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arXiv · 2510.19515

Intrinsic nonlinear Hall effect beyond Bloch geometry

Raffaele Resta
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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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Raffaele Resta. 2025-10-22. Intrinsic nonlinear Hall effect beyond Bloch geometry. https://doi.org/10.1103/rtdd-37y7

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