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The Andreev conductance across 2d normal metal (N)/superconductor (SC)junctions with relativistic Dirac spectrum is investigated theoretically in theBlonder-Tinkham-Klapwijk formalism. It is shown that for relativisticmaterials, due to the Klein tunneling instead of impurity potentials, the localstrain in the junction is the key factor that determines the transparency ofthe junction. The local strain is shown to generate an effective Dirac$\delta$-gauge field. A remarkable suppression of the conductance are observedas the strength of the gauge field increases. The behaviors of the conductanceare in well agreement with the results obtained in the case of 1d N/SCjunction. We also study the Andreev reflection in a topological material nearthe chiral-to-helical phase transition in the presence of a local strain. The Nside of the N/SC junction is modeled by the doped Kane-Mele (KM) model. The SCregion is a doped correlated KM t-J (KMtJ) model, which has been shown tofeature d+id'-wave spin-singlet pairing. With increasing intrinsic spin-orbit(SO) coupling, the doped KMtJ system undergoes a topological phase transitionfrom the chiral d-wave superconductivity to the spin-Chern superconductingphase with helical Majorana fermions at edges. We explore the Andreevconductance at the two inequivalent Dirac points, respectively and predict thedistinctive behaviors for the Andreev conductance across the topological phasetransition. Relevance of our results for the adatom-doped graphene isdiscussed.

Andreev reflection in 2D relativistic materials with realistic tunneling transparency in normal-metal-superconductor junctions