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arXiv:2507.08398 · Physical review. B./Physical review. B

Strengthened correlations near [110] edges of d -wave superconductors in the t − J model with the Gutzwiller approximation

A. Joki, M. Fogelström, T. Löfwander

Published Dec 9, 2025• 0 citations
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Abstract

We report results of a study of strongly correlated d -wave superconducting slabs within a t - model solved using the statistically consistent Gutzwiller approach. For different dopings, we model slabs cut at 45 ∘ relative to the main crystallographic a b axes, i.e., [110] orientation, and conclude that quasiparticle charge is drawn to the edges. Thus, the correlations are locally strengthened, and a region near the edge is closer to the Mott- insulating state with reduced hopping amplitudes on the links. Superconductivity is locally weakened near the edges in the correlated state, and the spectral weight of zero-energy Andreev bound states is substantially reduced compared to weak coupling theory. The renormalization of the edge states leaves no room for an extended s -wave component to form for hole dopings ranging from strongly underdoped to slightly overdoped.

DOI
10.1103/5bl6-g7x4

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We report results of a study of strongly correlated d -wave superconducting slabs within a t - model solved using the statistically consistent Gutzwiller approach. For different dopings, we model slabs cut at 45 ∘ relative to the main crystallographic a b axes, i.e., [110] orientation, and conclude that quasiparticle charge is drawn to the edges. Thus, the correlations are locally strengthened, and a region near the edge is closer to the Mott- insulating state with reduced hopping amplitudes on the links. Superconductivity is locally weakened near the edges in the correlated state, and the spectral weight of zero-energy Andreev bound states is substantially reduced compared to weak coupling theory. The renormalization of the edge states leaves no room for an extended s -wave component to form for hole dopings ranging from strongly underdoped to slightly overdoped.
We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.
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In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
The spectral weights (SW's) for adding and removing an electron of the Gutzwiller projected ddd-wave superconducting (SC) state of the $t\text{\ensuremath{-}}J$-type models are studied numerically on finite lattices. We restrict the study to the uniform system but exactly treat the strong correlation between electrons, we show that the product of weights is equal to the pairing amplitude squared, the same as in the weakly coupled case. In addition, we derive a rigorous relation of SW with doping in the electron doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the SC gap energy and, also, the anticorrelation between gap sizes and peak heights observed in tunneling spectroscopy on high Tc{T}_{c}Tc​ cuprates.
Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.
Antiferromagnetism, charge density wave, and d-wave superconductivity in the ttt-JJJ-UUU-VVV model of correlated electrons: Role of direct Coulomb interactions
We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the ttt-JJJ-UUU-VVV model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term VVV in stabilizing the CDW phase and show it appears only above some critical values of VVV and in a limited hole doping range δ\deltaδ. The effect of the term VVV on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.