Wave-packet scattering at a normal-superconductor interface in two-dimensional materials: A generalized theoretical approach
F. J. A. Linard, V. N. Moura, L. Covaci, M. V. Milošević, A. Chaves
DOI 10.1103/PhysRevB.107.165306 · Physical Review B
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Abstract
A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasiparticles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system 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 is easily adapted for other cases such as electrons in few-layer black phosphorus or any Schrödinger quasiparticles within the effective mass approximation in semiconductors. We employ the method to revisit Andreev reflection in mono-, bi-, and trilayer graphene, where specular- and retro-reflection cases are observed for electrons scattered by a steplike superconducting region. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.