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

Abstract

Motivated by recently discovered quasi-one-dimensional superconductor K2Cr3As3 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 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 non-degenerate (A ′ 1 ), and the system is at incommensurate filling. With the help of bosonization, the normal state is described by a threeband 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. Spin-singlet SC state is favored at 0 < J < U/3, and 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 two-fold degeneracy of E ′ 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∆kF x at U/3 < J < U/2. Possible experimental consequences and applications to K2Cr3As3 are discussed.

Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in K2Cr3AsWatson1, Feng2, Nicholson3 et al. 2017Phys. Rev. Lett.593410View full textAdd to dashboardCite

“…Superconductivity is found at 6.1 K in K 2 Cr 3 As 3 [4], which ranks amongst the highest T c for q1D systems, and has been suggested to be of an unconventional nature [1] with some experimental [5,6] and theoretical [3,7] support for a triplet pairing state. Finally the one-dimensionality of the system makes it a candidate for Tomonaga-Luttinger liquid (TLL) physics [7][8][9]. This rich set of phenomena constitutes a very strong motivation for experimental determinations of the electronic structure by Angle-Resolved Photoemission Spectroscopy (ARPES) measurements.…”

“…Our ARPES data shows that the TLL persists down to 10 K, near the superconducting T c . Therefore the best starting point for understanding superconductivity may be with TLLs hosted by 1-D Cr 3 As 3 stacks [7,9] and only weakly coupled by the K guest ions, rather than with quasiparticles occupying 3-D Fermi surfaces [3,31]. In q1D superconductors the guest ion type and disorder are crucial for controlling superconductivity, as exemplified in the M 2 Mo 6 Se 6 family with guest ion M=Tl, In, Na, K, Rb [32][33][34].…”