Journal of Physics Condensed Matter

Superconductivity in the two-dimensional t-J model at low electron density

M. Yu. Kagan, Thomas Maurice Rice

Published May 16, 1994• 62 citations

Abstract

The two-dimensional t-J model at low electron densities is unstable against various forms of electron pairing at low enough temperatures. At parameter values J/t<<1, the leading instability, although only at very low temperature, is to p-wave pairing similar to the Hubbard model. At values of J/t>1, an instability against d-wave pairing sets in at a higher temperature as found numerically by Dagotto et al (1993). In addition, at values of J/t>2, which are beyond the threshold for a bound state in the low-electron-density limit, a region of predominantly s-wave pairing is found.

DOI: 10.1088/0953-8984/6/20/016

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Journal of Physics Condensed Matter

Superconductivity in the two-dimensional t-J model at low electron density

M. Yu. Kagan, Thomas Maurice Rice

Published May 16, 1994• 62 citations

Publisher

Abstract

DOI: 10.1088/0953-8984/6/20/016

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Development of Superconducting Correlation at Low Temperatures in the Two-dimensionalt–JModel

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T \simeq 0.2 t

. By comparison of single-particle contributions in the correlation functions, we find an effective attractive interaction between quasi-particles in

d_{x^2-y^2}

-wave pairings. It is shown that d-wave correlation grows rapidly at low temperatures for 0.5 < n < 0.9, with n being the electron density. The temperature for this growth is roughly scaled by J/2. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there is no numerical evidence of superconductivity.

We show that for low and moderate fillings the ground state of the two-dimensional Hubbard model with positive-U and nearest-neighbor hopping is unstable with respect to d-wave pairing with

{\mathit{d}}_{\mathit{x}\mathit{y}}

symmetry of the gap wave function: \ensuremath{\Delta}\ensuremath{\sim}sin

{\mathit{k}}_{\mathit{x}}

sin

{\mathit{k}}_{\mathit{y}}

. The inclusion of the next-neighbor hopping may either suppress the pairing or change the symmetry of the superconducting state.

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-

{\mathit{T}}_{\mathit{c}}

cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.