The Unique Properties of Superconductivity in Cuprates

Copper oxides are the only materials that have transition temperatures, Tc, well above the boiling point of liquid nitrogen, with a maximum Tcm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{\mathrm {c}}^{\mathrm {m}}$\end{document} of 162 K under pressure. Their structure is layered, with one to several CuO2 planes, and upon hole doping, their transition temperature follows a dome-shaped curve with a maximum of Tcm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{\mathrm {c}}^{\mathrm {m}}$\end{document}. In the underdoped regime, i.e., below Tcm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{\mathrm {c}}^{\mathrm {m}}$\end{document}, a pseudogap Δ* ∝ T* is found, with T* always being larger than Tc, a property unique to the copper oxides. In the superconducting state, Cooper pairs (two holes with antiparallel spins) are formed that exhibit coherence lengths on the order of a lattice distance in the CuO2 plane and one order of magnitude less perpendicular to it. Their macroscopic wave function is parallel to the CuO2 plane near 100 % d at their surface, but only 75 % d and 25 % s in the bulk, and near 100 % s perpendicular to the plane in yttrium barium copper oxide (YBCO) [1]. There are two gaps with the same Tc [2]. As function of doping, the oxygen isotope effect is novel and can be quantitatively accounted for by a vibronic theory or by the presence of bipolarons [2, 3]. These cuprates are intrinsically heterogeneous in a dynamic way. In terms of quasiparticles, bipolarons are present at low doping and aggregate upon cooling [2] so that probably ramified clusters and/or stripes are formed, leading over to a more Fermi liquid-type behavior at large carrier concentrations.