Power-law liquids in the cuprates from unparticle interactions

Recent photoemission measurements of the cuprates reveal that, over a wide range of doping levels, scattering rates along the nodal direction exhibit power-law scaling as a function of frequency and temperature. We show that these observations can be qualitatively reproduced by considering interactions between electrons and unparticles --- a low-energy scale-invariant sector that emerges from integrating out the high-energy degrees of freedom. We perturbatively evaluate the electron self-energy $\Sigma$ due to interactions with both fermionic and bosonic unparticles. We find that, at low temperatures, Im$\Sigma$ exhibits the same power law in both temperature and frequency, with the exponent depending on the scaling dimension of the unparticle propagator. At high temperatures, Im$\Sigma$ is linear in temperature. We attribute these non-Fermi-liquid behaviors to the incoherent component of the unparticle propagator. We find that this incoherent nature also violates the sum rules for the density of states and the density-density correlation function. Such violations can, in principle, be observed experimentally. Our work indicates that power-law scaling in the cuprates originates from the incoherent background generated from Mott-scale physics.