Title: Andreev reflection in 2D relativistic materials with realistic tunneling transparency in normal-metal-superconductor junctions,
Abstract: The Andreev conductance across 2d normal metal (N)/superconductor (SC)
junctions with relativistic Dirac spectrum is investigated theoretically in the
Blonder-Tinkham-Klapwijk formalism. It is shown that for relativistic
materials, due to the Klein tunneling instead of impurity potentials, the local
strain in the junction is the key factor that determines the transparency of
the junction. The local strain is shown to generate an effective Dirac
$\delta$-gauge field. A remarkable suppression of the conductance are observed
as the strength of the gauge field increases. The behaviors of the conductance
are in well agreement with the results obtained in the case of 1d N/SC
junction. We also study the Andreev reflection in a topological material near
the chiral-to-helical phase transition in the presence of a local strain. The N
side of the N/SC junction is modeled by the doped Kane-Mele (KM) model. The SC
region is a doped correlated KM t-J (KMtJ) model, which has been shown to
feature d+id'-wave spin-singlet pairing. With increasing intrinsic spin-orbit
(SO) coupling, the doped KMtJ system undergoes a topological phase transition
from the chiral d-wave superconductivity to the spin-Chern superconducting
phase with helical Majorana fermions at edges. We explore the Andreev
conductance at the two inequivalent Dirac points, respectively and predict the
distinctive behaviors for the Andreev conductance across the topological phase
transition. Relevance of our results for the adatom-doped graphene is
discussed.