We study the optical conductivity $\sigma \left(\Omega \right)$ of an electron system near a quantum-critical point with finite-wavelength ordering. $\sigma \left(\Omega \right)$ vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical collective modes, which dissipate the current. This coupling introduces a nonuniversal energy scale. Depending on the parameters of each specific system, a variety of responses arise near criticality: scaling peaks at a temperature- and doping-dependent frequency, peaks at a fixed frequency, or no peaks to be associated with criticality. Therefore the lack of scaling in the far-infrared conductivity in cuprates does not necessarily call for new concepts of quantum criticality.

• Received 26 March 2007

DOI:https://doi.org/10.1103/PhysRevB.75.140505