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

Abstract

Motivated by recently discovered quasi-one-dimensional superconductor K${}_2$Cr${}_3$As${}_3$ with $D_{3h}$ lattice symmetry, we study one-dimensional three-orbital Hubbard model with generic electron repulsive interaction described by intra-orbital repulsion $U$, inter-orbital repulsion, and Hund's coupling $J$. As extracted from density functional theory calculation, two of the three atomic orbitals are degenerate ($E^{\prime }$ states) and the third one is non-degenerate ($A_1^{\prime }$), and the system is presumed to be at an incommensurate filling. With the help of bosonization, we have usual three-band Tomonaga-Luttinger liquid for the normal state. Possible charge density wave (CDW), spin density wave (SDW) and superconducting (SC) instabilities are analyzed by renormalization group. The ground state depends on the ratio $J/U$ and is sensitive to the degeneracy of $E^{\prime }$ bands. At $0<J<U/3$, spin-singlet SC state is favored, while spin-triplet superconductivity will be 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 two-fold degeneracy of $E^{\prime }$ bands is lifted, 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 K${}_2$Cr${}_3$As${}_3$ are discussed.

two more appendices are added

References in corpus (12)

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• Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in K2Cr3As3

Cited by in corpus (13)

• Multiband one-dimensional electronic structure and spectroscopic signature of Tomonoga-Luttinger liquid behavior in K${}_2$Cr${}_3$As${}_3$
• Superconductivity at 7.3 K in the 133-type Cr-based RbCr3As3 single crystals
• Coexistence of nontrivial topological properties and strong ferromagnetic fluctuations in $A_2$Cr${}_3$As${}_3$ ($A$=Na, K, Rb and Cs)
• Coupling of structure to magnetic and superconducting orders in quasi-one-dimensional ${\text{K}}_2{\text{Cr}}_3{\text{As}}_3$
• Singlet $s^{\pm }$-wave pairing in quasi-one-dimensional ACr${}_3$As${}_3$ (A=K, Rb, Cs) superconductors
• Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes
• Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A${}_2$Cr${}_3$As${}_3$ (A=Na, K, Rb, Cs) superconductors
• Lifshitz transition enhanced triplet $p_z$-wave superconductivity in hydrogen doped KCr${}_3$As${}_3$
• Competing phases and critical behavior in three coupled spinless Luttinger liquids
• The upper critical field and its anisotropy in RbCr${}_3$As${}_3$
• A magnetic excitation linking quasi-1D Chevrel-type selenide and arsenide superconductors
• Spin-triplet pair density wave superconductors
• Hydrogen Doping Induced $p_x\pm i{p}_y$ Triplet Superconductivity in Quasi-One-Dimensional K${}_2$Cr${}_3$As${}_3$