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arXiv:2304.14254 · Nature Communications

Charge stripe manipulation of superconducting pairing symmetry transition

Chao Chen, Peigeng Zhong, Xuelei Sui, Runyu Ma, Ying Liang, Shijie Hu, Tianxing Ma, Hai‐Qing Lin, Bing Qiang Huang

Published Nov 3, 2024• 7 citations
arXivHTMLPDF

Abstract

Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods ( $${{\mathcal{P}}}$$ ) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period $${{\mathcal{P}}}$$ , which is variable in different real material systems, could dictate the pairing symmetries—d wave for $${{\mathcal{P}}}\ge 4,s$$ and d waves for $${{\mathcal{P}}}\le 3$$ . In the latter, tuning hole doping and charge-stripe amplitude can trigger a d-s wave transition and magnetic-correlation shift, where the d-wave state converts to a pairing-density wave state, competing with the s wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of $${{\mathcal{P}}}=3$$ for the phase transition. In general, our findings offer important insights into the differences in the superconducting pairing mechanisms across many $${{\mathcal{P}}}$$ -dependent superconducting systems, highlighting the decisive role of charge stripe. Charge stripes have been observed in various unconventional superconductors, but their interplay with the superconducting properties is not fully understood. Here, the authors show, via large-scale numerical simulations based on an inhomogeneous Hubbard model, that the charge stripe period can dictate the superconducting pairing symmetry.

DOI
10.1038/s41467-024-53841-x

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Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods ( P{{\mathcal{P}}}P ) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period P{{\mathcal{P}}}P , which is variable in different real material systems, could dictate the pairing symmetries—d wave for P≥4,s{{\mathcal{P}}}\ge 4,sP≥4,s and d waves for P≤3{{\mathcal{P}}}\le 3P≤3 . In the latter, tuning hole doping and charge-stripe amplitude can trigger a d-s wave transition and magnetic-correlation shift, where the d-wave state converts to a pairing-density wave state, competing with the s wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of P=3{{\mathcal{P}}}=3P=3 for the phase transition. In general, our findings offer important insights into the differences in the superconducting pairing mechanisms across many P{{\mathcal{P}}}P -dependent superconducting systems, highlighting the decisive role of charge stripe. Charge stripes have been observed in various unconventional superconductors, but their interplay with the superconducting properties is not fully understood. Here, the authors show, via large-scale numerical simulations based on an inhomogeneous Hubbard model, that the charge stripe period can dictate the superconducting pairing symmetry.
We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale two-dimensional tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\ensuremath{\delta}\ensuremath{\sim}0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting ddd-wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.
We study the competition between stripe states with different periods and a uniform ddd-wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high-Tc{T}_{c}Tc​ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at 1/81/81/8 doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting ddd-wave superconducting order. The uniform ddd-wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.
Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO2{}_{2}2​ planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the ddd-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a $\ensuremath{\pi}$-phase shift in the magnetic order.
Competing orders represent a central challenge in understanding strongly correlated systems. In this work, we employ projector quantum Monte Carlo simulations to study a sign-problem-free bilayer extended Hubbard model. In this model, a charge stripe phase, characterized by a peak at (0±2πδ,0) is induced by highly anisotropic interlayer antiferromagnetic spin-exchange coupling Jz, and strongly suppressed by the decreasing spin-exchange anisotropy (i.e., introducing the spin-flip term J⊥); in contrast, the introduction of J⊥ favors the emergence of interlayer pairing superconductivity. We further demonstrate that the anisotropy of the interlayer spin-exchange directly governs the competition between these two phases, while the on-site interaction U plays a complex role in tuning both the charge stripe and superconductivity. Furthermore, against the background of charge stripes we discover the spin stripes, characterized by twice the period of charge stripes, indicating the profound internal connection between them. Our work identifies the key factors driving charge stripe formation, highlights the sensitivity of both the charge stripe and superconducting phases to interaction parameters, and thereby provides valuable insights into competing orders in strongly correlated systems.
Evolution of superconductivity from charge clusters to stripes in the ttt-t′t't′-JJJ model
Competition and coexistence of charge orders and superconductivity are hallmarks in many strongly correlated electron systems. Here, we unravel the precise role of charge fluctuations on the superconducting state in the ttt-t′t't′-JJJ model of the high-temperature cuprate superconductors. Using finite-temperature tensor network simulations, we investigate thermal snapshots in the underdoped regime where the ground state features a superconducting stripe phase. At intermediate temperatures, where stripes have melted and hole clustering is observed, we find that pairing correlations are tightly localized on the hole clusters. Upon entering the stripe regime at lower temperatures, pairing increasingly delocalizes across different hole clusters to ultimately become coherent across the full system in the ground state. This pair-charge locking gives rise to an intuitive picture of the parent state of the superconducting stripe phase: pairing is localized on hole clusters formed via hole attraction due to the onset of magnetic correlations at intermediate temperature. We discuss how this microscopic picture is consistent with a broad range of experimental observations in cuprate superconductors, including scanning tunneling microscopy (STM) evidence for local pairing above TcT_cTc​ and nuclear magnetic resonance (NMR) signatures of charge clustering in the underdoped regime.
Unidirectional ("stripe") charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of "optimal" inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated-mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi-long-range order with a Luttinger exponent, [Formula: see text].