Spin-orbit driven Peierls transition and possible exotic superconductivity in CsW₂O₆

We study \textit{ab initio} a pyrochlore compound, CsW$_{2}$O$_{6}$, which exhibits a yet unexplained metal-insulator transition. We find that (1) the reported low-$T$ structure is likely inaccurate and the correct structure has a twice larger cell; (2) the insulating phase is not of a Mott or dimer-singlet nature, but a rare example of a 3D Peierls transition, with a simultaneous condensation of three density waves; (3) spin-orbit interaction plays a crucial role, forming well-nested bands. The high-$T$ (HT) phase, if stabilized, could harbor a unique $e_{g}+ie_{g}$ superconducting state that breaks the time reversal symmetry, but is not chiral. This state was predicted in 1999, but never observed. We speculate about possible ways to stabilize the HT phase while keeping the conditions for superconductivity.