Controlling Current in Topological Insulators with Magnetic Impurities

Topological insulators are theoretical materials that allow for an ideal conductivity of electricity with minimal loss of energy. This proves to be of great use in the field of electronics, as it greatly increases the energy efficiency of electronic components. Local conductive properties of the material are dependent on the location and physical properties of impurities placed within the material, and this allows for control of direction and strength of the current traveling through this material. We implemented a discrete lattice model of a topological insulator known as the BHZ model and constructed its Hamiltonian matrix to predict the behavior of electrons in this lattice. We numerically explored the relationship between conductance and the location and energy of magnetic impurities in the BHZ model. We found that conductance is largely dependent on the dimensions of the lattice used in the model as well as the configuration of the coupling between the impurity and the lattice. This conductance was indirectly quantified by the transmission coefficient of incoming electrons. We observed a significant decrease of the transmission coefficient after altering the impurity coupling, yielding a greater control of the current.