Anderson localization in strongly anisotropic metals

Conditions for Anderson localization are derived for three cases: (1) anisotropic three-dimensional metal, (2) quasi-two-dimensional metal, and (3) quasi-one-dimensional metal. For all these cases the conductivity at T=0 as well as the interference correction are calculated. The simplest models are used. From the estimate Δσ/σ∼1, localization conditions are obtained. It is shown that localization takes place in all three cases but in cases (2) and (3) the critical value of the random potential is essentially reduced if the overlap integrals are small. In a two-dimensional metal this refers to the conductivity along the planes whereas for the conductivity perpendicular to the planes the three-dimensional condition applies, i.e., contrary to common wisdom localization in this direction is more difficult to reach than along the planes.