Optical conductivity of nodal metals*

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 quasi two-dimensional cuprate (optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, optimally and underdoped YBa$_2$Cu$_3$O$_{7-\delta}$) and iron-based materials ($A$Fe$_2$As$_2$, $A=$Ba, Ca) 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.