Intrinsic nonlinear Hall effect beyond Bloch geometry

TL;DR

This paper extends the understanding of the nonlinear Hall effect by developing a quantum geometric framework beyond traditional Bloch band theory, applicable to disordered and interacting systems.

Contribution

It introduces a general quantum geometry approach to describe the intrinsic nonlinear Hall effect beyond Bloch band geometry, applicable to many-body ground states.

Findings

Provides a compact geometric expression for the nonlinear Hall effect.

Shows the new formulation reduces to known results in the Bloch case.

Highlights the importance of quantum geometry in disordered and interacting systems.

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.