High Order Geometric Channels for Nonlinear Transport in Bloch Bands

Abstract:We develop a geometric perturbation theory of Bloch states for perturbations coupling via the interband Berry connection. The gauge-invariant Bargmann trace builds the dressed dispersion and connection order by order as a hierarchy \(Q^{(N)}\), starting with the quantum geometric tensor. Higher members encode multiband geometry beyond the quantum metric and Berry curvature. Connected amplitudes control vertex-order corrections, while strict-order corrections reduce to disconnected products. For a uniform electric field we find the fully coherent, purely geometric sector of the third-order response.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2607.20702 [cond-mat.mes-hall]

(or arXiv:2607.20702v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2607.20702 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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