Resolve the additional open transport problems in interacting anomalous Hall systems

Investigate dynamically screened Coulomb interactions, quantify the comparison with the first-order intrinsic anomalous Hall correction, incorporate distinguishable-species collision channels in multivalley systems, formulate finite-channel boundary-value problems, and derive conserving Hall-viscosity and anomalous-thermal-transport responses including magnetization contributions.

Background

The calculation is restricted to a single nondegenerate massive Dirac cone with weak contact interactions, bulk white-noise disorder, and no channel-wall boundary problem. The authors identify several extensions needed to determine how screening, intrinsic interaction corrections, multiple valleys or flavors, finite geometry, Hall viscosity, and anomalous thermal transport modify the hydrodynamic anomalous Hall response.

These topics are explicitly presented as open questions because the present calculation does not resolve them. In multivalley systems, the collision channels for distinguishable species must be included; equal populations of time-reversed valleys cancel the charge Hall response while allowing valley or spin Hall responses.

References

Other open questions include a controlled asymptotic evaluation of the collinear collision moments and their ratio (Sec.~\ref{sec:logs}), dynamically screened Coulomb interactions, and a quantitative comparison with the first-order intrinsic correction of Ref.. Multivalley systems require the distinguishable-species collision channels to be included; time-reversed valleys cancel the charge Hall response at equal populations and naturally support valley or spin Hall responses. Finally, a finite-channel calculation could combine the present bulk sources with the hydrodynamic framework of Ref.. Hall viscosity and anomalous thermal transport require separate conserving derivations, including the relevant magnetization contributions.

— Hydrodynamic Anomalous Hall Effect in a Two-Dimensional Dirac Fluid  (2610.10733 - Levchenko et al., 7 Oct 2026) in Summary, Conclusions, and Outlook (Section 6)