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

Abstract

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 \(T_{{\rm c}} - 300\) 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 A.