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arXiv:2603.25245

Spinon Singlet Pairing: Microscopic nature of plaquettes in stripy LDOS

Ying Liang, Yi-Da Chu, Hao Ding, Shijie Hu, Xue-Feng Zhang

Published Mar 26, 2026• 0 citations
arXivHTMLPDF

Abstract

Scanning tunneling microscopy (STM) is a powerful tool for visualizing the local density of states (LDOS) of individual stripes in cuprates. However, the microscopic nature of the observed exotic LDOS patterns and their connection to high-$T_c$ superconductivity remain open questions. Within the framework of the quantum colored string model, we reveal that the ubiquitous $4a_0\times4a_0$ plaquettes originate from either the breaking of local spinon singlet pairs through hole insertion, or the formation of an unpaired spinon upon electron addition in a stripe. Moreover, by comparing our data with LDOS of cuprates, we identify an effect of particle-hole symmetry breaking (PHSB): a $2a_0$ shift, which is predicted and confirmed in a longer stripe ($L=18$). At last, we establish and verify a general relation between hole density and plaquette size across multiple fillings. Our work offers a fresh wavefunction-based perspective on interpreting STM signals in cuprate experiments and demonstrates that their origin may arise from spinon singlet pairing in the ground state of fluctuating stripes, the same mechanism underlying the $d$-wave sign structure [Phys. Rev. Lett. \textbf{137}, 086702 (2026)].

DOI
10.48550/arxiv.2603.25245

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Scanning tunneling microscopy (STM) is a powerful tool for visualizing the local density of states (LDOS) of individual stripes in cuprates. However, the microscopic nature of the observed exotic LDOS patterns and their connection to high-TcT_cTc​ superconductivity remain open questions. Within the framework of the quantum colored string model, we reveal that the ubiquitous 4a0×4a04a_0\times4a_04a0​×4a0​ plaquettes originate from either the breaking of local spinon singlet pairs through hole insertion, or the formation of an unpaired spinon upon electron addition in a stripe. Moreover, by comparing our data with LDOS of cuprates, we identify an effect of particle-hole symmetry breaking (PHSB): a 2a02a_02a0​ shift, which is predicted and confirmed in a longer stripe (L=18L=18L=18). At last, we establish and verify a general relation between hole density and plaquette size across multiple fillings. Our work offers a fresh wavefunction-based perspective on interpreting STM signals in cuprate experiments and demonstrates that their origin may arise from spinon singlet pairing in the ground state of fluctuating stripes, the same mechanism underlying the ddd-wave sign structure [Phys. Rev. Lett. \textbf{137}, 086702 (2026)].
Significant research advances have led to a consensus that the Fermi-Hubbard model and its extended variants are archetypical frameworks for elucidating the intertwined relationship between stripe orders and superconductivity in hole-doped high-T_{c} materials. Notably, the Hubbard quantum simulator has recently achieved several remarkable breakthroughs, e.g., being cooled down to the cryogenic regime and enabling the observation of stable fluctuating stripes. However, the microscopic mechanism underlying the d-wave pairing of electrons in the presence of stripes at low temperatures remains poorly understood due to the intricate interplay between strongly correlated effects and non-negligible thermal fluctuations. Here, we conduct a close investigation of a partially filled stripe in the representative t-J and t-t^{'}-U models with both numerical and analytical methods. Analogous to quantum gas microscopy, the perfect sampling technique allows us to obtain the high-confidence-level statistics of the Fock basis states appearing in the ground-state wave function. In a novel physical paradigm, these data demonstrate that two spinons with opposite chiralities tend to pair spontaneously into a singlet state, thereby naturally giving rise to the d-wave pairing pattern. Then, using the updated effective theory of quantum colored string, we have reconstructed the wave function and have determined the nature of spinon pairing and its connection to the d-wave sign structure of pair-pair correlation. Furthermore, spinon singlet pairs enable the establishment of a long-range pair-pair correlation between the two stripes. Our Letter offers new insights into the microscopic physics of stripes and paves the way for further exploration of multistripe-mediated pairing mechanisms in the Fermi-Hubbard model.
Spinon Singlet in Quantum Colored String: Origin of ddd-Wave Pairing in a Partially-Filled Stripe
Although both experimental observations and numerical simulations have reached a consensus that the stripe phase is intertwined with superconductivity in cuprates, the microscopic mechanism behind ddd-wave pairing in the presence of stripes remains unclear. Using the effective theory of quantum colored strings, we derive the wavefunction in Fock space. Our results show that two spinons with opposite chiralities tend to pair into a spinon singlet, which in turn facilitates the formation of negative pair-pair correlations between distant xxx-bonds and yyy-bonds, a hallmark of the ddd-wave pairing pattern. The same pair-pair correlation pattern is observed across various models, as confirmed by large-scale density matrix renormalization group calculations. Based on these results, we conclude that the spinon singlet is the origin of ddd-wave superconductivity in a fluctuating, partially-filled stripe, and this mechanism may also extend to multi-stripe configurations.
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.
We present additional details of the scanning tunneling microscopy (STM) spectra predicted by the model of pinning of dynamic spin collective modes in d-wave superconductor proposed by Polkovnikov et al. (Phys. Rev. B 65, 220509 (2002)). Along with modulations at the twice the wavevector of the spin collective mode, the local density of states (LDOS) displays features linked to the spectrum of the Bogoliubov quasiparticles. The former is expected to depend more strongly on an applied magnetic eld or the doping c oncentration. The spin collective mode and the quasiparticles are distinct, co-existing, low energy excitations of the d-wave superconductor (strongly coupled only in some sectors of the Brillouin zone), and should not be viewed as mutually exclusive sources of LDOS modulation.
In high-TC cuprates, the presence of parallel superconducting stripes or rivers of charge is well established experimentally. These also act as domain walls for the antiferromagnetic order. To readily explain the pattern of superconducting stripes near and at optimal doping levels, we propose a novel strong pairing mechanism, devoid of Coulomb repulsion, for high-TC cuprates. This new mechanism is based on the quantum entanglement and connement or degree of entanglement. Some quantum entanglement experiments with antiferromagnetic-chain links directly support our proposed entanglement pairing mechanism. Depending on doping levels, the triplet and singlet pairing can either exist independently, as a "lattice" of Bell basis states with unpolarized rivers of charge for underdoped regime, or as a mixed triplet-singlet or interacting Bell basis states with spatially alternating spin-polarized superconducting stripes of charge for overdoped range. Several spin resolved (SR)-ARPES experiments on the complex spin texture of cuprates are qualitatively interpreted in the light of our novel "lattice" of coupled triplet-singlet pairing leading to polarized rivers of charge in line with experimentally-found doping-level dependence. The resulting simple intuitive model suggests that entanglement is indeed a new strong pairing mechanism, devoid of Coulomb repulsion, leading to high-TC superconductivity and strange metal behavior above TC. Moreover, our model can possibly accommodate the Meissner effect, probably as superconducting plaquettes formed by "spokes" of antiferromagnetic-chain entanglement link.
Abstract A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.