Executive Summary : | Topological materials are a special category of materials with a characteristic topological order, allowing them to behave as insulators from inside and bear conducting states on the surface. These materials are known as topological crystalline insulators (TCIs), which have high electron mobilities at high temperatures. The presence of free charge carriers in the bulk of these materials hinders the unambiguous detection and address of surface states through established electronic means. This project proposes two novel all-optical approaches: the 'optical-pump-THz-probe' and 'two-dimensional nonlinear' spectroscopy. The project combines an optical beam or a high-field THz pulse to perturb the system and drive it to the nonlinear regime of light-matter interaction. A second low-energy THz pulse probes locally the charge carriers within a single experiment. These experiments map out the entire linear and nonlinear electric susceptibility, allowing for a full map of the complex-valued conductivity at THz frequencies. One essential trick in the experiment is employing micro-cavities to locally and selectively enhance the perturbation field close to the surface of the TCIs. This allows the surface states (currents associated with the surface charge carriers) to be driven far away from its equilibrium, tracing the relevant dynamics and the microscopic picture of the surface state nonlinearities. The output of this project will substantially promote our understanding of carrier dynamics in TCI materials and provide a broad prospect towards new topological materials. |