Triplet superconductivity in a model of Li$_{0.9}$Mo$_6$O$_{17}$

Superconductivity in the quasi-one-dimensional material Li$_{0.9}$Mo$_6$O$_{17}$ is analyzed based on a multiorbital extended Hubbard model. We found strong charge fluctuations at two different momenta ${\bf Q_1}$ and ${\bf Q_2}$ giving rise to two different charge ordered phases. Evaluating the superconducting vertex, we found superconductivity near strong charge fluctuations at ${\bf Q_1}$. The order parameter has the p-wave symmetry with nodes on the Fermi surface. The metallic state displays a characteristic charge collective mode ${\bf Q_1}$ due to nesting and for on-site Hubbard repulsion sufficiently large, a charge critical mode ${\bf Q_2}$ driven by Coulomb repulsion, which softens at the proximity to the transition. The results are quite robust for different coupling parametrizations. A phase diagram discussing the relevance of the model to the physics of the material is proposed.