Spin-triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9_{0.9}Mo6_6O17_{17}

The purple bronze Li$_{0.9}$Mo$_6$O$_{17}$ is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has accidental nodes, i.e. it has more sign changes than required by the point-group symmetry.Comment: Update

Band structure effects on the superconductivity in Hubbard models

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, starting from the square-lattice (zero nematicity) limit where a nodal d-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a p-wave- and a d-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces-a situation that may be relevant to the Bechgaard salts. (2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a d-wave to an s(+/-)-wave state reminiscent of the iron-based superconductors. (3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from d(x2-y2) to d(xy); in the context of the cuprates, this suggests that were the pseudogap entirely due to a competing CDW order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment)

Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound Li0.9Mo6O17

Previous theoretical studies [W. Cho, C. Platt, R. H. McKenzie, and S. Raghu, Phys. Rev. B 92, 134514 (2015)10.1103/PhysRevB.92.134514; N. Lera and J. V. Alvarez, Phys. Rev. B 92, 174523 (2015)10.1103/PhysRevB.92.174523] have suggested that Li0.9Mo6O17, a quasi-one-dimensional "purple bronze" compound, exhibits spin-triplet superconductivity and that the gap function changes sign across the two nearly degenerate Fermi surface sheets. We investigate the role of spin-orbit coupling (SOC) in determining the symmetry and orientation of the d vector associated with the superconducting order parameter. We propose that the lack of local inversion symmetry within the four-atom unit cell leads to a spin-orbit coupling analogous to that proposed for graphene, MoS2, or SrPtAs. In addition, from a weak-coupling renormalization group treatment of an effective model Hamiltonian, we find that SOC favors the odd parity A1u state with Sz=±1 over the B states with Sz=0, where z denotes the least-conducting direction. We discuss possible definitive experimental signatures of this superconducting state