The intrinsic heterogeneity of superconductivity in the cuprates

In the hole-doped, high-temperature superconducting cuprates, an intrinsic heterogeneity is found, from the early observations to recent data. Below optimum doping, the heterogeneity consists of dynamic metallic and, at low temperatures, superconducting regions in the form of clusters or stripes, which develop and decay as a function of time and location in the antiferromagnetic lattice. This behaviour is underlined by the interesting linear relation between the oxygen isotope shifts of the magnetic penetration depth and the critical temperature with a slope that is a factor 2 larger than expected for the homogeneous distribution of superfluid density. Allusion is also made to the Bose-Einstein condensation reported in structurally heterogeneous, polycrystalline polymer platelets as well as especially to the heterogeneous distribution of visible and dark matter in the Universe, which point to a change of paradigm in modern physics. perspective Copyright c © EPLA, 2015 In his seminal papers, Fritz London very early assumed that a superconductor is a macroscopic quantum state as is a Bose-Einstein quantum fluid [1,2]. These states are homogeneous in space. This is also presupposed in the Bardeen, Cooper and Schrieffer (BCS) theory [3], which is well confirmed in classical elementary and intermetallic superconductors [4]. After the discovery of superconductivity in doped copper oxides [5,6], experimental evidence grew that a heterogeneity existed in these compounds, with in part remarkably high transition temperatures. This property was attributed to either the presence of chemical or structural inhomogeneity in the samples or to the existence of intrinsic heterogeneities [7]. With the remarkable advances in sample preparation, the former possibilities could be eliminated [6]. In the following, we will present evidence that in the copper oxides the observed superconductivity is present intrinsically in a dynamic inhomogeneous matrix, contrary to the original assumption of London. This invalidates a substantial part of the theories published on the subject that assume homogeneity at the outset, such as the often used RVB or t-J models. Later we discuss related superconductors, such as granular aluminium, ending with allusions to Bose-Einstein condensates in heterogeneous systems, such as polymer platelets, and the dark matter present in the Universe. Quite early after the discovery of superconductivity in the doped cuprates, a number of experiments indicated the existence of two intrinsic components. These were reviewed at the conference on “High-Tc Superconductivity 1996: Ten Years after the Discovery” by Mihailovic and Müller [8]. It was pointed out that the different techniques employed supported each other if their characteristic time scales were considered. The results of extended X-ray absorption fine-structure spectroscopy (EXAFS) with a time scale of 10−15 s by Bianconi’s group and the somewhat slower neutron pair distribution function (PDF) of Billinge’s group supported the presence of an inhomogeneous structure on the scale of the superconducting coherence length, with two distinctly different Cu-O bond lengths in the CuO2 plane. From NMR investigations on a much slower time scale of ∼10−8 s by Hammel and collaborators, a narrow line attributed to tetragonal Cu sites and a broadened signal as resulting from octahedral Cu sites with tilted axis were deduced, in agreement with the EXAFS results [8]. Furthermore, the extensive investigation of 165Tm NMR and Cu NQR in Teplov’s group in Kazan also revealed the existence of centers with orthorhombic and tetragonal symmetry [8]. The authors regarded their finding as a result of an inhomogeneous charge and spin distribution. The slow NQR and NMR observations, as compared to fast EXAFS and PDF’s,