A study of the Transport properties of Topological materials
In this work we try to study the electronic transport in the so-called 2-Dimensional topological insulators, where the Spin-Orbit Coupling makes possible an interaction between states coming from the valence and conduction bands in such a way that a new state previously unknown arises with peculiar characteristics, amongst them, the existence of surface states with counter propagating modes carrying opposite spins. As it’s been argued, this new state of matter is protected by some symmetries, like Time Reversal Symmetry (TRS) for instance, where it’s necessary that at some point in the Brillouin zone, the edge states mentioned above crossed and form a Kramer’s pair, this degeneracy protects the opening of a gap as long as the perturbation under the system does not break the underlying symmetry very badly, in colloquial terms, as long as the symmetry remains unbroken in average, but, what does this ’in average’ exactly mean?. In order to obtain quantitative results we use together two well established theories, first of all, for the description and electronic structure of these systems we use the Density Functional Theory (DFT), which has been proved to be an excellent tool to explore in detail the electronic nature that takes places in these materials. On the other hand, when we talk about disorder, where the system loses part of the translational symmetry as the inclusion of structural defects or another atoms, or when the TRS could be broken by the inclusion of magnetic atoms, we refer to the theory of Non-Equilibrium Green’s Function (NEGF), in this manner we explore the electronic properties in these systems performing calculations using the data from previous DFT results, this allows to find quantities, for instance, the spin coherence lengths in terms of the Transmission which maybe characterizes some Spin Filter behaviour in our samples, or even better, maybe shed light on the quest of the so called Quantum Anomalous Hall effect (QAHE).