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arXiv:2606.11056

On pseudogap phase as precursor to a superconducting dome in high-Tc cuprates: Non-analytic T* as a function of doping

Felix A. Buot

cond-mat.supr-conquant-phSubmitted Jun 9, 2026• Announced Jun 10, 2026
v1 · Jun 9, 2026v2 · Jul 14, 2026v3 · Jul 17, 2026v4 · Sep 27, 2026
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Abstract

We generalize the condition under which a quantum material exhibiting a pseudogap phase is a precursor to a superconducting (SC) dome. The result reveals the non-analytic T* as a function of doping. A well-known example is the high-Tc cuprates. Essentially, the SC dome is generated under two conditions: (1) that the pseudogap T* is a decreasing function of doping, due to the decrease in size of extended pairing of doped holes with doping, and most importantly, (2) that the rate of configurational-ordering parameter is an increasing function of doping as a result of the decrease in extended length of the disordered pairs. These two conditions are provided by the new entanglement and confinement pairing mechanism of high-Tc cuprates. This is a theory that has recently been discussed in the literature by Buot et al. It hinges on a novel strong entanglement and confinement hole pairing (ECHP) mechanism that unravels the microscopic features of the entire phase diagram of both electron and hole-doped high-Tc cuprates.

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8 pages 3 figures

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We generalize the condition under which a quantum material exhibiting a pseudogap phase is a precursor to a superconducting (SC) dome. The result reveals the non-analytic T* as a function of doping. A well-known example is the high-Tc cuprates. Essentially, the SC dome is generated under two conditions: (1) that the pseudogap T* is a decreasing function of doping, due to the decrease in size of extended pairing of doped holes with doping, and most importantly, (2) that the rate of configurational-ordering parameter is an increasing function of doping as a result of the decrease in extended length of the disordered pairs. These two conditions are provided by the new entanglement and confinement pairing mechanism of high-Tc cuprates. This is a theory that has recently been discussed in the literature by Buot et al. It hinges on a novel strong entanglement and confinement hole pairing (ECHP) mechanism that unravels the microscopic features of the entire phase diagram of both electron and hole-doped high-Tc cuprates.
We demonstrate that entanglement and confinement hole pairing (ECHP) is a precise physics of the entanglement framework of the RVB theory of high-Tc cuprates. Our novel strong ECHP mechanism explains the entire phase diagram of both electron and hole-doped cuprates, notably the linearly decreasing T* at the pseudogap but with "T*-singularity" at the peak of the superconducting (SC) dome, the Tc=T* at the optimum doping and the rest of the overdoped regions of the SC dome, the duality of the spin gap and strange metal phase, the presence of the parallel superconducting stripes in the CuO plane (spin-polarized and spin-unpolarized channels), and the linear-T resistivity of the strange metal phase above the overdoped regions of the SC dome. This also explains the experimental spin textures of the cuprates. We refer to our new ECHP model as a resonating entanglement and confinement hole pair (RECHP) theory. Based on RECHP theory, we were able to provide a conceptual and comprehensive semiquantitative explanation of the entire phase diagram, thus providing the sought-after pairing mechanism responsible for the entire phase diagram of high-T_{C} cuprates.
Abstract Previous theoretical studies (Phillips et al 2020 Nat. Phys. 16 1175) based on the Hatsugai–Kohmoto model have examined the stability of s -wave superconductivity in strongly correlated systems, demonstrating that correlations alone can substantially modify superconducting (SC) behavior. Motivated by this perspective, but going beyond these studies, we perform self-consistent microscopic calculations of d -wave superconductivity in strongly correlated systems by employing an exactly solvable correlated model that hosts a pseudogap phase and a partially flat band (Worm et al 2024 Phys. Rev. Lett. 133 166501). We show that pseudogap correlations and SC order affect the low-energy spectrum in qualitatively different ways: the former leads to a momentum-localized suppression of spectral weight, whereas the latter induces a coherent reorganization of quasiparticle excitations. Moreover, we demonstrate that the interplay between SC order and pseudogap correlations naturally generates a SC dome in the temperature-doping phase diagram, with optimal doping located near the quantum critical point separating the pseudogap and metallic phases. Furthermore, d x 2 − y 2 -wave superconductivity is found to be remarkably robust, remaining energetically dominant over both d x y -wave and s -wave pairing channels across a wide doping range. Our results offer a potential route for a direct and controlled connection between pseudogap correlations and the emergence of the SC dome in cuprates.
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xc{x}_{c}xc​, the end point of the superconducting dome on the overdoped side, where the cuprate is believed to be well described by the Fermi-liquid theory. This is the most evident in the observed ${\ensuremath{\rho}}_{s}(0)\ensuremath{-}{T}_{c}$ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the ddd-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around x∗{x}^{*}x∗, the so called pseudogap end point. Through a systematic variational Monte Carlo (VMC) study of the disordered 2D $t\ensuremath{-}J$ model from the resonating valence bond (RVB) perspective, we find that the ddd-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional ddd-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the ddd-wave RVB pairing of the charge-neutral spinons becomes essentially immune to the disorder potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at x∗{x}^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>{x}^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xc{x}_{c}xc​.
We use a variational approach to gain insight into the strongly correlated ddd-wave superconducting state of the high Tc{T}_{c}Tc​ cuprates at T=0T=0T=0. We show that strong correlations lead to qualitatively different trends in pairing and phase coherence: the pairing scale decreases monotonically with hole doping while the superconducting order parameter shows a nonmonotonic dome. We obtain detailed results for the doping dependence of a large number of experimentally observable quantities, including the chemical potential, coherence length, momentum distribution, nodal quasiparticle weight and dispersion, incoherent features in photoemission spectra, optical spectral weight, and superfluid density. Most of our results are in remarkable quantitative agreement with existing data and some of our predictions, first reported in Phys. Rev. Lett. 87, 217002 (2001), have been recently verified.
The phase diagram of the superconducting cuprates is a manifestation of quantum phase transition (QPT). There is still controversy if the quantum fluctuations generating the pseudogap region is a precursor to the superconducting region or they are competing phases. By modelling the basic possible Hamiltonian for this class of materials as a nonlinear dynamic system, using doping as the tuning parameter, it is possible to obtain a visualized phase diagram which captures fairly the phase diagram of the superconducting cuprates. The numerical results depict that as we doped from slight to optimal, there are three quantum critical points (QCPs): the first at the QPT from the Mott insulator and antiferromagnetic (AFM) phase to the pseudogap at slight doping, the second at the QPT from the pseudogap to the superconducting phase at minimum doping and the third is a hidden QPT due to collapse of the pseudogap around optimal doping. Therefore, the results obtained here in the context of nonlinear dynamic visualization shed new light on the study of the phase diagram of the high TC superconducting cuprates.
A tale of two pairs: on the origin of the pseudogap end point in the high-Tc_{c}c​ cuprate superconductors
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xcx_{c}xc​, the end point of the superconducting dome on the overdoped side, where the cuparte is believed to be well described by the fermi liquid theory. This is the most evident in the observed ρs(0)−Tcρ_{s}(0)-T_{c}ρs​(0)−Tc​ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the d-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around x∗x^{*}x∗, the so-called pseudogap end point. Through a systematic variational optimization of the disordered 2D t−Jt-Jt−J model from the resonating valence bond(RVB) perspective, we find that the d-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional d-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the d-wave RVB pairing of the charge neutral spinons becomes essentially immune to the impurity potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at x∗x^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>x^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xcx_{c}xc​.