Hall coefficient in two-dimensional metals with spiral magnetic order and application to cuprate high-T_c superconductors

Charge transport measurements in high magnetic fields recently shed new light on the non-superconducting ground state in cuprate high-T_c superconductors [1]. In particular, Hall measurements yield a drop of the Hall number indicating a phase transition associated with a Fermi surface reconstruction. On the theoretical side, spiral magnetic order (or quasi-order) remains a hot candidate for the Fermi surface reconstruction mechanism.

The electromagnetic response of spiral magnetic states has already been analyzed by Voruganti et al. for small relaxation rates [2]. However, the relaxation rate in the cuprate samples studied experimentally is sizable. We have, thus, derived, for the first time, a complete formula (including all interband contributions) for the Hall conductivity in the low field limit ω_cτ«1. [3]

We use the complete expressions to study the importance of a sizable relaxation rate and show that the observed Hall number drop in cuprates can be fitted with realistic parameters.

[1] Badoux et al., Nature 531, 210 (2016)
[2] Voruganti et al., Phys. Rev. B 45, 13945 (1992)
[3] Mitscherling and Metzner, Phys. Rev. B 98, 195126 (2018)