Transverse conductivity in Pr $$_y$$ y Y $$_1-y$$ 1 - y Ba $$_2$$ 2 Cu $$_3$$ 3 O $$_7-\delta $$ 7 - δ single crystals in a wide range of praseodymium concentrations

The electrical resistance across the layers of high-quality Pr(_y)Y(_1-y)Ba(_2)Cu(_3)O(_7-delta ) single crystals is measured in the temperature interval (T_{{ m c}} - 300) K and the praseodymium concentration range (0 le y le 0.5). The experimental data are approximated by a relation accounting for the fluctuation conductivity in the 3D Aslamazov–Larkin model, a metal-like contribution limited by scattering on impurities and phonons for (0 le y le 0.23), as well as a semiconductor-like contribution for (0.23 le y le 0.5), where the carriers mobility is determined by scattering on ionized impurities. Our analysis of the concentration dependences of the fitting parameters shows that at (0.23 le y le 0.5) the samples are heterogeneous and the conductivity is realized by variable-range hopping between regions with different praseodymium concentrations. The in-plane coherence length (xi _xy(0)) amounts to 100 Å.