The appearance of the gap nodes intersecting the Fermi surface in Fig. 2(d) of our Letter was due to an error in the final stage of the calculation, i.e., the unitary transformation from the orbital representation (in which we have solved the Eliashberg equation) to the band representation. The correct Fig. 2 is shown below, where the main changes appear in (d), while (a),(b) are the same, and (c),(e) remain essentially unchanged as far as the features on the Fermi surface are concerned. The diagonal elements of the gap in the band representation is fully open on the Fermi surface [schematically the upper panel of Fig. 2(b)], and the off-diagonal elements are less important in this sense. However, the main conclusions of the original Letter related to this figure do remain unaltered in the following sense. (i) The magnitude of the gap along the Fermi surface still varies significantly. (ii) Regarding the way in which the gap nodes intersecting the Fermi surface appear depending on the parameter values, we do find that the nodes in the s-wave gap nearly touch or intersect the Fermi surface for band fillings beyond 6.3, or also when we adopt a band structure obtained for the theoretically optimized lattice parameters. This is consistent with the result recently obtained by Graser et al., who have adopted a five-band model obtained by fitting a band structure of the theoretically optimized lattice structure [1]. In these cases, d wave closely competes with or dominates over s wave. This can be naturally understood as a consequence of the coexistence of (, =2) and (, 0) spin fluctuations as asserted in the original Letter.
For a newly discovered iron-based high Tc superconductor LaFeAsO1−xFx, we have constructed a minimal model, where inclusion of all the five Fe d bands is found to be necessary. Random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.
In order to explore the reason why the single-layered cuprates, La(2-x)(Sr/Ba)(x)CuO4 (T(c)≃40 K) and HgBa2CuO(4+δ) (T(c)≃90 K) have such a significant difference in T(c), we study a two-orbital model that incorporates the d(z2) orbital on top of the d(x2-y2) orbital. It is found, with the fluctuation exchange approximation, that the d(z2) orbital contribution to the Fermi surface, which is stronger in the La system, works against d-wave superconductivity, thereby dominating over the effect of the Fermi surface shape. The result resolves the long-standing contradiction between the theoretical results on Hubbard-type models and the experimental material dependence of T(c) in the cuprates.
We theoretically examine the superconducting state of BaFe 2 (As 1Àx P x ) 2 , an isovalent doping 122-iron-pnictide superconductor. We construct a three-dimensional 10-orbital model by first-principles band calculation, and investigate the superconducting gap within the spin-fluctuation-mediated pairing mechanism. The gap is basically sAE, where the gap changes its sign between electron and hole Fermi surfaces, but three-dimensional nodal structures appear in the largely warped hole Fermi surface having a strong Z 2 =XZ=YZ orbital character. The present result, together with our previous study of the 1111 systems, explains the strong material dependence of the superconducting gap in iron pnictides.
In order to understand the material dependence of T c within the single-layered cuprates, we study a two-orbital model that considers both d x 2 −y 2 and d z 2 orbitals. We reveal that a hybridization of d z 2 on the Fermi surface substantially affects T c in the cuprates, where the energy difference E between the d x 2 −y2 and the d z 2 orbitals is identified to be the key parameter that governs both the hybridization and the shape of the Fermi surface. A smaller E tends to suppress T c through a larger hybridization, whose effect supersedes the effect of diamond-shaped (better-nested) Fermi surface. The mechanism of the suppression of d-wave superconductivity due to d z 2 orbital mixture is clarified from the viewpoint of the ingredients involved in the Eliashberg equation, that is, the Green's functions and the form of the pairing interaction described in the orbital representation. The conclusion remains qualitatively the same if we take a three-orbital model that incorporates the Cu 4s orbital explicitly, where the 4s orbital is shown to have an important effect of making the Fermi surface rounded. We have then identified the origin of the material and lattice-structure dependence of E, which is shown to be determined by the energy difference E d between the two Cu 3d orbitals (primarily governed by the apical oxygen height) and the energy difference E p between the in-plane and apical oxygens (primarily governed by the interlayer separation d).
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