CONICET | Buscador de Institutos y Recursos Humanos

The two-dimensional charge transport with parallel (in plane) magnetic field is consideredfrom the physical and mathematical point of view. To this end, we start withthe magnetic field parallel to the plane of charge transport, in sharp contrast to theconfiguration described by the theorems of Aharonov and Casher where the magneticfield is perpendicular. We explicitly show that the specific form of the arising equationenforces the respective field solution to fulfill the Majorana condition. Consequently, assoon any physical system is represented by this equation, the rise of fields with Majoranatype behavior is immediately explained and predicted. In addition, there existsa quantized particular phase that removes the action of the vector potential producinginteresting effects. Such new effects are able to explain due to the geometrical frameworkintroduced, several phenomenological results recently obtained in the area of spintronicsand quantum electronic devices. The quantum ring as spin filter is worked out in thisframework and also the case of the quantum Hall effect.