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arXiv:2303.14723 · Physical review. B./Physical review. B

Robust superconducting correlation against intersite interactions in the extended two-leg Hubbard ladder

Zongsheng Zhou, Weinan Ye, Hong‐Gang Luo, Jize Zhao, Jun Chang

Published Nov 17, 2023• 17 citations
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Abstract

The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a ${t}^{\ensuremath{'}}$-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the ${t}^{\ensuremath{'}}$-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain ${\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping $t$. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.

DOI
10.1103/physrevb.108.195136

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The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain Ba2\ensuremath−xSrxCuO3+\ensuremathδ{\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}Ba2\ensuremath−x​Srx​CuO3+\ensuremathδ​, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping ttt. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.
A recent experiment has unveiled an anomalously strong electron-electron attraction in the one-dimensional copper-oxide chain ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$. While the effect of the near-neighbor electron attraction VVV in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction VVV can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (JJJ) and correlated hopping (KKK) interaction. Detailed numerical analysis of sss-, ppp-, and ddd-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (ttt) and next-nearest- (t2{t}_{2}t2​) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the ddd-wave and the extended sss-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the t2t\frac{{t}_{2}}{t}tt2​​ ratio, giving in particular for t2=0{t}_{2}=0t2​=0 sss-wave (ddd-wave) pairing as most favorable in the low (high) density limit, but increasing t2{t}_{2}t2​ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects sss-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
In quantum materials, the electronic interaction and the electron-phonon coupling are in general two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional (1D) copper-oxide chain compound. Yet it is unclear how this strong near-neighbor (NN) attraction VVV influences the superconductivity pairing. In this work, we employ the density-matrix renormalization group (DMRG) method to study this experiment-relevant extended Hubbard model with on-site Coulomb repulsion U>0U>0U>0 and NN attraction V<0V<0V<0, relevant for the 1D cuprate chain and likely other similar transition-metal materials. We find this extended ttt-UUU-VVV model hosts a rich quantum phase diagram consisting of the spin density wave phase, phase separation phases, the Tomonaga-Luttinger liquid (TLL) phase, and especially an intriguing TLL regime with divergent superconducting susceptibility and dominant spin-triplet pair correlations. Upon doping, such a spin-triplet pairing regime can be further broadened in the parameter space and extends to larger UUU. Our results show robust triplet pairing induced by attractive interaction VVV, offering a feasible mechanism to realize ppp-wave superconductivity in 1D cuprates.
Motivated by the recent discovery of anomalously strong nearest-neighbor attraction in the one-dimensional hole-doped cuprate ${\text{Ba}}_{2+x}{\text{Sr}}_{x}{\text{CuO}}_{3+\ensuremath{\delta}}$, we investigate the ddd-wave superconducting property of an extended checkerboard Hubbard model, which includes an intraplaquette nearest-neighbor attraction VVV. Our quantum Monte Carlo simulations reveal that, for small interplaquette hopping integral ${t}^{\ensuremath{'}}$, VVV induces a drastic enhancement of long-range ddd-wave pairing correlations in the parameter range of $0.0\ensuremath{\le}U\ensuremath{\le}6.0t$ (ttt is the intraplaquette hopping integral) when the electron density lies between half-filling and quarter-filling. At $V=\ensuremath{-}0.4t$, one order of magnitude larger ddd-wave pairing correlations are observed compared to the ones at V=0.0tV=0.0tV=0.0t and, more importantly, they exceed the values of the free electron system, signifying the existence of ddd-wave superconductivity. The exact diagonalization calculations on the $2\ifmmode\times\else\texttimes\fi{}2$ plaquette indicate that the enhancement of ddd-wave pairing correlations can be attributed to the VVV-induced enhancement of pair-binding energy. Our findings provide a new perspective on the realization of high-temperature ddd-wave superconductivity via the combination of nearest-neighbor attraction and electronic inhomogeneity.
The role of near-neighbor electron attraction V V in strongly correlated systems has been at the forefront of recent research of unconventional superconductivity. However, its implications in the doped Hubbard model on expansive systems remain predominantly unexplored. In this study, we employ the density-matrix renormalization group to examine its effect in the lightly doped t t - t' t ′ -Hubbard model on six-leg square cylinders, where t t and t' t ′ are the first and second neighbor electron hopping amplitudes. In the electron-doped regime ( t'>0 t ′ > 0 ), we find that attractive V V can substantially enhance superconducting correlations, driving the system into a pronounced superconducting phase when the attraction exceeds a modest value V_c ≈ 0.5t V c ≈ 0.5 t . In contrast, in the hole-doped regime ( t' <0 t ′ < 0 ), while heightened superconducting correlations have also been observed in the charge stripe phase, the systems remain insulating with pronounced charge density wave order. Our results demonstrate the importance of the electron attraction in boosting superconductivity in broader doped Hubbard systems and highlight the asymmetry between the electron and hole-doped regimes.
The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism, ferromagnetism, superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.