Coherence, incoherence and scaling along the c axis of YBa_2Cu_3O_{6+x}

TL;DR

This study investigates the c-axis optical properties of YBa_2Cu_3O_{6+x} across various doping levels, revealing a transition from incoherent to more coherent transport and confirming a scaling relation consistent with Josephson coupling in the superconducting state.

Contribution

It demonstrates a universal scaling relation between superconducting condensate strength, critical temperature, and normal-state conductivity along the c axis across different doping levels.

Findings

Crossover from incoherent to coherent transport with increased doping

Scaling relation  ho_{s,c} propto  \sigma_{dc} T_c observed

Materials tend towards coherence at higher oxygen dopings

Abstract

The optical properties of single crystals of YBa_2Cu_3O_{6+x} have been examined along the c axis above and below the critical temperature (T_c) for a wide range of oxygen dopings. The temperature dependence of the optically-determined value of the dc conductivity (\sigma_{dc}) in the normal state suggests a crossover from incoherent (hopping-type) transport at lower oxygen dopings (x \lesssim 0.9) to more coherent anisotropic three-dimensional behavior in the overdoped (x \approx 0.99) material at temperatures close to T_c. The assumption that superconductivity occurs along the c axis through the Josephson effect yields a scaling relation between the strength of the superconducting condensate (\rho_{s,c}, a measure of the number of superconducting carriers), the critical temperature, and the normal-state c-axis value for \sigma_{dc} just above T_c; \rho_{s,c} \propto \sigma_{dc} T_c. This scaling relation is observed along the c axis for all oxygen dopings, as well as several other cuprate materials. However, the agreement with the Josephson coupling model does not necessarily imply incoherent transport, suggesting that these materials may indeed be tending towards coherent behavior at the higher oxygen dopings.