QUANTUM TRANSPORT IN TOPOLOGICAL MATERIALS

In this thesis, we examine five main transport properties: nonlinear optical conductivity, self-focusing, thermionic conductivity, photogalvanic conductivity and magneto-optical conductivity across a number of topological materials. In the case of Weyl, Dirac and gapped semimetals as well as the α-T3 model, minimal coupling Hamiltonia are able to capture multiple topological phases through the same equation. This allows us to survey nonlinear optical conductivity, self-focusing and thermionic conductivity for the nodal semimetals whilst only nonlinear conductivity is studied for the α-T3 lattice. Shift current generation and circularly polarised photogalvanic conductivity are uncovered for a symmetry broken nodal ring material whilst twisted bilayer graphene is the system in which we study both nonlinear and magneto-optical conductivity.