Hugo Keller

Celebrating 40 years of superconductivity in ceramic oxides, we review the history and milestones, beginning in 1986, the year of the discovery, until today. While the first years after the discovery were marked by almost daily news on cuprate oxides with enthusiastic developments and hopes for rapid applications, nowadays the interest has decreased, but the electron pairing mechanism remains a matter of debate. What has happened in these 40 years and what can be expected for the future?

Low-temperature superconductivity has been known since 1957 to be described by BCS theory for effective single-band metals controlled by the density of states at the Fermi level, very far from band edges, the electron–phonon coupling constant l, and the energy of the boson in the pairing interaction w₀, but BCS has failed to predict high-temperature superconductivity in different materials above about 23 K. High-temperature superconductivity above 35 K, since 1986, has been a matter of materials science, where manipulating the lattice complexity of high-temperature superconducting ceramic oxides (HTSCs) has driven materials scientists to grow new HTSC quantum materials up to 138 K in HgBa₂Ca₂Cu₃O₈ (Hg1223) at ambient pressure and near room temperature in pressurized hydrides. This perspective covers the major results of materials scientists over the last 39 years in terms of investigating the role of lattice inhomogeneity detected in these new quantum complex materials. We highlight the nanoscale heterogeneity in these complex materials and elucidate their special role played in the physics of HTSCs. Especially, it is highlighted that the geometry of lattice and charge complex heterogeneity at the nanoscale is essential and intrinsic in the mechanism of rising quantum coherence at high temperatures.

Early on, oxides were ruled out from superconductivity, since they are typically large-band-gap insulators. Nevertheless, a rather small number of them were found to be superconducting, with transition temperatures up to 14 K and a remarkably low carrier density. This was the starting point of K. Alex Müller (KAM) becoming interested in superconductivity in oxides. Step by step, he advanced the research on oxides and finally discovered, together with J. Georg Bednorz, high-temperature superconductivity (HTSC) in the perovskite-type compound Ba-La-Cu-O. Even though he was inspired by specific and clear ideas in his search, he added new impact in the understanding of HTSC for many years after receipt of the Nobel prize for this discovery.

The question as to why deoxidized SrTiO_3−δ becomes metallic and superconducting at extremely low levels of oxygen vacancy concentration has been a mystery for many decades. Here, we show that the real amount of effused oxygen during thermal reduction, which is needed to induce superconducting properties, is in the range of only 10¹⁴/cm³ and thus even lower than the critical carrier concentrations assumed previously (10¹⁷–10¹⁹/cm³). By performing detailed investigations of the optical and electrical properties down to the nanoscale, we reveal that filaments are forming during reduction along a network of dislocations in the surface layer. Hence, a reduced epi-polished SrTiO_3−δ crystal has to be regarded as a nano-composite consisting of a perfect dielectric matrix with negligible carrier density, which is short-circuited by metallic filaments with a local carrier density in the range of 10²⁰/cm³. We present that electro-degradation leads to a more pronounced evolution of filamentary bundles and thus can generate a superconducting state with higher T_C than thermal reduction. These findings indicate that traditional homogeneous models of superconductivity in self-doped SrTiO_3−δ need to be revised, and we propose an alternative explanation taking into account the coexistence of metallic dislocation cores with polar insulating regions allowing for polaronic coupling.

Early on oxides were ruled out from superconductivity, since these are typically large band gap insulators. Nevertheless a rather small number of them were found to be superconducting with transition temperatures up to 14 K and a remarkable low carrier density. This was the starting point of K. Alex Müller (KAM) to get interested in superconductivity in oxides. Step by step he advanced in the research in oxides and finally discovered together with J. Georg Bednorz high-temperature superconductivity (HTSC) in the perovskite type compound Ba-La-Cu-O. Even though inspired from specific and clear ideas in his search, he added new impact in the understanding of HTSC for many years after receipt of the Nobel prize for this discovery.

In this article, we review the essential properties of high-temperature superconducting cuprates, which are unconventional isotope effects, heterogeneity, and lattice responses. Since their discovery was based on ideas stemming from Jahn–Teller polarons, their special role, together with the Jahn–Teller effect itself, is discussed in greater detail. We conclude that the underlying physics of cuprates cannot stem from purely electronic mechanisms, but that the intricate interaction between lattice and charge is at its origin.

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.