Dirac Green's function approach to graphene-superconductor junctions with well defined edges

TL;DR

This paper introduces a microscopic Green's function approach to analyze spectral properties and Andreev reflections in graphene-superconductor junctions with well-defined edges, advancing understanding of their quantum behavior.

Contribution

It develops an analytical Green's function method for graphene-superconductor junctions, incorporating boundary conditions and microscopic hopping, to study spectral properties and Andreev reflections.

Findings

Derived Green functions for normal and superconducting graphene layers.

Identified signatures of specular Andreev reflections.

Calculated local density of states and pairing correlations.

Abstract

This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the Green functions for normal and superconducting graphene layers. Importing the idea used in tight-binding (TB) models of a microscopic hopping that couples different regions, we are able to set up and solve an algebraic Dyson's equation describing a graphene-superconductor junction. For this coupled system we analytically derive the Green functions and use them to calculate the local density of states and the spatial variation of the induced pairing correlations in the normal region. Signatures of specular Andreev reflections are identified.