Topological insulators are one of the most important developments in condensed-matter physics in the past decade. These materials behave as insulators in the bulk but have robust metallic surface states with highly nontrivial spin structures. In this project, we will investigate the absorption of photons by surface electrons and their relaxation via the emission of phonons for two-dimensional and three-dimensional topological insulators both from a fundamental point of view and with regards to possible applications as sensors.It remains a challenge to clearly distinguish topologically nontrivial edge states from trivial ones. To address this problem, we will first develop tight-binding models, in which their interplay can be studied. Moreover, we will propose an experimental setup to detect topological edge states in a contactless setting, where an edge state current is induced by a time-dependent magnetic field. We will show that this will make it easier to avoid the contribution of trivial edge states in transport measurements.Moreover, we will investigate more generally the infrared photon absorption in topological insulator surfaces and the relaxation of surface electrons via the emission of phonons into the bulk of the system. We will address interesting thermodynamic questions about the heat and entropy transport between the conducting surfaces and the insulating bulk. Moreover, with a view on possible applications as sensors, we will study quantitatively in particular the photon absorption properties of bismuth based three-dimensional topological insulators.Hence, this research will lead to a better fundamental understanding of topological insulator surface states and could be an important step towards future technological applications.