Scaling behaviour and superconducting instability in anisotropic non-Fermi liquids

TL;DR

This paper investigates the scaling properties of optical conductivity, free energy, and shear viscosity at a quantum critical point in an anisotropic non-Fermi liquid, highlighting non-universality and potential superconducting instabilities.

Contribution

It provides a detailed analysis of anisotropic scaling behaviors and the impact of hot-spot fermion-boson coupling on superconductivity in a 2D metallic system.

Findings

Optical conductivity and free energy follow expected anisotropic scalings.

Viscosity to entropy ratio varies with direction, not universal.

Fermion-boson coupling influences superconducting instability estimates.

Abstract

We study the scaling behaviour of the optical conductivity $(\sigma)$, free energy density $(F)$, and shear viscosity of the quantum critical point associated with the spin density wave phase transition for a two-dimensional metallic system with $C_2$ symmetry. A non-Fermi liquid behaviour emerges at two pairs of isolated points on the Fermi surface, due to the coupling of a bosonic order parameter to fermionic excitations at those so-called ``hot-spots''. We find that near the hot-spots, $\sigma$ and $F$ obey the scalings expected for such an anisotropic system, and the direction-dependent viscosity to entropy density ratio is not a universal number due to the anisotropy. Lastly, we also estimate the effect of the fermion-boson coupling at the hot-spots on superconducting instabilities.