Absence of Quantum-Metric-Induced Intrinsic Longitudinal Response

TL;DR

This paper proves that the intrinsic longitudinal nonlinear response induced by the quantum metric in solids is zero, clarifying theoretical inconsistencies and refining understanding of quantum geometric effects in charge transport.

Contribution

It demonstrates that the quantum-metric-induced intrinsic longitudinal response vanishes, resolving previous theoretical ambiguities and challenging recent claims of such effects.

Findings

Quantum-metric-induced intrinsic longitudinal response is identically zero.

Intrinsic nonlinear Hall response remains allowed and non-zero.

Clarifies the dissipationless nature of intrinsic currents in quantum transport.

Abstract

Nonlinear charge transport in solids has emerged as a powerful probe of the quantum geometric properties of Bloch electrons. While the Berry curvature underlies the intrinsic anomalous Hall effect, recent studies have suggested that the quantum metric may generate both \emph{intrinsic} nonlinear Hall and longitudinal transport. Here, using standard quantum-mechanical perturbation theory, we demonstrate that the quantum-metric-induced intrinsic longitudinal response identically vanishes, even though the corresponding intrinsic Hall response is allowed. This conclusion follows from the dissipationless nature of intrinsic currents and holds independently of band structure details and to all orders in the nonlinear response. Our work resolves existing inconsistencies in the theoretical formulation of quantum-metric-induced nonlinear transport and suggests a reexamination of recently reported intrinsic longitudinal responses attributed to the quantum metric.