, and Mathematica, as well as hand-based techniques in applied mathematics. The significance of this research is that it will increase the general understanding of the phenomena being examined and the class of materials they are being examined in. The results obtained from this work will benefit condensed matter physics, particularly the field of topological materials, as the current understanding is restricted to continuum models, which are known to host unphysical attributes, including unbounded dispersion. The use of more realistic models will provide more concrete results and predictions regarding the phenomena being explored. |