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Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
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Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
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The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea property like Landau diamagnetism, as has been previously supposed. Berry phases are a new topological ingredient that must be added to Landau Fermi-liquid theory in the presence of broken inversion or time-reversal symmetry.
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