Unconventional isotope effects in cuprate high-temperature superconductors

A brief review on unconventional oxygen-isotope ($^{16}$O/$^{18}$O) 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 H TS is discussed. For all cuprate HTS families the OIE exponent of $T_{c}$ ($\alpha_{\rm O}$) shows a generic trend: In the underdoped regime $\alpha_{\rm O}$ is large ($\alpha_{\rm O} > 0.5$) and becomes small in the optimally doped and overdoped re gime. Magnetization, magnetic torque, and muon-spin rotation ($\mu$SR) studies of the OIE on the in-plane penetration depth $\lambda_{ab}(0)$ in La$_{2-x}$Sr$_{x}$CuO$_{4}$ and Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$O$_{7-\delta}$ indicate a substantial oxygen-mass dependence of $\lambda_{ab}(0)$ which increases with reduced doping. It is remarkable that even in optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$ and La$_{2-x}$Sr$_{x}$CuO$_{4}$ a substantial OIE on $\lambda_{ab}(0)$ is observed, although the OIE o n $T_{c}$ is rather small. The oxygen-isotope shifts of $T_{c}$ and $\lambda_{ab}(0)$ exhibit a correlation that appears to be generic for various families of HTS. Furthermore, site-selective OIE investigations of Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$O$_{7-\ de lta}$ clearly reveal that the planar oxygen atoms mainly contribute to the total OIE on $T_{c}$ as well as on $\lambda_{ab}(0)$ at all doping levels. These unusual OIE, which are beyond the scheme of BCS theory, may be explained with a polaron theory.$^{1}$ It is found that the coupling of the electronic degrees of freedom to the Jahn-Teller $Q_{2}$-type mode is the origin of these isotope effects. ~\\ $^{1}$~A.~Bussmann-Holder and H.~Keller, cond-mat/0409738.