Dinâmica de pacotes de onda e reflexão de Andreev em interfaces normal-supercondutor

Abstract

A time evolution method for wave packets, based on the split-operator technique, has been developed to investigate the scattering of quasi-particles by a normal/superconducting interface with arbitrary profile and geometry. As a practical application, the method is generalized to any situation where low energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials such as graphene and transition metal dichalcogenides. However, the method developed here can be easily adapted to other cases, such as electrons in few layer black phosphorus, or any Schrodinger quasi-particle within the effective mass approximation in semiconductors. We employ the method to the revisit the study of Andreev’s reflection in mono, bi, and trilayer graphene, where specular reflection and retroreflection cases are naturally expected for electrons scattered by a step-like normal/superconductor interface. As a second example, the method is also applied to simulate wave packet dynamics in a graphene based device where electron propagation trajectories are guided, by an applied magnetic field, towards a normal/superconductor interface. The magnetic field controls the incidence angle of the electronic wave packet at the interface, thus resulting in a tunable electron-hole ratio in the reflected wave function, due to the angular dependence of the Andreev reflection. In this case, the mapped control of quasi-particle trajectories via external magnetic fields defines an experimental probe for future fundamental studes of Andreev reflection in graphene, while also paving the way for the development of magnetic focusing devices based on nanoengineered superconducting two dimensional materials.