Quantum Critical Transport and the Hall Angle

TL;DR

The work addresses the puzzling difference in temperature scaling between the Hall angle and the DC conductivity in strongly interacting quantum critical systems. Using holographic lattices within an Einstein-Maxwell-Dilaton framework, it reveals a two-term decomposition of the DC conductivity, $\sigma_{DC} = \sigma_{ccs} + \sigma_{diss}$, where $\sigma_{ccs}$ is charge-conjugation symmetric and persists at finite density, while $\sigma_{diss}$ encodes momentum relaxation. In contrast, the Hall angle is governed by a single dissipative term, yielding $\theta_H \sim \sigma_{diss}$ (with $\theta_H \sim (B/\mathcal{Q})\sigma_{diss}$ in the small-$B$ limit), thereby decoupling its scaling from $\sigma_{DC}$. This mechanism provides a natural route to anomalous Hall scaling in strongly coupled quantum critical systems and may extend beyond holography to hydrodynamics and other strongly interacting theories. The results offer qualitative insights into cuprate phenomenology and suggest a crossover scenario for resistivity driven by the competing roles of $\sigma_{ccs}$ and $\sigma_{diss}$.

Abstract

In this letter we study the Hall conductivity in holographic models where translational invariance is broken by a lattice. We show that generic holographic theories will display a different temperature dependence in the Hall angle as to the DC conductivity. Our results suggest a general mechanism for obtaining an anomalous scaling of the Hall angle in strongly interacting quantum critical systems.

Figures (2)

• Figure 1: At weak coupling, the conductivity of a charge-conjugation symmetric theory can be understood as arising from particle hole pairs of opposite momenta.
• Figure 2: In the presence of a magnetic field, the particle-hole pairs responsible for $\sigma_{ccs}$ are deflected in the same direction. They therefore cannot carry a Hall current.