Andreev reflection at the interface of a normal Weyl semimetal and a superconducting type-II Weyl semimetal

Abstract

We study Andreev reflection at the interface of a time-reversal invariant Weyl semimetal without band tilting in the normal or ferromagnetic state with a type-II Weyl semimetal possessing an overtilted anisotropic energy spectrum in the superconducting state. We find that the Andreev reflection at the normal-superconductor interface is tremendously anisotropic, reflecting the anisotropic energy spectrum of the type-II Weyl semimetal. There is a critical junction direction relative to the band tilting direction which, below it, the Andreev reflection acquires distinct properties without any other counterpart. Further, the conductance of this junction is constant and independent of the energy at subgap energies in two extreme limits of the zero and infinite chemical potentials. We can attribute them to the perfect specular and retro Andreev reflections, respectively. In particular, we find a universal value for the zero-energy conductance independent of the chemical potential on each side of the junction. At the interface of the ferromagnet-superconductor, the Andreev reflection can be switched between the specular and retro regimes by varying the exchange energy. This results in different asymptotic values for conductance at high exchange energies depending on if the junction direction is below or above the critical direction. Moreover, we see that tunneling conductance of the normal-ferromagnet-superconductor junction in the thin barrier limit is independent of the potential barrier strength, while it periodically oscillates in terms of the exchange barrier strength. Furthermore, we find a $\ensuremath{\pi}/4$ phase shift in the periodic oscillation of the conductance of the junctions with directions below and above the critical direction. This highly anisotropic conductance of the junctions studied here can be used as a way, accompanied by the other methods, for detecting the anisotropic spectrum and band-tilting direction of type-II Weyl semimetals.