Hall effects#
Hall responses at any Fermi level, from the Berry curvature of the bands: the anomalous Hall conductivity of the Haldane model (its quantized plateau in the gap, and its non-quantized value in the bands), the same plateau surviving disorder in a real-space Kubo-Bastin (kernel polynomial) calculation on a torus, and the intrinsic spin Hall conductivity of the Kane-Mele model with its departure from quantization under Rashba coupling. The same curvature, weighted by entropy or by energy, drives the anomalous Nernst effect (with the Mott relation) and the thermal Hall effect (with the Wiedemann-Franz law and its quantized Chern plateau).
The Anomalous Hall Effect in Real Space: a Disordered Chern Insulator
The Anomalous Hall Effect: from the Anomalous Velocity to the Berry Phase
The Intrinsic Spin Hall Effect: Kane-Mele Plateau and Rashba Coupling
The Intrinsic Thermal Hall Effect and the Wiedemann-Franz Law