Enhanced Pairing of Quantum Critical Metals Near d=3+1

TL;DR

This paper investigates the dynamics of quantum critical metals near d=3+1, focusing on instabilities like BCS and CDW, and explores conditions for non-Fermi liquid behavior at intermediate energy scales.

Contribution

It develops a systematic approach to analyze BCS and CDW instabilities in quantum critical metals, including treatment of higher-order singularities and parametric regimes.

Findings

Identifies conditions where Landau damping can be controlled parametrically.

Analyzes the scales of BCS and CDW instabilities in different regimes.

Explores the possibility of non-Fermi liquid behavior above instability scales.

Abstract

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies > Lambda_{BCS}, Lambda_{CDW}.