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arXiv:cond-mat/0303544 · Physical review. B, Condensed matter

Coexistence of dx2−y2 -wave superconductivity and antiferromagnetism induced by a staggered field

Yasuhiro Saiga, Masaki Oshikawa

Published Sep 17, 2003• 2 citations
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Abstract

The two-dimensional $t\ensuremath{-}J$ model in a staggered field is studied by exact diagonalization of small clusters. For the low-hole-density region and a realistic value of $J/t,$ it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting correlations are enhanced while the extended-s-wave ones hardly change. This implies that coexistence of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.

DOI
10.1103/physrevb.68.094511

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The two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model in a staggered field is studied by exact diagonalization of small clusters. For the low-hole-density region and a realistic value of J/t,J/t,J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-wave superconducting correlations are enhanced while the extended-s-wave ones hardly change. This implies that coexistence of the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.
The two‐dimensional t‐J model in a staggered field is studied by exact diagonalization up to 20 sites. For the low‐hole‐density region and a realistic value of J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the dx2−y2‐wave superconducting correlations are enhanced while the extended‐s‐wave ones hardly change. This implies that coexistence of the dx2−y2‐wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.
The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-JJJ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the xy\mathrm{xy}xy components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.
The possibility of coexistence of superconductivity (SC) and antiferromagnetic long-range order (AFLRO) of the two-dimensional extended $t\text{\ensuremath{-}}J$ model in the very underdoped region is studied by the variational Monte Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and ddd-wave SC for the physical parameters, J∕t=0.3J∕t=0.3J∕t=0.3, ${t}^{\ensuremath{'}}∕t=\ensuremath{-}0.3$ and ${t}^{\ensuremath{''}}∕t=0.2$, is located near hole density ${\ensuremath{\delta}}_{c}\ensuremath{\cong}0.06$, and there is no coexistence. The phase transition is first order between these two homogeneous phases at ${\ensuremath{\delta}}_{c}$.
A two-dimensional fermionic model with attractive interactions is discussed. Its form is motivated by the phenomenology of the underdoped high-Tc{T}_{c}Tc​ cuprates, as discussed in previous literature. The exact solution to the two-particle problem leads to a bound state in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ subspace. Numerical techniques show that the model has strong ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlations in the ground state at low fermionic density. Within a self-consistent random phase approximation diagrammatic study, the model has a ddd-wave superconducting (SC) phase. The density dependence of the critical temperature is calculated. We argue that in the context of ddd-wave SC this model fulfills the role that the attractive on-site Hubbard model has played for sss-wave SC. We also show that another candidate, the attractive $t\ensuremath{-}U\ensuremath{-}V$ model, is actually not useful as a toy model for ddd-wave SC for a variety of reasons.
We examine the influence of a staggered magnetic field on states involving a few holes in the one-dimensional t-J and Hubbard models. We apply exact diagonalizations of small systems, an analytical treatment of an anisotropic model, and a high-field perturbation expansion. Our results suggest that even modest staggered fields, h\ensuremath{\ll}t, induce the formation of bound hole pairs in a broad range of parameters, in particular for J/t1 in the t-J model and for U/t>1 in the Hubbard model. In the same regions, by studying the density-density correlations and the compressibility, we argue that many holes form a paired state and that phase separation does not occur.