a, Thermal conductivity of Nd-LSCO at four different dopings, above p* (p = 0.24) and below p* (p = 0.20, 0.21, 0.22), plotted as κ xx /T versus T, at H = 18 T (data points). We see that κ xx increases below p*. b, Same as a but for Nd-LSCO p = 0.21 (blue; H = 18 T) and LSCO p = 0.06 (green, H = 16 T). We see that κ xx continues to increase as we lower p further. This shows that phonons conduct better at lower p. A natural explanation is that they are less scattered by charge carriers as the material becomes less metallic. c, Same data as in a for Nd-LSCO p = 0.21 (blue data points) and p = 0.24 (red data points), compared to the electrical conductivity of those same samples, plotted as L 0 /ρ versus T (lines; measured at H = 33 T (ref. 17)). The latter curves are a reasonable estimate of the electronic thermal conductivity \({\kappa }_{xx}^{{\rm{el}}}\), exact at T → 0 (since the Wiedemann–Franz law is satisfied40), as seen in Fig. 2a. d, Estimate of the phonon conductivity, defined as \({\kappa }_{xx}^{{\rm{ph}}}={\kappa }_{xx}-{L}_{0}T/\rho \), plotted as \({\kappa }_{xx}^{{\rm{ph}}}/T\) versus T (using data from c) (data points). We see that \({\kappa }_{xx}^{{\rm{ph}}}(T)\) increases upon crossing below p*, most probably because electron–phonon scattering is weakened by the loss of carrier density. There is no evidence that the phonons suddenly suffer from the onset of strong spin scattering below p* (which would cause \({\kappa }_{xx}^{{\rm{ph}}}(T)\) to drop below p*), such as would be required to explain the appearance of the large negative κ xy signal below p* (Fig. 3) as being due to phonon transport.