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 "hotspots" 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.

Incoherent transport in a model for the strange metal phase: Memory-matrix formalism

“…We now proceed to calculate the transport properties of this effective model within the memory-matrix (MM) formalism [33][34][35] (for more information about the technicalities of this method, see, e.g., Refs. [18,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]). The MM approach emerges as a more suitable framework to describe the non-Fermi liquid phase exhibited, since (i) it does not rely on the existence of well-defined quasiparticles at low energies, and (ii) it successfully captures the hydrodynamic regime that is expected to describe the non-equilibrium dynamics of this strongly correlated metallic phase.…”

Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals

“…( 5). As mentioned before, this method has the important advantage of not relying on the existence of long-lived quasiparticles in the system [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71].…”

“…This non-quasiparticle regime is not easily ac-cessed via the conventional Boltzmann equation approach, which usually assumes the opposite hierarchy of relaxation rates [57]. To this end, we will use here an alternative approach to describe the dynamics of these systems, namely the memory matrix approach, which does not rely on the existence of long-lived quasiparticles [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. The memory matrix method turns out to be a very useful tool to study the hydrodynamic regime in the NFL systems.…”

Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals

“…The second method that we will use in this work to calculate transport properties is the Mori-Zwanzig memory matrix approach (see, for example, Refs. [34][35][36][37][38][39][40][41][42][43][44][45][46][47]). Here, we will be very concise in explaining the technicalities of this formalism, as more details can be found in the literature [46].…”