A scattering treatment on relativistic electronic transports in normal metal-superconductor junctions of Dirac materials

The Blonder-Tinkham-Klapwijk formalism has been widely applied to analyze the electronic transport in normal metal-superconductor (N-S) junctions via the electronic scattering through various degrees of junction impurities. While effectively treating conventional materials with quadratically dispersed electrons, its key assumption of a<i>δ</i>-function repulsive potential that represents the impurity strength, however, leads to a mathematical inconsistency for Dirac materials with linearly dispersed electrons. In this work, we propose a modified scattering treatment for Dirac materials by considering an impurity-induced repulsive potential over the N-S interface with a finite-thickness. Our model not only resolves the inconsistency of the conventional treatment but also reveals distinctive transport properties attributed to the linear dispersion of Dirac fermions, which exhibit largely suppressed normal reflections and the resulting robust conductance plateau against impurities. Our modified scattering treatment is supported by a real-material analysis using a non-equilibrium Green's function method and ought to provide a general framework for analyzing the N-S junctions of linearly dispersed materials.