What determines the Hall and Thermal Hall coefficients of metals, magnets and superconductors?

The Hall coefficient has long been used to characterize the number and sign of charge carriers in metals and semiconductors. This assignment has only been justified in the weak disorder and interactions regimes. Unexpected Hall coefficient sign reversals (a.k.a. ``Hall anomalies’’) have been observed in strongly interacting metals, thermal Hall effect in antiferromagnets, and in the flux flow regime of cuprate superconductors.
I review recent theoretical advances [1,2] which shed light on Hall anomalies. New computable formulas [1] for Hall, Nernst and Thermal Hall coefficients in gapless (metallic) phases are applied to strongly correlated Hubbard and Heisenberg models, where traditional Chern number calculations and Drude-Boltzmann theory are innaplicable. We show that Hall sign reversal is a consequence of proximity to a Mott insulator,
and that a negative thermal Hall coefficient is produced in the square lattice antiferromagnet with three-spin exchanges. A revised theory of magnetotransport in the flux flow regime of superconductors [3] explains Hall anomalies caused by moving vortex charge.

1. Equilibrium formulae for transverse magnetotransport of strongly correlated metals, A. Auerbach, Phys. Rev. B 99, 115115 (2019).
2. Hall Number of Strongly Correlated Metals, A. Auerbach, Phys. Rev. Lett. 121, 066601 (2018).
3. A. Auerbach and D.P. Arovas, to be published.