Metallic In-Plane and Divergent Out-of-Plane Resistivity of a High-TcCuprate in the Zero-Temperature Limit

The normal-state in-plane resistivity ${\rho }_{\mathrm{ab}}$ and out-of-plane resistivity ${\rho }_c$ are measured in La-doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_y$ $\left(T_c\simeq 13\mathrm{K}\right)$ by suppressing superconductivity with 61 T pulsed magnetic fields. In the sample with the smallest ${\rho }_{\mathrm{ab}}$ ( $130\mu \Omega \mathrm{cm}$ at 100 K), metallic ${\rho }_{\mathrm{ab}}$ coexists with “semiconducting” ${\rho }_c$ down to the lowest experimental temperature, 0.66 K $(T/T_c=0.05\mathrm{})$, evidencing the non-Fermi-liquid nature of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_y$.