Single- and double-slit electron diffraction in an anisotropic two-dimensional medium

We theoretically investigate the effect of anisotropy on electron diffraction in two-dimensional (2D) systems. The calculations are performed by means of both analytical semiclassical and microscopic tight-binding approaches, with the anisotropy being introduced by assuming direction-dependent effective masses and hoppings, respectively. Single and double slits with different orientations with respect to the anisotropy axis are considered. Using these models, we obtain analytical expressions for the wave function and numerical results for the probability current density for both investigated cases. In addition, we specify the conditions under which there is constructive or destructive interference in the interference pattern in the double-slit case. The results show that anisotropy can lead to a collimation effect, as well as a steering of the diffracted electronic beam, which may, in turn, allow the control of the charge carriers' propagation to be used in nanoelectronic devices based on anisotropic 2D media systems.