Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order

TL;DR

This paper derives comprehensive formulas for longitudinal and Hall conductivities in a 2D metal with spiral magnetic order, accounting for scattering effects, and relates findings to experimental observations in cuprates.

Contribution

It provides exact expressions for conductivities including interband and intraband effects, valid for any scattering rate, and connects theoretical results with recent experimental data.

Findings

Conductivities depend on scattering rate and magnetic order.

Interband contributions are negligible at small scattering rates.

Results support the applicability of simplified formulas in cuprate experiments.

Abstract

We compute the longitudinal dc conductivity and the Hall conductivity in a two-dimensional metal with spiral magnetic order. Scattering processes are modeled by a momentum-independent relaxation rate $\Gamma$. We derive expressions for the conductivities, which are valid for arbitrary values of $\Gamma$. Both intraband and interband contributions are fully taken into account. For small $\Gamma$, the ratio of interband and intraband contributions is of order $\Gamma^2$. In the limit $\Gamma \to 0$, the conductivity formulas assume a simple quasiparticle form, as derived by Voruganti et. al. [Phys. Rev. B 45, 13945 (1992)]. Using the complete expressions, we can show that relaxation rates in the regime of recent transport experiments for cuprate superconductors in high magnetic fields are sufficiently small to justify the application of these simplified formulas. The longitudinal conductivity exhibits a pronounced nematicity in the spiral state. The drop of the Hall number as a function of doping observed recently in several cuprate compounds can be described with a suitable phenomenological ansatz for the magnetic order parameter.