Cuprate superconductors: Universal properties and trends; evidence for Bose-Einstein condensation?

Abstract

We explore the compatibility of empirical trends in various thermodynamic properties of cuprate superconductors with the Bose-Einstein condensation scenario. These trends include the relations between transition temperature, hole concentration and superfluid density, the rise and the upper limit of the transition temperature, the dependence of pressure and isotope coefficients on the transition temperature, as well as the observed critical behavior, reminiscent of threedimensional systems with a scalar complex order parameter and short-range interactions. For this purpose we consider an interacting charged Bose gas. Owing to the high polarizability of the cuprates, the Coulomb interaction is strongly screened. Hence, the problem of calculating thermodynamic properties becomes essentially equivalent to that of the uncharged gas with short-range interactions. This problem, however, has not been solved either. Nevertheless, in the dilute limit the problem reduces to the ideal Bose gas treated by Schafroth, while in the dense regime condensation and superfluidity are suppressed, because bosons of finite extension fill the available volume. This limiting behavior provides an interpolation scheme for the dependence of both transition temperature and zero temperature superfluid density on boson density. On this basis and by relating the hole concentration in the cuprates which corresponds to the boson density and the superfluid density to the square of the inverse London penetration depth, the compatibility of the empirical trends in the cuprates with the Bose gas behavior can be verified. Our analysis reveals remarkable agreement between these trends and the corresponding Bose gas behavior. There is even strong evidence of the most striking implication of this scenario, the dependence of the transition temperature on the zero temperature superfluid density, resembling the outline of a fly’s wing. This evidence emerges from recent muon spin resonance (µSR) data for Tl2Ba2CuO6+δ and kinetic inductance measurements for La2−x Sr x CuO4 films, revealing that the penetration depths of under and overdoped samples with T c ≃ 15 K do not differ much. In view of this we have provided considerable evidence for the nature of the superconducting transition in the cuprates, without invoking any specific pairing mechanism.