In-Plane and Out-of-Plane Charge Dynamics of High-$T_c$ Cuprates

Abstract

We propose a theoretical expression for the $k$- and $ω$-dependent dielectric function of a stack of two-dimensional layers coupled along the direction perpendicular to the layers, and discuss some of its properties. We argue that the plasma frequencies at $k=0$ should correspond to those which are experimentally obtained from optical measurements on {\em e.g.} La$_{1-x}$Sr$_{x}$CuO$_4$ via the $f$-sum rule analysis, regardless of the fact that such systems are strongly correlated. We discuss some of the ramifications due to strong anisotropy of the charge transport in these systems, and the lack of coherence for the transport in the direction perpendicular to the layers.