Josephson current mediated by odd-frequency equal-spin triplet pairing on the surface of Weyl nodal loop semimetals*

We explore proximity-induced pairing on the surface of a Weyl nodal loop semimetal (WNLS) sandwiched between two conventional spin-singlet s-wave superconductors in a Josephson junction set-up. The fully spin-polarizated drumheadlike surface states (DSSs) and the intrinsic spin-orbit interation of the WNLS cause odd-frequency (odd-ω) equal-spin triplet pairing to be induced on the surface of the WNLS, whereas, the spin-singlet pairing decays inside the WNLS very fast. We show finite Josephson current in the junction contributed by the equal-spin triplet odd-ω pairing. Odd-ω mixed-spin triplet pairing can be generated by placing an additional ferromagnet in the junction if the direction of the magnetization of the ferromagnet opposes the spin-polarization direction of the DSSs. The pairing and the current are not affected if the magnetization direction is orthogonal to the DSS spin polarization, which further confirms the equal-spin structure of the odd-ω pairing.