Metal-insulator transition in YBa$_2$Cu$_3$O$_{\delta}$

The non-superconducting ground state of the underdoped cuprates YBa$_2$Cu$_2$O$_{\delta}$ and YBa$_2$Cu$_4$O$_8$ was examined by measuring the electrical resistivity of high-quality single crystals in magnetic fields up to 60 T. A metal-insulator-like crossover is observed near a critical doping $p$~=~0.1, i.e., far in the underdoped region. This shows that the pseudogap phase present below $T^{\star}$ is a metal, characterized by a resistivity of the Fermi-liquid form, $\rho_0 + AT^2$, where $\rho_0$ is small, just as in the strongly overdoped regime. In the metallic phase, the transverse magneto-resistance undergoes a qualitative change between $p$~=~0.14, where it saturates at high field, and $p$~=~0.11, where it does not saturate. This would suggest that a change in the nature of the ground state occurs in the vicinity of $p$~=~1/8.