Searching for high-temperature superconductivity: from Mendeleev to Seiberg–Witten via Madelung and beyond

Abstract

Recently, noticeable progress has been achieved in the area of high-temperature superconductors. Maximum temperatures Tc of 250 K (−23○ C) for LaH10 and 288 K (+15○ C) for CSH8 have been reported at megabar pressures. The highest possible Tcs were achieved by employing hydrides of chemical elements. Empirically, many of these are made of Madelung-exceptional atoms. Here, the theoretical background is provided to explain this observation. The, thus far empirical, Madelung rule controls Mendeleev’s law of periodicity. Although the majority of elements do obey this rule, there are some exceptions. Thus, it is of interest to derive it and its exceptions theoretically in view of experimental findings. As a by-product, such a study yields a plausible explanation of the role of Madelung-exceptional atoms in the design of high-Tc superconductors. Thus far the atoms obeying the Madelung rule and its exceptions have been studied with help of relativistic Hartree–Fock calculations. In this work we reobtain both the rule and the exceptions analytically. The newly developed methods are expected to be of value in quantum many-body theory and, in particular, in the theory of high-Tc superconductivity. Ultimately, the new methods involve some uses of the Seiberg–Witten theory known as the extended Ginzburg–Landau theory of superconductivity. Using results of Sieberg–Witten theory, the difference between Madelung-regular and Madelung-exceptional atoms is explained in terms of the topological transition. The extension of this single-atom result to solids of the respective elements is also discussed.