Localization in highly anisotropic systems and anomalous resistivity in cuprate-oxide superconductors

Anderson localization in highly anisotropic systems is briefly discussed. We point out that both the highly anisotropic band structure and the anisotropic disordered potential may lead to metallic behaviors of the electric resistivity in one or two directions, and nonmetallic behaviors of the electric resistivity in other directions, while the electron states on the Fermi surface are still extended in all directions. In particular, we found that when the disordered potential is anisotropic, the electric resistivity in the nonmetallic direction approaches a saturated value as T → 0, via a mechanism completely different from the mechanism proposed by Jonson and Girvin. These results are then used to qualitatively explain the anomalous behaviors of the electric resistivity in various cuprate-oxide superconducting samples.