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A wave-packet time evolution method, based on the split-operator technique,is developed to investigate the scattering of quasi-particles at anormal-superconductor interface of arbitrary profile and shape. As a practicalapplication, we consider a system where low energy electrons can be describedas Dirac particles, which is the case for most two-dimensional materials, suchas graphene and transition metal dichalcogenides. However the method is easilyadapted for other cases such as electrons in few layer black phosphorus, or anySchr\"odinger quasi-particles within the effective mass approximation insemiconductors. We employ the method to revisit Andreev reflection in graphene,where specular and retro reflection cases are observed for electrons scatteredby a step-like superconducting region. The effect of opening a zero-gap channelacross the superconducting region on the electron and hole scattering is alsoaddressed, as an example of the versatility of the technique proposed here.

Wave-packet scattering at a normal-superconductor interface in two-dimensional materials: a generalized theoretical approach