A brief review on unconventional oxygen-isotope (¹⁶O/¹⁸O) effects (OIE) in cuprate high-temperature superconductors (HTS) is presented. First the doping dependence of the OIE on the superconducting transition temperature T_C in various HTS is discussed. For all cuprate HTS families the OIE exponent of T_C (α_O) shows a generic trend: In the underdoped regime α_O is large (α_O > 0.5) and becomes small in the optimally doped and overdoped regime. Magnetization, magnetic torque, and muon-spin rotation OIE studies of the in-plane penetration depth λ_ab(0) in doped La_2-xSr_xCuO₄ and Y_1-xPr_xBa₂Cu₃O_7-δ indicate a substantial oxygen-mass dependence of the quantity λ_ab^-2(0), proportional to the superfluid density ρ_s(0) which increases with reduced doping. Even at optimal doping, where the OIE on T_C is small, a pronounced OIE on λ_ab(0) is present [1]. Note that an OIE on the penetration depth is not expected for a conventional phonon-mediated superconductor (for which the Migdal adiabatic approximation holds). The oxygen-isotope shifts of T_C and λ_ab(0) exhibit a correlation that appears to be generic for various families of HTSC. Site-selective OIE investigations of Y_1-xPr_xBa₂Cu₃O_7-δ clearly reveal that the planar oxygen atoms mainly contribute to the total OIE on T_C as well as on λ_ab(0) at all doping levels. These unusual isotope effects strongly suggest that lattice effects play an essential role in the basic physics of cuprate HTS and have to be considered in any realistic theoretical model.
[1] R. Khasanov et al., Phys. Rev. Lett. 92, 057602-1 (2004).

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