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Journal of the Physical Society of Japan

A New Mean-Field Superconducting Phase in Two-Dimensionalt-JModel near Half-Filling

Masao Ogata

Published Nov 15, 1997• 22 citations
Publisher

Abstract

A new superconducting phase is found in the two-dimensional t - J model near half-filling within the mean-field theory and Gutzwiller approximation. This state has a spatial dependence of order parameters which is interpreted as a mixing of the extended s -wave component with the finite total momentum in addition to the d x 2 - y 2 -wave symmetry. The origin of this peculiar pairing is investigated. There is no node in the gap function in the new state and possible experimental consequences are discussed.

DOI
10.1143/jpsj.66.3375

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Journal of the Physical Society of Japan•May 15, 2000•0 citations
A new superconducting phase is found in the two-dimensional t - J model near half-filling within the mean-field theory and Gutzwiller approximation. This state has a spatial dependence of order parameters which is interpreted as a mixing of the extended s -wave component with the finite total momentum in addition to the d x 2 - y 2 -wave symmetry. The origin of this peculiar pairing is investigated. There is no node in the gap function in the new state and possible experimental consequences are discussed.
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
New interpretation of slave boson mean-field theory of the t−Jt-Jt−J model: short-range antiferromagnetic and d-wave pairing correlations
The t−Jt-Jt−J Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field approximation and the limitation of the t−Jt-Jt−J model near half-filling, we give a new interpretation to the slave boson mean-field theory of the t−Jt-Jt−J model. We argue that due to phase coherence-breaking antiferromagnetic fluctuations and quantum fluctuations, superconducting long-range order does not appear strictly in two dimensions. TcT_{c}Tc​ resulting from interlayer pairing hopping can lead to a universal relation, when TcT_{c}Tc​ is scaled by TcmaxT^{max}_{c}Tcmax​. Systematic reduction of superfluid density and increase of (Δd)max/KBTc(Δ_{d})_{max}/K_{B}T_{c}(Δd​)max​/KB​Tc​ ratio below and near optimal doping have their natural explanation in our picture. A crossover temperature T0T^{0}T0 found in some of magnetic experiments such as NMR is also easily understood in the present framework.
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.
Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional t-J model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in the dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2-wave channel and the energy gap has a size ${\mathrm{\ensuremath{\Delta}}}_{\mathit{d}}$\ensuremath{\simeq}0.15J--0.27J between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectra is demonstrated.
Recent calculation found a new type of pairing states, i.e., a spatially oscillating d + s -wave symmetry, in the two-dimensional t - J model [M. Ogata: J. Phys. Soc. Jpn. 66 (1997) 3375.] The d + s -wave state is a possible candidate for electron-doped cuprates because the quasiparticle states in the bulk are fully-gapped reflecting the lack of nodes in k space. We calculate the local density of states near the surface for the case of d + s -wave symmetry. It is shown that a zero-energy peak shows up in the local density of states near a (110) surface, even though there is no nodes in the d + s -wave state. However, due to the absence of the nodes, we find that the zero-energy peak splits. This means that the d + s -wave state has a very unique character. The present result is compared with experimental data on Nd 1.85 Ce 0.15 CuO 4 .