Pairing correlations in electron-doped cuprates A. A. Aligia 1 and Liliana Arrachea 2 1 Centro Ato ´mico Bariloche and Instituto Balseiro, Comisio ´n Nacional de Energı ´a Ato ´mica, 8400 Bariloche, Argentina 2 Departamento de Fı ´sica, FCEyN Universidad de Buenos Aires, Pabello ´n I, Ciudad Universitaria, 1428 Buenos Aires, Argentina Received 3 June 2001; published 13 November 2001 We calculate on-site s, extended s and d x 2 -y 2 pairing correlation functions in a generalized Hubbard model for the cuprates, for parameters appropriate for electron-doped systems, using numerical diagonalization of a 4 4 cluster. We find indications of d-wave superconductivity for small doping ( 0.1 electrons per unit cell and s-wave superconductivity for overdoped systems ( 0.5 electrons per unit cell or small U. The magnitude of the pairing correlation functions and the vertex contributions to them are in general much smaller than in the hole-doped case. We also present results for the spin-structure factor. DOI: 10.1103/PhysRevB.64.214518 PACS numbers: 74.20.-z, 71.27.+a I. INTRODUCTION The origin of the pairing mechanism and the symmetry of the order parameter in electron-doped cuprate superconduct- ors, such as Nd 1 -x Ce x CuO 4 NCCO or Pr 1 -x Ce x CuO 4 PCCO remains controversial. Tunneling experiments 1 indi- cate the presence of at least some s-wave components in the superconducting gap, and Raman measurements are consis- tent with a nearly uniformly gapped Fermi surface. 2 Microwave-penetration-depth experiments in NCCO were considered as evidence for s-wave pairing, 3 but a recent re- interpretation of similar experiments suggests a strongly an- isotropic gap in both NCCO and PCCO. 4 Also, phase- sensitive experiments in tricrystal films suggest that the order parameter has a large component with d x 2 -y 2 symmetry, 5 which is in agreement with photoemission experiments. 6 An important part of the experimental evidence might be ren- dered consistent if the order parameter contains both s and d x 2 -y 2 components. On the theoretical side, this feature is obtained in a generalized t -J model 7,8 where the ground state has a significant overlap with a resonance-valence-bond wave function. 8 However, an analysis based on a Ginzburg- Landau theory indicates that a mixed order parameter would require two phase transitions as the temperature is increased. 9 While the experimental situation is still not settled, it is important to clarify if any realistic effective model for the electron cuprates can lead to nonconventional s-wave super- conductivity or not. The electron-phonon interaction usually gives rise to an s-wave superconducting gap, but it is not expected to lead to T c of the order of 20 K in systems with a comparatively low density of states and number of carriers. Conventional superconductivity with T c =39.5 K, has been recently found in MgB 2 . 10 However, this compound is mark- edly different from the cuprates since there is a strong cou- pling with high-frequency phonon modes and a very small Coulomb repulsion. 11 Theoretically, it has been proposed that electron-phonon interaction can lead to high T c in the cu- prates, even with d x 2 -y 2 symmetry 12 if the Fermi level is near a van Hove singularity of the two-dimensional band structure leading to a high density of states at the Fermi level. As discussed below, this is clearly not the case of electron-doped cuprates. In principle, one could expect that the t -J model including next-nearest-neighbor hopping t ' is the appropriate model to describe electron-doped superconductors 13,14 see the Appen- dix. It is known that this model leads to d x 2 -y 2-wave super- conductivity. To our knowledge, a similar model leading to s-wave superconductivity has not been derived. One possi- bility in this direction is to consider excitonic pairing mechanisms 15,16 that have been proposed in the search for a common pairing mechanism in all perovskite superconduct- ors, including doped BaBiO 3 . 17 However, the results of Ref. 15 might be an artifact of the particular form chosen for the distance dependence of interatomic repulsions. An effective attraction between electrons added in next-nearest-neighbor positions, driven by nearest-neighbor Cu-O repulsion, has been obtained using perturbation theory. 16 However, a nu- merical study of the appropriate generalized t -J model that contains this interaction, indicates that this term does not lead to superconductivity. 18 The derivation of this effective model is described in the Appendix. Another effective model for the cuprates in which double occupancy at each effective Cu site is allowed is the Hubbard model with nearest-neighbor correlated hopping and next- nearest-neighbor hopping t ' . 19–21 Since the effective on-site repulsion U in this model is related to the Cu-O charge- transfer energy  , 20 and this energy is lower in electron- doped cuprates due to the absence of apical O atoms, 22 it seems particularly important here to consider a finite U. In addition, a finite U enhances the mobility of superconducting pairs. 23,24 The superconductivity in this model was studied previously within a Hartree-Fock Bardeen-Cooper-Schrieffer BCS approximation. 25,26 If t ' =0, only s-wave supercon- ductivity for high-enough doping is obtained. 25 However, for the hole-doped system with realistic or large t ' , d x 2 -y 2-wave superconductivity takes place at dopings for which the Fermi level is near the van Hove singularity, if the correlated hop- ping is large enough to overcome the antiferromagnetic instability. 26 Furthermore, the d x 2 -y 2-wave superconductiv- ity survives if the effect of short-range antiferromagnetic spin fluctuations is included. 26 This picture suggests that if the system is doped with electrons instead of holes, the Fermi surface moves away from the van Hove singularities and the dominant superconducting instability would have s-wave symmetry. This is an interesting situation; the same PHYSICAL REVIEW B, VOLUME 64, 214518 0163-1829/2001/6421/2145187/$20.00 ©2001 The American Physical Society 64 214518-1