Conductivity sum rule, implication for in-plane dynamics and c-axis response

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 $σ_{1}(ω)$ implies a large in-plane scattering rate $Γ$ around $(0,π)$ 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 $Γ$ and gives a more consistent picture of the observed sum rule violation which, we find in some cases, can be less than half.