Power-law liquid in high-temperature superconductors

Inspired by recent photoemission measurements, we demonstrate that the normal state of cuprate superconductors can be described by a power-law liquid, a state of matter with a power-law self-energy $\Sigma^{\pr\pr}\sim(\omega^{2}+\pi^{2}T^{2})^{\alpha}$. The scaling exponent decreases from $\alpha\sim1$ in the overdoped Fermi-liquid state to $\alpha\lesssim\frac{1}{2}$ in the optimal and underdoped regime. We find that broad scale invariance of a power-law liquid leads to the cuprates' superconducting dome, vanishing Fermi velocity, and diverging effective mass. We propose that a power-law liquid can arise from the presence of a scale-invariant sector known as unparticles. To extend the power-law liquid framework to include the ubiquitous magnetic phases of high-$T_{c}$ superconductors, we study the local-itinerant dichotomy in iron pnictides. We show that an interplay between localized moments and itinerant electrons is needed to reproduce the spin excitations observed in inelastic neutron scattering experiments. These results further our understanding of the degrees of freedom in high-$T_{c}$ superconductors and will help formulate a consistent framework incorporating the physics of the antiferromagnetic, normal, and superconducting states