Local and nonlocal Andreev reflections in graphene-superconductor hybrid structures based on tilted Dirac cone systems

Abstract

We study the scattering processes, the local and nonlocal Andreev reflections in graphene-superconductor hybrid structures based on tilted Dirac cone systems. The Dirac theory of graphene was deformed, which is characterized by two parameters $\zeta =\zeta (\cos \theta ,\sin \theta )$. This tilt deformation breaks the chiral symmetry of the energy band, and the tilted energy band makes the reflections and transmissions of electrons and holes show distinctive characteristics. We show that even if the incident angle is 0, the nonzero ζ will make both local and nonlocal Andreev reflections to be nonzero when $E\gg E_F$ (E is the excitation energy, and $E_F$ is the Fermi energy). Furthermore, as ζ approaches 1, the reflected electrons and holes are always perpendicular to the interface, regardless of whether $E\gg E_F$ or $E\ll E_F$. This perpendicular reflection is another type of reflections besides the specular reflection and the retro reflection. The tilt dependence of the conductance curves can be used to extract information about the direction and magnitude of the tilt.