Wiedemann-Franz law and abrupt change in conductivity across the pseudogap critical point of a cuprate superconductor

The thermal conductivity $\kappa$ of the cuprate superconductor La${}_{1.6-x}$Nd${}_{0.4}$Sr${}_x$CuO${}_4$ was measured down to 50 mK in seven crystals with doping from $p=0.12$ to $p=0.24$, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term ${\kappa }_0\mathrm{/}T$ as $T\to 0$ across the pseudogap critical point $p^{\star }=0.23$. In the normal state, we observe an abrupt drop in ${\kappa }_0\mathrm{/}T$ upon crossing below $p^{\star }$, consistent with a drop in carrier density $n$ from $1+p$ to $p$, the signature of the pseudogap phase inferred from the Hall coefficient. A similar drop in ${\kappa }_0\mathrm{/}T$ is observed at $H=0$, showing that the pseudogap critical point and its signatures are unaffected by the magnetic field. In the normal state, the Wiedemann-Franz law, ${\kappa }_0\mathrm{/}T=L_0\mathrm{/}\rho (0)$, is obeyed at all dopings, including at the critical point where the electrical resistivity $\rho (T)$ is $T$-linear down to $T \to 0$. We conclude that the non-superconducting ground state of the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as conventional electrons do.