Anisotropic resistivity of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CuO}}_{\mathit{x}}$ crystals

We report measurements of the anisotropic resistivity of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CuO}}_{\mathit{x}}$ crystals using the Montgomery method. We find that the ab-plane resistivity is nearly linear with temperature down to 10 K, but deviates slightly from linearity below 40 K. The out-of-plane resistivity is metallic above 105 K, but nonmetallic below 105 K. The anisotropy ratio ${\mathrm{\rho }}_{\mathit{c}}$/${\mathrm{\rho }}_{\mathit{a}\mathit{b}}$ is temperature dependent and the maximum value is 9×${10}^4$ at low temperature. We estimate the effective mass, the Fermi energy, and Fermi velocity, etc., using Kresin and Wolf’s model. The plasma frequency and the transport electron-phonon coupling constant ${\lambda }_{\mathrm{tr}}$ are also calculated in a self-consistent way in combination with our resistivity and Hall coefficient data. We discuss the resistivity in the context of existing theories.