Transport properties and magnetic field induced localization in the misfit cobaltite [Bi$_2$Ba$_{1.3}$K$_{0.6}$Co$_{0.1}$]$^{RS}$[CoO$_2$]$_{1.97}$ single crystal

Resistivity under magnetic field, thermopower and Hall coefficient are systematically studied for [Bi$_2$Ba$_{1.3}$K$_{0.6}$Co$_{0.1}$]$^{RS}$[CoO$_2$]$_{1.97}$ single crystal. In-plane resistivity ($ρ_{ab}$(T)) shows metallic behavior down to 2 K with a $T^2$ dependence below 30 K; while out-of-plane resistivity ($ρ_{c}(T)$) shows metallic behavior at high temperature and a thermal activation semiconducting behavior below about 12 K. Striking feature is that magnetic field induces a ln(1/$T$) diverging behavior in both $ρ_{ab}$ and $ρ_{c}(T)$ at low temperature. The positive magnetoresistance (MR) could be well fitted by the formula based on multi-band electronic structure. The ln(1/$T$) diverging behavior in $ρ_{ab}$ and $ρ_{c}(T)$ could arise from the magnetic-field-induced 2D weak localization or spin density wave.

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