Evolution of the resistivity anisotropy in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>−</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>single crystals for a wide range of hole doping

To elucidate how the temperature dependence of the resistivity anisotropy of the cuprate superconductors changes with hole doping, both the in-plane and the out-of-plane resistivities $({\ensuremath{\rho}}_{\mathrm{ab}}$ and ${\ensuremath{\rho}}_{c})$ are measured in a series of high-quality ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ (BSLCO) single crystals for a wide range of $x(0.23&lt;~x&lt;~1.02),$ which corresponds to the hole doping per Cu, p, of 0.03--0.18. The anisotropy ratio, ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}},$ shows a systematic increase with decreasing p at moderate temperatures, except for the most underdoped composition where the localization effect enhances ${\ensuremath{\rho}}_{\mathrm{ab}}$ and thus lowers ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}}.$ The exact p dependence of ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}}$ at a fixed temperature is found to be quite peculiar, which is discussed to be due to the effect of the pseudogap that causes ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}}$ to be increasingly more enhanced as p is reduced. The pseudogap also causes a rapid growth of ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}}$ with decreasing temperature, and, as a result, the ${\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{\mathrm{ab}}$ value almost reaches ${10}^{6}$ in underdoped samples just above ${T}_{c}.$ Furthermore, it is found that the temperature dependence of ${\ensuremath{\rho}}_{c}$ of underdoped samples show two distinct temperature regions in the pseudogap phase, which suggests that the divergence of ${\ensuremath{\rho}}_{c}$ below the pseudogap temperature is governed by two different mechanisms.

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