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Intrinsic nonlinear Hall effect beyond Bloch geometry
Phys. Rev. B 113, 125136 – Published 19 March, 2026
DOI: https://doi.org/10.1103/rtdd-37y7
Abstract
The theory of the intrinsic Hall effect, both linear and nonlinear, is rooted in a geometry which is defined in the Bloch-vector parameter space; the formal expressions are mostly derived from semiclassical concepts. When disorder and interaction are considered, there is no Bloch vector to speak of; one needs a more general quantum geometry, defined in a different parameter space. The nonlinear Hall effect is a fundamental geometric response of the many-body ground state, not a band-structure peculiarity. The higher-level geometrical formulation of the intrinsic Hall effect provides very compact expressions, which have the additional virtue—in the Bloch special case—of yielding the known results in a straightforward way: The logic is not concealed by the algebra.
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