Logarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ in the Zero-Temperature Limit

The low-temperature normal-state resistivities of underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ crystals with $T_c$ of 20 and 35 K were studied by suppressing the superconductivity with pulsed magnetic fields of 61 T. Both in-plane resistivity ${\rho }_{\mathrm{ab}}$ and out-of-plane resistivity ${\rho }_c$ are found to diverge logarithmically as $\frac{T}{T_c}\to 0$. Logarithmic divergence is accompanied by a nearly constant anisotropy ratio, $\frac{{\rho }_c}{{\rho }_{\mathrm{ab}}}$, suggesting an unusual three-dimensional insulator.