Quantum focusing and filtering of electrons propagating coherently through non-uniform potential barriers

The possibility of engineering the coherent propagation of electrons through a confined medium with potential energy barriers of various spatial shapes is investigated. Using basic quantum mechanical principles, a semi-analytical method is developed to compute the current density of the particle's localization probability in a nanoscale strip, across regions with different values of potential energy and with various geometries. The results show uneven spatial distribution of the probability current density, with possible extreme contrast between electron flows through neighbouring areas. Thus, interactions of the confined electronic wave with customized shapes of potential energy barriers are shown to lead to either focusing or filtering effects of the electron propagation. It is further demonstrated that the method can be adapted for studying the probability flow scattering by insular potential energy obstacles. Though the present method is illustrated on a narrow two-dimensional strip, it can be straightforwardly generalized for three-dimensional cases.