The Wiedemann-Pranz ratio in YBa₂Cu₃O_7-δ determined from the thermal Hall conductivity

The Wiedemann Franz ratio, expressed as the Lorenz number ℒ= (e/k_B)²κ_e/σT, provides important information on the charge and entropy carriers. In the normal state of the cuprates, ℒ is not known reliably because the phonon conductivity dominates the electronic thermal conductivity κ_e. To get around the phonon background, we have measured with high precision the thermal Hall conductivity κ_xy (which does not involve phonons), and formed the Hall Lorenz number ℒ_xy = (e/k_B)²κ_xy/σ_xyT. The method was checked against high purity copper. We find that ℒ_xy in YBCO is linear in T and strongly suppressed from the Sommerfeld value, in conflict with previous claims. Implications of the finding will be discussed.