Electronic Energy Levels in High-Temperature Superconductors

Abstract

Parent materials of high-temperature superconductors (HTSC) need to be doped to become superconducting. The optimum doping for maximum critical transition temperature T c has been analyzed for more than 20 materials. Assuming a uniform doping distribution the distance x between doped unit cells-projected into the CuO 2 plane for cuprates-shows a strong linear correlation to the inverse of T c in the form (2x) 2 = m 1 1/T c with a slope of m 1 = (2.786 ± 0.029) × 10 −15 m 2 K. The mercury cuprate homologous series HgBa 2 Ca n − 1 Cu n O 2n+2+δ with n = 1, 2, 3 has been used to demonstrate the procedure deriving the doping distance x from the optimum doping value δ.

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

“…All data fall within a small error margin on a straight line, as was already shown in the first analysis on the bcc metals by Roeser et al [31]. The obtained slope is 2.9813 × 10 −18 m 2 K, and the y-axis intersect is 0.0052 × 10 −18 m 2 K. The theoretical value would be m = h 2 /(2πk B m p ) = 3.02586 × 10 −18 m 2 K. The deviation is 0.10756 × 10 −18 m 2 K (3.55%), which is less exact as compared to the results obtained on various HTSc materials [26][27][28]. This may point out that some more refinements may be required to describe all the various crystal structures properly.…”

“…The striking result was that all data fall on a straight line when plotting the optimum doping distance, x, for the maximum T c as (2x) 2 N eff versus the inverse of T c . The resulting straight line follows the equation of a particle in a box [30] with the energy h 2 /(8M eff x 2 ) = πk B T c for n =1, where n is the number of Cu-O planes per chemical formula [28].…”

“…The calculations of the superconducting transition temperatures, T c , using this approach were started on high T c superconductors (HTSc), realizing that the distance x between the doping centers (e.g., oxygen vacancies) in the Cu-O planes may play an important role for the resulting superconducting properties of the material. In [26][27][28], such calculations were performed on YBa 2 Cu 3 O 7−δ (YBCO), the the Bi based HTSc family (Bi-2201, Bi-2212 and Bi-2223), the Tl based HTSc family (Tl-2201, Tl-2212, Tl-2223, Tl-1234), the Hg based HTSc family (Hg-1201, Hg-1212, Hg-1223) and some iron based HTSc of the so-called 1111 family [29]. The striking result was that all data fall on a straight line when plotting the optimum doping distance, x, for the maximum T c as (2x) 2 N eff versus the inverse of T c .…”

“…In the present contribution, we employ the Roeser-Huber equation developed for various types of HTSc [26][27][28][29] to calculate the superconducting transition temperatures of several metallic superconductors (elements and simple alloys) using only the data of the crystal structure and the electronic configuration, which offers a much simpler approach to calculate T c . We discuss the required changes to the formalism and present the calculation steps for several metals and simple alloys, including Pb, Al (fcc structure), Nb, V (bcc), Sn (tetragonal), NbN, NbTi, the A15 compounds and MgB 2 .…”

A correlation between ionization energies and critical temperatures in superconducting A3C60 fullerides

“…Given the relatively large separation between the alkali atoms in the molecule and the uniform background provided by the C 60 3+ anions, we use the sum of the first ionization energies of the isolated atoms. It is worth noticing that the importance of considering the ionization energies of the outermost electrons has already been mentioned by the authors in an earlier paper on HTSCs [24].…”