Real-space formulation of the quantum-mechanical electronic scattering under static n-fold axially symmetric electric and magnetic fields in a projection microscope

A numerical technique is developed to compute electronic propagation in three-dimensional potential-energy and vector-potential distributions, as required for the quantum-mechanical modelization of scattering in static electric and magnetic fields in a projection microscope. The technique is implemented in a transfer-matrix and Greenʹs functions general procedure to simulate field-emission and electronic projection microscopy. In particular, simulated observations of a transverse magnetic field confirms the occurrence of diffraction fringes that are oriented in the direction of the field. These diffraction fringes are mainly associated with the detection of a magnetic flux and tend to be more pronounced as this quantity increases. In the conditions of this paper, the smallest magnetic flux that was detected could be associated with a phase shift of around 2π/8 rad.