Quantum interference effects in quasi-two-dimensional metals

Abstract

In connection with two groups of experimental data, a calculation is performed of quantum interference corrections in a quasi-two-dimensional metal to conductivity as a function of temperature and magnetic field. For the temperature dependence a cross-over between a two-dimensional (2D) (higher temperatures) and 3D (lower temperatures) behavior is obtained. In the 3D limit the relative correction is isotropic. In the 2D limit it is extremely anisotropic having a logarithmic dependence in the ab plane, and a power law for the c conductivity. The interaction correction to the density of states is calculated as a function of temperature. A criterion for the crossover from 2D to 3D behavior differs strongly from the interference correction, and makes the 2D limit unlikely. In the 3D limit this correction is proportional to $\sqrt{T}.$ Comparison between corrections of different origins favors the interference logarithmic correction for the in-plane conductivity, in agreement with experiment. The c-axis correction can be of either origin, and is nonlogarithmic, as observed in some experiments. The dependence of the relative correction on magnetic field in the 3D limit is always proportional to $\sqrt{H},$ in agreement with experiment, and the coefficient depends only on the orientation of the magnetic field.