Real-space fluctuations of effective exchange integrals in high-Tc cuprates

We present ab-initio calculations of effective magnetic exchange, J , as well as Hubbard parameters (t, U and δε) as a function of the local distribution of doping atoms for the high-Tc superconducting (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy family. We found that both the exchange and the energies of the magnetic orbitals are strongly dependant on the local dopant distribution, both through the induced modification of the apical oxygen location and of the induced local electrostatic potential. The J real-space map, for a random distribution of dopants, positively compares with observed STS gap inhomogeneity maps. Similarly, the orbital energy fluctuations induce weak charge inhomogeneities on copper sites, that can be positively compared with the observed LDOS inhomogeneities. These results clearly support an extrinsic origin of both the gap inhomogeneities and LDOS. Since their discovery by Müller in 1986 [1], high-Tc superconductors have been the subject of an extensive research activity, both experimentally and theoretically. Recently, the question of the spatial (in)homogeneities of the superconducting state has attracted a lot of attention. Indeed, in the recent years, the improvement and development of the tunneling microscopy techniques such as Scanning Tunneling Spectroscopy (STS) have allowed the access to spatial imaging of quantities such as the density of states and the superconducting gap. Using these techniques, nanoscale spatial inhomogeneities of the gap amplitude were observed [2]. Strong fluctuations of the superconducting gap or even suppression of the superconductivity was found within islands of typical size of one nanometer in the Bi2Sr2CaCu2O8+δ (Bi-2212) compound at 4.2K, that is far below the critical temperature [3]. The origin of these gap inhomogeneities is quite controversial, however crucial since some models link the high value of Tc to electronic phases separation or disorder. The controversy opposes authors defending the idea that this is an intrinsic feature of the superconducting state [3–5], to authors defending the idea of an extrinsic origin [6], linked to the chemical inhomogeneities. The first issue is directly related to the models originating the high-Tc superconductivity in electronic phases separation [7]. Indeed, in such a case, the gap inhomogeneities would be a pure electronic effect in an otherwise (chemically and structurally) homogeneous system. The second issue emphasizes the role of the always present chemical disorder resulting from the doping process out of the Mott-Hubbard insulating parent system. Despite the unknown origin of high-Tc superconductivity it is widely accepted that the antiferromagnetic correlations play an important role in its onset, either as a competing phase [8] or as a pairing mechanism [9]. Some authors even claim a direct scaling of the critical temperature with the effective magnetic exchange, J , between adjacent copper atoms [10, 11]. In any case J plays a central role in the superconductivity onset and thus its fluctuations as a function of the chemical and structural inhomogeneities is expected to yield valuable new insight on the origin (intrinsic or extrinsic) of the observed gap and Tc spatial fluctuations. The present work proposes to study the local fluctuations of the effective exchange integral, J , as a function of the chemical and structural disorder in the (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy (CLBLCO) copper oxides family. Indeed, this family presents two determinant characteristics, (i) the effect of hole doping and of chemical disorder is decoupled 1 (ii) structural informaA simple formal charges analysis shows that the doping in the CLBLCO family is independent of the amount of calcium, x, in-