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.
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.
Previous theoretical studies [Nat. Phys. {\bf 16}, 1175 (2020)] 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 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 [Phys. Rev. Lett. {\bf 133}, 166501 (2024)]. We show that pseudogap correlations and superconducting 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 superconducting order and pseudogap correlations naturally generates a superconducting dome in the temperature-doping phase diagram, with optimal doping located near the quantum critical point separating the pseudogap and metallic phases. Furthermore, dx2−y2-wave superconductivity is found to be remarkably robust, remaining energetically dominant over both dxy-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 superconducting dome in cuprates.
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. The theory behind these 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, recently discussed in the by Buot et al. The ECHP configurational ordering (CO) at the underdoped and overdoped regions qualitatively agrees with spin texture experiments, and strongly suggests that strange metal phase can only occur in the overdoped region, in agreement with experiments.
We use a variational approach to gain insight into the strongly correlated d-wave superconducting state of the high Tc cuprates at T=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.
In a recent publication [Chen et al., Phys. Rev. B 86, 165136 (2012)], we identified a line of Lifshitz transition points separating the Fermi liquid and pseudogap regions in the hole-doped two-dimensional Hubbard model. Here, we extend the study to further determine the superconducting transition temperature in the phase diagram. By means of large-scale dynamical cluster quantum Monte Carlo simulations, we are able to identify the evolution of the d-wave superconducting dome in the hole-dope side of the phase diagram, with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. To obtain the superconducting transition temperature Tc, we employ two-particle measurements of the pairing susceptibilities. As ${t}^{\ensuremath{'}}$ goes from positive to negative values, we find the d-wave projected irreducible pairing vertex function is enhanced, and the curvature of its doping dependence changes from convex to concave, which fixes the position of the maximum superconducting temperature at the same filling ($n\ensuremath{\approx}0.85$) and constraints the dome from precisely following the Lifshitz line. We furthermore decompose the irreducible vertex function into fully irreducible, charge and spin components via the parquet equations, and consistently find that the spin component dominates the pairing vertex function in the doping range where the dome is located. Our investigations deepen the understanding of the phase diagram of the two-dimensional Hubbard model and, more importantly, pose new questions to the field. For example, we found as ${t}^{\ensuremath{'}}$ goes from positive to negative values, the curvature of the pairing strength as a function of doping changes from convex to concave, and the nature of the dominant fluctuations changes from charge degree of freedom to spin degree of freedom. The study of these issues will lead to further understanding of the phase diagram of the two-dimensional Hubbard model and also the physics of the hole-doped cuprate high-temperature superconductors.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature Tc is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have d-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.
A tale of two pairs: on the origin of the pseudogap end point in the high-Tc cuprate superconductors
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around 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)−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∗, the so-called pseudogap end point. Through a systematic variational optimization of the disordered 2D t−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∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xc.