Spin-orbit driven Peierls transition and possible exotic superconductivity inCsW2O6

We study ab initio a pyrochlore compound, ${\mathrm{CsW}}₂{\mathrm{O}}₆$, 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 three-dimensional Peierls transition, with a simultaneous condensation of three density waves; (3) the spin-orbit interaction plays a crucial role, forming well-nested bands. The high-$T$ (HT) phase, if stabilized, could harbor a unique ${e}_g+i{e}_g$ superconducting state that breaks time reversal symmetry, but is not chiral. This state was predicted in 1999, but not observed. We speculate about possible ways to stabilize the HT phase while keeping the conditions for superconductivity.