Conductivity sum rule, implication for in-plane dynamics, andc-axis response
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abstract

Recently observed $c$-axis optical sum rule violations indicate non-Fermi
liquid in-plane behavior. For coherent $c$-axis coupling, the observed flat,
nearly frequency independent $c$-axis conductivity $\sigma_{1}(\omega)$ implies
a large in-plane scattering rate $\Gamma$ around $(0,\pi)$ and therefore any
pseudogap that might form at low frequency in the normal state will be smeared.
On the other hand incoherent $c$-axis coupling places no restriction on the
value of $\Gamma$ and gives a more consistent picture of the observed sum rule
violation which, we find in some cases, can be less than half.