Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound Li$_{0.9}$Mo$_6$O$_{17}$

TL;DR

This paper explores how spin-orbit coupling influences the symmetry and orientation of the superconducting order parameter in the quasi-one-dimensional compound Li$_{0.9}$Mo$_6$O$_{17}$, suggesting a favored odd-parity state with specific spin orientation.

Contribution

It introduces the role of staggered spin-orbit coupling due to lack of local inversion symmetry in Li$_{0.9}$Mo$_6$O$_{17}$ and predicts the favored superconducting state using renormalization group analysis.

Findings

SOC favors the odd parity $A_{1u}$ state with $S_z = ext{±}1$.

Lack of local inversion symmetry leads to staggered SOC similar to graphene and MoS$_2$.

Possible experimental signatures of the predicted superconducting state are discussed.

Abstract

Previous theoretical studies [W. Cho, C. Platt, R. H. McKenzie, and S. Raghu, Phys. Rev. B 92, 134514 (2015); N. Lera and J. V. Alvarez, Phys. Rev. B 92, 174523 (2015)] have suggested that Li$_{0.9}$Mo$_6$O$_{17}$, 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 staggered spin-orbit coupling analogous to that proposed for graphene, MoS$_2$, or SrPtAs. In addition, from a weak-coupling renormalization group treatment of an effective model Hamiltonian, we find that SOC favors the odd parity $A_{1u}$ state with $S_z = \pm 1$ over the $B$ states with $S_z=0$, where $z$ denotes the least-conducting direction. We discuss possible definitive experimental signatures of this superconducting state.