Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$

We study a twisted Hubbard tube modeling the $[\mathrm{CrAs}{]}_{\infty }$ 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two kinds of spin-triplet superconducting instabilities due to gapless spin excitations, with one of them being superseded by the spin-density-wave phase in the intermediate Hund’s coupling regime.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.

Figure 1

(a) A CrAs cluster in the $ab$ plane. The solid (dotted) circles connected by the solid (dotted) lines represent the Cr atoms in the first (second) triangle in a unit cell. The isolated outer solid (dotted) circles represent the As atoms in the corresponding planes. (b) A Q1D CrAs tube. The blue (green) filled circles represent the Cr atoms in each triangles. The As atoms are not shown.

Figure 2

Fitting the band structure: The upper band is twofold degenerate. The lower inset is the schematic picture for the three partially filled bands with three pairs of Fermi points.

Figure 3

Luttinger parameters for the channel 2: $K_{s,2}>1$ everywhere, and $K_{c,2}<1$ only in the intermediate regime between the lines $J_H=0.2U$ and $J_H=0.6U$.