Memory matrix theory of the dc resistivity of a disordered antiferromagnetic metal with an effective composite operator

TL;DR

This paper develops a memory-matrix theoretical framework to calculate the temperature-dependent dc resistivity in disordered antiferromagnetic metals near a spin-density-wave transition, relevant to cuprates and pnictides.

Contribution

It introduces a novel application of the memory-matrix approach combined with an epsilon expansion to analyze non-Fermi liquid behavior in disordered antiferromagnetic metals.

Findings

Resistivity shows specific temperature and doping dependence consistent with experiments.

The theory unifies transport data across different doping regimes in correlated materials.

Provides insights into non-Fermi liquid fixed points near quantum criticality.

Abstract

We perform the calculation of the dc resistivity as a function of temperature of the "strange-metal" state that emerges in the vicinity of a spin-density-wave phase transition in the presence of weak disorder. This scenario is relevant to the phenomenology of many important correlated materials, such as, e.g., the pnictides, the heavy-fermion compounds and the cuprates. To accomplish this task, we implement the memory-matrix approach that allows the calculation of the transport coefficients of the model beyond the quasiparticle paradigm. Our computation is also inspired by the $\epsilon=3-d$ expansion in a hot-spot model embedded in $d$-space dimensions recently put forth by Sur and Lee [Phys. Rev. B 91, 125136 (2015)], in which they find a new low-energy non-Fermi liquid fixed point that is perturbatively accessible near three dimensions. As a consequence, we are able to establish here the temperature and doping dependence of the electrical resistivity at intermediate temperatures of a two-dimensional disordered antiferromagnetic metallic model with a composite operator that couples the order-parameter fluctuations to the entire Fermi surface. We argue that our present theory provides a good basis in order to unify the experimental transport data, e.g., in the cuprates and the pnictide superconductors, within a wide range of doping regimes.