Pseudogap in the microwave response of YBa_2Cu_3O_{7-x}

Abstract

The in-plane and out-of-plane surface impedance and microwave conductivity components of one and the same YBa_2Cu_3O_{7-x} (0.07\le x\le 0.47) single crystal are determined in the wide ranges of temperature T and carrier concentration p in CuO_2 planes. The following features of the superfluid density n_s(T,p)\propto\lambda_{ab}^{-2}(T,p) are observed at T<Tc/2 and 0.078\le p\le 0.16: (i) n_s(0,p) depends linearly on p, (ii) the derivative |dn_s(T,p)/dT|_{T\to 0} depends on p slightly in the optimally and moderately doped regions (0.10<p\le 0.16); however, it rapidly increases with p further lowering and (iii) the latter finding is accompanied by the linear low-temperature dependence \Delta n_s(T)\propto(-T) changing to \Delta n_s(T)\propto(-\sqrt{T}). For optimum oxygen content the temperature dependence of the normalized imaginary part of the c-axis conductivity \lambda_c^2(0)/\lambda_c^2(T) is found to be strikingly similar to that of \lambda_{ab}^2(0)/\lambda_{ab}^2(T) and becomes more convex with p lowering. \lambda_c^{-2}(0,p) values are roughly proportional to the normal state conductivities \sigma_c(T_c,p) along the c-axis. All these properties can be treated in the framework of d-density wave order of pseudogap.