Quenched disorder at antiferromagnetic quantum critical points in $2d$ metals

Abstract

We study spin density wave quantum critical points in two dimensional metals with a quenched disorder potential coupling to the electron density. Adopting an $\epsilon$-expansion around three spatial dimensions, where both disorder and the Yukawa-type interaction between electrons and bosonic order parameter fluctuations are marginal, we present a perturbative, one-loop renormalization group analysis of this problem, where the interplay between fermionic and bosonic excitations is fully incorporated. Considering two different Gaussian disorder models restricted to small-angle scattering, we show that the non-Fermi liquid fixed point of the clean SDW hot-spot model is generically unstable and the theory flows to strong coupling due to a mutual enhancement of interactions and disorder. We study properties of the asymptotic flow towards strong coupling, where our perturbative approach eventually breaks down. Our results indicate that disorder dominates at low energies, suggesting that the ground-state in two dimensions is Anderson-localized.

arXiv comment20 pages, 5 figures

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Cited by in corpus (5)

• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Effects of general non-magnetic quenched disorder on a spin-density-wave quantum critical metallic system in two spatial dimension
• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals