Instability of three-band Tomonaga-Luttinger liquid: Renormalization group analysis and possible application to K2Cr3As3

Motivated by recently discovered quasi-one-dimensional superconductor K2Cr3As3 with D-3h lattice symmetry, we study a one-dimensional three-orbital Hubbard model with generic electron repulsive interaction described by intraorbital repulsion U, interorbital repulsion U', and Hund's coupling J. As extracted from density functional theory calculation, two of the three atomic orbitals are degenerate (E' states) and the third one is nondegenerate (A'(1)), and the system is at incommensurate filling. With the help of bosonization, the normal state is described by a three-band Tomonaga-Luttinger liquid. Possible charge density wave (CDW), spin density wave (SDW), and superconducting (SC) instabilities are analyzed by renormalization group method. The ground state depends on the ratio J/U and is sensitive to the degeneracy of E' bands. The spin-singlet SC state is favored at 0 < J < U/3, and the spin-triplet SC state is favored in the region U/3 < J < U/2. The SDW state has the lowest energy only in the unphysical parameter region J > U/2. When the twofold degeneracy of E' bands is lifted, the SDW instability has the tendency to dominate over the spin-singlet SC state at 0 < J < U/3, while the order parameter of the spin-triplet SC state will be modulated by a phase factor 2 Delta k(F)x at U/3 < J < U/2. Possible experimental consequences and applications to K2Cr3As3 are discussed.