Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder

Abstract

We compute the Hall angle and the magnetoresistance of the spin-fermion model, which is a successful phenomenological theory to describe the physics of the cuprates and iron-based superconductors within a wide range of doping regimes. We investigate both the role of the spin-fermion interaction that couples the large-momentum antiferromagnetic fluctuations to the so-called "hot-spots" at the Fermi surface and also of an effective higher-order composite operator in the theory. The latter operator provides a scattering mechanism such that the momentum transfer for the fermions close to the Fermi surface can be small. We also include weak disorder that couples to both the bosonic order-parameter field and the fermionic degrees of freedom. Since the quasiparticle excitations were shown in recent works to be destroyed at the "hot-spots" in the low-energy limit of the model, we employ the Mori-Zwanzig memory-matrix approach that permits the evaluation of all transport coefficients without assuming well-defined Landau quasiparticles in the system. We then apply this transport theory to discuss universal metallic-state properties as a function of temperature and magnetic field of the cuprates from the perspective of their fermiology, which turn out to be in qualitative agreement with key experiments in those materials.