Superconductor-to-Insulator Transition and Transport Properties of Underdoped ${{\mathrm{YBa}}_2{\mathrm{Cu}}_{3}O}_{\mathit{y}}$ Crystals

The carrier-concentration-driven superconductor-to-insulator (SI) transition as well as transport properties in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ twinned crystals is studied. The SI transition takes place at $y\simeq 6.3$, carrier concentration $n_H^{\mathrm{SI}}\simeq 3\times {10}^{20}{\mathrm{cm}}^{-3\mathrm{}}$, anisotropy ${\rho }_c/{\rho }_{\mathrm{ab}}\simeq {10}^3$, and the threshold resistivity ${\rho }_{\mathrm{ab}}^{\mathrm{SI}}\sim 0.8\mathrm{m}\Omega \mathrm{cm}$ which corresponds to a critical sheet resistance $\frac{h}{{4e}^2}\simeq 6.5\mathrm{k}\Omega$ per ${\mathrm{CuO}}_2$ bilayer. The evolution of a carrier, $n_H\propto y-6.2\mathrm{}$, is clearly observed in the underdoped region. The resistivity and Hall coefficient abruptly acquire strong temperature dependence at $y\simeq 6.5$ indicating a radical change in the electronic state.