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8
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84926550538
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Similar ideas have been discussed recently in the context of the Hubbard model by N. Bulut, D. Scalapino, and R. Scalettar (unpublished); see also R. Fye et al. (unpublished).
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In our approach a strong singlet is formed because the length of the lattice in the c direction is of only one lattice spacing. If more layers ( L) were added and keeping J prime as the dominant interaction, the model would reduce to a bundle of Heisenberg chains which are known to be gapless when L -> inf. Then, our model, Eq. (1), superconducts when the number of layers is small enough such that a spin gap exists.
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15
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Other models have been presented in the literature where tunneling of hole pairs between the Cu-O layers plays an essential role.
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J. C. Phillips (unpublished). However, in these approaches the pairs are already preformed in each plane while in the present model the pairs are formed across a link (rung) between the planes (chains).
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We have observed that at quarter filling the superconducting state is degenerate with a CDW state as in the case of the attractive Hubbard model at half filling. However, away from these fillings superconductivity dominates in both models.
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Another interesting but more speculative scenario considering the cuprate YBaCu32 O6+x has recently been discussed (see Ref. 2). In this case there are two CuO2 planes in the unit cell with J prime / J = case 1 over 40 probably outside the range of validity of our model. [See J. Jorgensen, Phys. Today 44 (6), 35 (1991), and references therein;
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The coupling J prime between the Cu-O layers of the unit cell should not be confused with the coupling between double layers which governs the Néel temperature and is much smaller.] If a new material with oxygen atoms between the two Cu-O layers of the unit cell could be prepared, then the superexchange constants would be similar ( J prime app J ) and our model could apply.
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