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The electron scattering from periodic line defects on the surface of topological insulators with hexagonal warping effect is investigated theoretically by means of a transfer matrix method. The influence of surface line defects, acting as structural ripples on propagation of electrons are studied in two perpendicular directions due to the asymmetry of warped energy contour under momentum exchange. The transmission profiles and the details of resonant peaks which vary with the number of defects and the strength of their potentials are strongly dependent on the direction in which the line defects extend. At low energies, the quantum interference between the incident and reflected propagating electrons has the dominant contribution in transmission resonances, while at high energies the multiple scattering processes on the constant-energy contour also appear because of the strong warping effect. By increasing the spatial separation between the line defects, the minimum value of electrical conductance remains significantly high at low incident energies, while the minimum value may approach zero at high energies as the number of defects is increased. Our findings suggest that the potential ripples on the surface of topological insulators can be utilized to control the local electronic properties of these materials.

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This article aims to microscopically investigate the matter of transmitting energy in a simple electrical circuit. In order to do this, energy transmission from the source to the consumer is investigated from two different approaches. In the first, the energy transmitted due to the collision of electrons is calculated; in the second, energy transmission in the circuit is accounted for based on the Poynting vector. Finally, the results obtained from the two approaches are evaluated through macroscopic relations and by establishing the equilibrium of electromagnetic energy conservation.