# The Unique Properties of Superconductivity in Cuprates

Müller, K A (2014). The Unique Properties of Superconductivity in Cuprates. Journal of Superconductivity and Novel Magnetism, 27(10):2163-2179.

## Abstract

Copper oxides are the only materials that have transition temperatures, T c, well above the boiling point of liquid nitrogen, with a maximum T c m $T_{\mathrm {c}}^{\mathrm {m}}$ 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 T c m $T_{\mathrm {c}}^{\mathrm {m}}$ . In the underdoped regime, i.e., below T c m $T_{\mathrm {c}}^{\mathrm {m}}$ , a pseudogap Δ* ∝ T* is found, with T* always being larger than T c, 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 T c [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.

## Abstract

Copper oxides are the only materials that have transition temperatures, T c, well above the boiling point of liquid nitrogen, with a maximum T c m $T_{\mathrm {c}}^{\mathrm {m}}$ 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 T c m $T_{\mathrm {c}}^{\mathrm {m}}$ . In the underdoped regime, i.e., below T c m $T_{\mathrm {c}}^{\mathrm {m}}$ , a pseudogap Δ* ∝ T* is found, with T* always being larger than T c, 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 T c [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.

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