Quantum critical metals in 4 − ε dimensions

Abstract

We study the quantum theory of a Fermi surface coupled to a gapless boson scalar in D = 4 − ε space-time dimensions as a simple model for non-Fermi liquids (NFL) near a quantum phase transition. Our analysis takes into account the full backreaction from Landau damping of the boson, and obtains an RG flow that proceeds through three distinct stages. Above the scale of Landau damping, the Fermi velocity flows to zero, while the coupling evolves according to its classical dimension. Once damping becomes important, its backreaction leads to a crossover regime where dynamic and static damping effects compete and the fermion self-energy does not respect scaling. Below this crossover and having tuned the boson to criticality, the theory flows to a z = 3 scalar interacting with an NFL. We finally analyze the IR phases of the theory with arbitrary number of flavors N c . When N c is small, the superconducting dome covers the NFL behavior; strikingly, for moderately large N c , we find that NFL effects become important first, before the onset of superconductivity. A generic prediction of the theory is that the Fermi velocity and quasiparticle residue vanish with a power law ω ε as the fixed point is approached. These features may be useful for understanding some of the phenomenology of high- T c materials in a systematic ε expansion.