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Physical review. B, Condensed matter

Superconducting pairing of holes in the antiferromagnetic state of the two-dimensional Hubbard model

Giovanni Vignale, K. S. Singwi

Published Feb 1, 1989• 22 citations
Publisher

Abstract

The weak-coupling form of the effective interaction between two holes in the antiferromagnetic state of the two-dimensional Hubbard model near half-filling is derived. It is shown to predict a Cooper instability in the singlet $d$-wave channel, with binding temperature ${T}_{c}>100$ K. Our results differ from those of the "spin-bag" theory of Schrieffer, Wen, and Zhang.

DOI
10.1103/physrevb.39.2956

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The weak-coupling form of the effective interaction between two holes in the antiferromagnetic state of the two-dimensional Hubbard model near half-filling is derived. It is shown to predict a Cooper instability in the singlet ddd-wave channel, with binding temperature Tc>100{T}_{c}>100Tc​>100 K. Our results differ from those of the "spin-bag" theory of Schrieffer, Wen, and Zhang.
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We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.
In order to investigate possible nonphonon mechanisms for superconductivity in the copper oxide compounds, the two-dimensional Hubbard model is studied in the weak-coupling limit. A scaling theory is developed which allows a consistent treatment of the coupled ln 2 ( T )-singularities arising from density wave and Cooper pairing fluctuations. For a half-filled band a spin-density-wave (antiferromagnetic) phase transition occurs, whereas for small deviations from half-filling spin fluctuations lead to a d -type superconducting phase. The method generalizes straightforwardly to finite-range interactions. The possible relevance to oxide superconductors and experimental tests are briefly discussed.
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.
We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale ${\ensuremath{\Lambda}}_{\mathrm{MF}}$ in one-loop approximation, which captures in particular the generation of an attraction in the ddd-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity, and triplet $\ensuremath{\pi}$ pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet $\ensuremath{\pi}$ pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.