Instability of the Non-Fermi-Liquid Fixed Point in the Dissipative Gauge Theory of Fermions (I)Impurity Effects

Abstract

We study a dissipative gauge theory of nonrelativistic fermions in 2+1 dimensions at zero temperature by the Wilsonian renormalization-group method. In this theory, we incorporate in the fermion propagator a new term of the form $ i κ\cdot\sign(ω)$ (where $κ$ is a parameter and $ω$ is the fermion frequency), which is usually induced by impurity effects. In the previous papers, we studied this system for $κ= 0$, and showed that there exists a non-Fermi-liquid infrared fixed point. In this paper, we address the question whether this non-Fermi-liquid behavior remains stable or not in the presence of impurity effects, i.e., the $κ$ term. Our results show that the non-Fermi-liquid fixed point is unstable for $κ\neq 0$ and an effective gauge coupling constant tends to vanish at low energies. However, in intermediate energy scales, the behavior of correlation functions for $κ\neq 0$ is controlled by the non-Fermi-liquid fixed point at $κ=0$, i.e., a crossover phenomenon appears. Physical implications of this phenomenon are discussed.