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Europhysics Letters (EPL)

Superconductivity and spin gap in the high-doping regime of a CuO chain model

Anders W. Sandvik, Asle Sudbø

Published Nov 20, 1996• 7 citations
Publisher

Abstract

A two-band Hubbard model describing a CuO chain is studied using quantum Monte Carlo simulation. The Luttinger-liquid exponent K ρ is extracted as a function of the nearest-neighbor repulsion V , at hole fillings ⟨ n ⟩ between 1 (half-filled lower band) and 2. Evidence is presented for the existence of a regime with dominant singlet superconducting fluctuations and a gap in the spin excitation spectrum at ⟨ n ⟩ = 1.75, in the neighborhood of the V for which the system phase separates. Closer to half-filling (⟨ n ⟩≲1.6), spin-density-wave fluctuations always dominate.

DOI
10.1209/epl/i1996-00249-7

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Physical review. B, Condensed matter•Sep 1, 1992•12 citations
A two-band Hubbard model describing a CuO chain is studied using quantum Monte Carlo simulation. The Luttinger-liquid exponent K ρ is extracted as a function of the nearest-neighbor repulsion V , at hole fillings ⟨ n ⟩ between 1 (half-filled lower band) and 2. Evidence is presented for the existence of a regime with dominant singlet superconducting fluctuations and a gap in the spin excitation spectrum at ⟨ n ⟩ = 1.75, in the neighborhood of the V for which the system phase separates. Closer to half-filling (⟨ n ⟩≲1.6), spin-density-wave fluctuations always dominate.
The phase-separation instability occurring with increasing nearest-neighbor repulsion VVV in a two-band Hubbard model (CuO chain) is discussed. Quantum Monte Carlo simulations indicate that this transition is strongly discontinuous if the filling fraction 〈n〉〈n〉〈n〉 is close to 1 (half-filled lower band). Spin-density-wave fluctuations then dominate before phase separation. Superconducting fluctuations dominate in the neighborhood of phase separation only at considerably higher doping levels, where the transition to the phase-separated state is much smoother.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\ensuremath{\gg}U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=VPS.{V=V}_{\mathrm{PS}}.V=VPS​. Using quantum Monte Carlo methods on lattices much larger than in previous Lancz\"os diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent ${K}_{\ensuremath{\rho}},$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For V<VPS,V<{V}_{\mathrm{PS}},V<VPS​, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with ${K}_{\ensuremath{\rho}}<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.
Using the numerical diagonalization method, we examine the one-dimensional t1–t2–J1–J2 model (zigzag-chain t–J model) which is an effective model for metallic CuO double chains in the superconductor Pr2Ba4Cu7O15-δ. Based on the Tomonaga–Luttinger liquid theory, we calculate the Luttinger liquid parameter Kρ as a function of the electron density n. It is found that superconductivity is realized in the parameter region, which is in accordance with experimental results. We show the phase diagram of a spin gap in the t2/|t1|–n plane by analyzing the expectation value of the twist operator Zσ in the spin sector. The spin gap appears in the region with a large t2/|t1|, where the phase boundary at half filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches ∼100 K in the realistic parameter region of Pr2Ba4Cu7O15-δ.
Using the numerical diagonalization method, we examine the one-dimensional t_1-t_2-J_1-J_2 model (zigzag chain t-J model) which represents an effective model for metallic CuO double chain in the superconductor Pr_2Ba_4Cu_7O_15-δ. Based on the Tomonaga-Luttinger liquid theory, we calculate the Luttinger-liquid parameter K_ρas a function of electron density n. It is found that superconductivity is realized in parameter region corresponding to the experimental result. We show phase diagram of spin gap on the t_2/|t_1|-n plane by analyzing the expectation value of twist-operator Z_σin the spin sector. The spin gap appears in the region with large t_2/|t_1|, where the phase boundary at half-filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches 100K in the realistic parameter region of Pr_2Ba_4Cu_7O_15-delta.
A one-dimensional two-band Hubbard model describing CuO chains is considered in the limit of zero bandwidth. Onsite and nearest-neighbor Coulomb interactions are included in the description. Various density correlation functions are calculated exactly at arbitrary concentration of holes. For increasing values of the intersite Coulomb interaction V, the system is driven towards both a charge-transfer instability and a phase separation instability when doped away from half filling. In the case of one hole added to the half-filled system, it is shown that a hole binds to a biexciton. Three-body bound states recently proposed to produce the marginal Fermi-liquid spectrum also occur naturally in the model, but a finite amount of doping away from half filling is necessary for them to form to an appreciable extent in the thermodynamic limit.