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

TL;DR

This paper investigates how impurity effects, modeled by a new term in the fermion propagator, destabilize the non-Fermi-liquid fixed point in a 2+1D dissipative gauge theory, leading to a crossover behavior at intermediate energies.

Contribution

It demonstrates that impurity effects destabilize the non-Fermi-liquid fixed point, revealing a crossover phenomenon in the gauge theory of fermions.

Findings

Non-Fermi-liquid fixed point is unstable with impurity effects.

Effective gauge coupling vanishes at low energies.

Crossover behavior occurs at intermediate energy scales.

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 \kappa \cdot\sign(\omega)$ (where $\kappa$ is a parameter and $\omega$ is the fermion frequency), which is usually induced by impurity effects. In the previous papers, we studied this system for $\kappa = 0$, 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 $\kappa$ term. Our results show that the non-Fermi-liquid fixed point is unstable for $\kappa \neq 0$ and an effective gauge coupling constant tends to vanish at low energies. However, in intermediate energy scales, the behavior of correlation functions for $\kappa \neq 0$ is controlled by the non-Fermi-liquid fixed point at $\kappa=0$, i.e., a crossover phenomenon appears. Physical implications of this phenomenon are discussed.