The Exceptional Properties of Superconductivity in Cuprates

Copper oxides are the only materials that have transition temperatures, $T_c$, \textit{above} the boiling point of liquid nitrogen, with a maximum $T_c^m$ of 162 K under pressure. Their structure is layered, with one to several CuO$_2$ planes, and upon hole doping, their transition temperature follows a dome-shaped curve with a maximum at $T_c^m$. In the underdoped regime, i.e., below $T_c^m$, a pseudogap $T$* is found, with $T$* always being larger than $T_c$, a property unique to the copper oxides [1]. In the superconducting state, Cooper pairs (two holes with antiparallel spins) are formed that exhibit coherence lengths on the order of a lattice distance \textit{in the} CuO$_2$ plane and one order of magnitude less perpendicular to it. Their macroscopic wave function is parallel to the CuO$_2$ 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 YBCO. There are two gaps with the same $T_c$ [2]. As function of doping, the oxygen isotope effect is novel and can be quantitatively accounted for by a two-band vibronic theory [3]. These cuprates are intrinsically heterogeneous in a dynamic way. In terms of quasiparticles, bipolarons are present at low doping, and aggregate upon cooling [1], so that probably ramified clusters and/or stripes are formed, leading over to a more Fermi-liquid-type behavior at large carrier concentrations above $T_c^m$. \newline \newline [1] For an overview, see: K.A.\ M\"uller, J. Phys:\ Condens.Matter \textbf{19}, 251002 (2007). \newline [2] R.\ Khasanov, A.\ Shengelaya \textit{et al.}, Phys.\ Rev.Lett.\ \textbf{98}, 0570007 (2007). \newline [3] H.\ Keller, A.\ Bussmann-Holder, and K.A.\ M\"uller, Materials Today \textbf{11}, 38 (2008).