Valleytronics of quantum dots of topological materials

The local minima (maxima) in the conduction (valence) band of crystalline materials are referred to as valleys. Similar to the role of spin in spintronics, the manipulation of the electron's valley degree of freedom may lead to technological applications of the new field of research called valleytronics. Those crystalline solids that have two or more degenerate but well separated valleys in their band structure are considered to be potential valleytronic systems. This thesis presents a theoretical investigation of the valley degree of freedom of electrons in quantum dots of two-dimensional topological materials such as monolayer and bilayer graphene and monolayer bismuthene on SiC. To this end, a method for the calculation of the valley polarization of electrons induced by the electric current flowing through nanostructures was developed in this thesis. The method is based on a projection technique applied to states calculated by solving the Lippmann-Schwinger equation within Landauer-Büttiker theory. Applying the proposed method, this thesis addresses several valleytronic problems of current interest, including: the valley currents, valley polarization, and non-local resistances of four-terminal bilayer graphene quantum dots in the insulating regime, a valley filtering mechanism in monolayer graphene quantum dots decorated by double lines of hydrogen atoms, and the valley polarization of the edge and bulk states in quantum dots of monolayer bismuthene on SiC, a candidate for a high-temperature two-dimensional topological insulator.