Delocalized Fermions in Underdoped Cuprate Superconductors

Low-temperature heat transport was used to investigate the ground state of high-purity single crystals of the lightly doped cuprate ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.33}$. Samples were measured with doping concentrations on either side of the superconducting phase boundary. We report the observation of delocalized fermionic excitations at zero energy in the nonsuperconducting state, which shows that the ground state of underdoped cuprates is a thermal metal. Its low-energy spectrum appears to be similar to that of the $d$-wave superconductor, i.e., nodal. The insulating ground state observed in underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ is attributed to the competing spin-density-wave order.

Figure 1

Thermal conductivity of underdoped cuprates YBCO and LSCO. Both have a hole concentration $p$ close to, but less than $p_{\mathrm{SC}}$, the critical concentration for the onset of superconductivity. The YBCO sample shows a sizable residual linear term ${\kappa }_0/T$, indicating the presence of delocalized fermionic carriers of heat. The LSCO sample shows a vanishingly small value of ${\kappa }_0/T$, consistent with an insulating state.

Figure 2

Residual thermal conductivity as a function of carrier density $p$ for YBCO (circles) and LSCO (triangles). The fermionic heat conductivity decreases with decreasing $p$ in both cases, but at $p_{\mathrm{SC}}$ it goes to zero in LSCO while it remains finite in YBCO. Dashed lines are guides to the eye. Inset: Zoom on region close to $p_{\mathrm{SC}}$.

Figure 3

Temperature dependence of thermal conductivity for $p>p_{\mathrm{SC}}$ in YBCO and LSCO, in both the superconducting state ($H=0$) and the normal state ($H>H_{c2}$). The doping $p$ is just above $p_{\mathrm{SC}}$, $p=0.051$ with $T_c=0.1\mathrm{K}$ in YBCO and $x=p=0.06$ with $T_c=5\mathrm{K}$ in LSCO.