Er’el Granot
This paper investigates electron transport through a precisely engineered quantum system model that features a localized, inhomogeneous magnetic field coupled with a partially compensating electrostatic potential. Our analysis reveals several surprising findings, which, to the best of our knowledge, have not been investigated. Firstly, the transmission coefficient for electrons incident on this barrier is found to be independent of the particle's energy and mass . Instead, it depends solely on the incident angle and the vector potential profile (strength and width). Crucially, these results are valid in the narrow potential barrier regime. This behavior challenges conventional expectations for quantum scattering, where energy dependence and resonance phenomena are typically ubiquitous. Secondly, despite the presence of the magnetic field, which breaks the system’s symmetry, the transmission coefficient is a symmetric function of the incident angle. Thirdly, when this compensated barrier is situated within a narrow quantum wire, it acts as a two-dimensional point impurity. This confinement induces sharp Fano resonances that drastically alter the wire's conductance. Finally, at specific local conductance maxima the barrier's contribution to conductance is shown to be independent of both Planck's constant and the Fermi energy, relying solely on classical parameters such as electron density. This demonstrates emergence of classical-like transport behavior governed directly by deep quantum mechanisms.