Interference of quantum critical excitations and soft diffusive modes in a disordered antiferromagnetic metal

TL;DR

This paper investigates how quantum critical spin fluctuations and diffusive modes interact in a disordered 2D antiferromagnetic metal, revealing that higher-order processes lead to singular conductivity corrections at low temperatures.

Contribution

It introduces a low-energy theory incorporating composite modes from higher-order spin fluctuation processes, showing their dominant effect on conductivity corrections.

Findings

Higher-order spin fluctuation processes generate singular corrections.

Composite modes induce a positive 0T ln^2 T correction to conductivity.

Singular corrections dominate over non-singular first-order effects at low temperatures.

Abstract

We study the temperature-dependent quantum correction to conductivity due to the interplay of spin density fluctuations and weak disorder for a two-dimensional metal near an antiferromagnetic (AFM) quantum critical point. AFM spin density fluctuations carry large momenta around the ordering vector $\mathbf{Q}$ and, at lowest order of the spin-fermion coupling, only scatter electrons between "hot spots" of the Fermi surface which are connected by $\mathbf{Q}$. Earlier, it was seen that the quantum interference between AFM spin density fluctuations and soft diffusive modes of the disordered metal is suppressed, a consequence of the large-momentum scattering. The suppression of this interference results in a non-singular temperature dependence of the corresponding interaction correction to conductivity. However, at higher order of the spin-fermion coupling, electrons on the entire Fermi surface can be scattered successively by two spin density fluctuations and, in total, suffer a small momentum transfer. This higher-order process can be described by composite modes which carry small momenta. We show that the interference between formally subleading composite modes and diffusive modes generates singular interaction corrections which ultimately dominate over the non-singular first-order correction at low temperatures. We derive an effective low-energy theory from the spin-fermion model which includes the above-mentioned higher-order process implicitly and show that for weak spin-fermion coupling the small-momentum transfer is mediated by a composite propagator. Employing the conventional diagrammatic approach to impurity scattering, we find the correction $\delta \sigma \sim +\ln^2 T$ for temperatures above an exponentially small crossover scale.