The 2016 Nobel prize in Physics was awarded to physicists working on topological phases. The story begins in 1980s in the search of an explanation of the quantization of Hall conductivity found by Klaus von Klitzing. Starting from the Kubo formula, Thouless and collaborators proposed a formula (later called TKNN) to calculate the quantized Hall conductivity. We use the Green's function technique and Kubo formula to study the spectral function, density of states, optical and magneto-optical conductivity in topological insulators and valleytronic materials. Quasiparticles in those materials can be described by the Dirac equation in which the gamma matrices can have Dirac representation, Weyl representation and also Majorana representation. In 1+1D and 3+1D the chirality can be defined while in 2+1D no definition of chirality can be found but the valley degree of freedom plays a similar role. We found interesting predictions which could be verified in future measurements.