# Conductivity sum rule, implication for in-plane dynamics, andc-axis response Academic Article

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• 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.