  Fermi liquid theory is remarkably successful in describing the transport and
optical properties of metals; at frequencies higher than the scattering rate,
the optical conductivity adopts the well-known power law behavior
$\sigma_1(\omega) \propto \omega^{-2}$. We have observed an unusual non-Fermi
liquid response $\sigma_1(\omega) \propto \omega^{-1\pm 0.2}$ in the ground
states of several cuprate and iron-based materials which undergo electronic or
magnetic phase transitions resulting in dramatically reduced or nodal Fermi
surfaces. The identification of an inverse (or fractional) power-law behavior
in the residual optical conductivity now permits the removal of this
contribution, revealing the direct transitions across the gap and allowing the
nature of the electron-boson coupling to be probed. The non-Fermi liquid
behavior in these systems may be the result of a common Fermi surface topology
of Dirac cone-like features in the electronic dispersion.
