Hydrodynamic Anomalous Hall Effect in a Two-Dimensional Dirac Fluid

A. Levchenko; D. A. Pesin

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arXiv · 2610.10733

Hydrodynamic Anomalous Hall Effect in a Two-Dimensional Dirac Fluid

A. Levchenko·D. A. Pesin

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Abstract

In ultraclean conductors, electron-electron collisions can make transport hydrodynamic. In a Berry-curved band, these collisions can also produce two-particle coordinate shifts, which contribute to the anomalous Hall current in the presence of a transport electric field. We develop a kinetic theory of this contribution for a two-dimensional massive Dirac Fermi liquid with weak contact interactions and weak short-range disorder. The computed response is independent of interaction strength at leading Born order. Its contribution to the anomalous Hall conductivity is comparable to the thermal correction to the intrinsic anomalous Hall conductivity. The existence of the momentum zero mode of the electron-electron collision integral leads to a nontrivial frequency dependence of the anomalous Hall response considered in this work. In particular, the limits of vanishing frequency (dc) and vanishing disorder do not commute. In the dc limit, the momentum response to the transport field grows inversely with the momentum relaxation rate. This allows arbitrarily weak, energy-dependent impurity scattering to produce a finite correction by coupling conserved momentum to the modes relaxed by electron-electron scattering. This correction disappears when the clean limit is taken before the zero-frequency limit. As a result, the interaction-induced Hall response retains information about the mechanism of momentum relaxation even as the overall disorder strength tends to zero.

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A. Levchenko, D. A. Pesin. 2026-10-07. Hydrodynamic Anomalous Hall Effect in a Two-Dimensional Dirac Fluid. https://arxiv.org/abs/2610.10733

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