Heat Transport in a Strongly Overdoped Cuprate: Fermi Liquid and a Pured-Wave BCS Superconductor

The transport of heat and charge in the overdoped cuprate superconductor ${\mathrm{T}\mathrm{l}}_2{\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_{6+\delta }$ was measured down to low temperature. In the normal state, obtained by applying a magnetic field greater than the upper critical field, the Wiedemann-Franz law is verified to hold perfectly. In the superconducting state, a large residual linear term is observed in the thermal conductivity, in quantitative agreement with BCS theory for a $d$-wave superconductor. This is compelling evidence that the electrons in overdoped cuprates form a Fermi liquid, with no indication of spin-charge separation.