Field-Induced Thermal Metal-to-Insulator Transition in Underdoped ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_{4+\delta }$

The transport of heat and charge in cuprates was measured in single crystals of ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_{4+\delta }$ (LSCO) across the doping phase diagram at low temperatures. In underdoped LSCO, the thermal conductivity is found to decrease with increasing magnetic field in the $T\to 0$ limit, in striking contrast to the increase observed in all superconductors, including cuprates at higher doping. In heavily underdoped LSCO, where superconductivity can be entirely suppressed with an applied magnetic field, we show that a novel thermal metal-to-insulator transition takes place upon going from the superconducting state to the field-induced normal state.

Figure 1

$\kappa /T$ vs $T^{\alpha -1}$ for ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_{4+\delta }$ with $x$ as shown. The lines are fits to Eq. (1).

Figure 2

${\kappa }_0(H)/T$ [normalized to $\kappa (0\mathrm{T})/T$] vs $H$. For $x=0.20$ and 0.17, an isotherm of $\kappa (H)/T$ at 60 mK is plotted instead of ${\kappa }_o/T$. The dashed lines are guides to the eye.

Figure 3

(a) Low-temperature resistivity of LSCO with $x=0.06$ in magnetic fields of 6, 8, 9, 10, 11, 12, 13, 15, and 16 T. By 12 T the superconducting transition has been suppressed to below 40 mK. Inset: resistivity of LSCO with $x=0.05$ on a semilog scale. (b) ${\kappa }_o(H)/T$ vs $H$ for LSCO with $x=0.06$. ${\kappa }_o/T$ is also shown for $x=0$ and 0.05 at zero field. The dotted line represents the estimated resolution of our experiment (see text). The error bars are statistical errors in the fitted values of ${\kappa }_o/T$ and do not include errors in the geometric factors (which do not change with field) or systematic errors in the fitting procedure (discussed in the text). The dashed line is a guide to the eye.