Anisotropy of microwave conductivity of YBaCuO in superconducting and normal states: Crossover 3D-2D

Imaginary part of the microwave conductivity \sigma''(T<T_c) and the resistivity \rho(T)=1/\sigma(T>T_c) along (\sigma_{ab}'' and \rho_{ab}) and perpendicular to (\sigma_c'' and \rho_c) cuprate ab-planes of YBa_2Cu_3O_{7-x} crystal were measured in the temperature range 5\leq T \leq 200 K, having varied the oxygen doping level x in the crystal from 0.07 to 0.47. The superconducting state was found to have the dependences \sigma_{ab}''(T)/\sigma_{ab}''(0) and \sigma_c''(T)/\sigma_c''(0) coincide in the optimally doped (x=0.07) crystal. With the increase of x the dependences \sigma_c''(T)/\sigma_c''(0) have smaller slope at T<T_c/3 with \sigma_{ab}''(T)/\sigma_{ab}''(0) changing slightly. The ab-plane transport in the normal state of YBa_2Cu_3O_{7-x} crystal always remains metallic. However, a crossover from Drude conductivity (at x=0.07) along the c-axis to the hopping one (at x>0.07) takes place. This is proved by both estimating minimum metallic c-conductivity and maximum tunneling c-conductivity and quantitatively comparing the measured dependences \rho_c(T) with the ones calculated in the polaron model of quasiparticles' c-transport.