Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in K_{2}Cr_{3}As_{3}.

We study a twisted Hubbard tube modeling the $[\mathrm{CrAs}{]}_{\ensuremath{\infty}}$ structure of quasi-one-dimensional superconductors ${A}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$ ($A=\mathrm{K}$, Rb, Cs). The molecular-orbital bands emerging from the quasi-degenerate atomic orbitals are exactly solved. An effective Hamiltonian is derived for a region where three partially filled bands intersect the Fermi energy. The deduced local interactions among these active bands show a significant reduction compared to the original atomic interactions. The resulting three-channel Luttinger liquid shows various interaction-induced instabilities including two kinds of spin-triplet superconducting instabilities due to gapless spin excitations, with one of them being superseded by the spin-density-wave phase in the intermediate Hund's coupling regime. The implications of these results for the alkali chromium arsenides are discussed.