Nonadiabatic Origin of Quantum-Metric Effects in Bloch Electron Dynamics: Nonadiabatic Metric and Analogue Gravity
ORAL
Abstract
The adiabatic wave-packet dynamics of Bloch electrons has been a cornerstone of modern condensed-matter theory, providing the foundation for semiclassical transport, Berry-phase effects, and topological phenomena.
However, when perturbations vary slowly in space and time but induce interband coherence, nonadiabatic corrections beyond the adiabatic approximation are necessary.
We develop a unified framework for nonadiabatic wave-packet dynamics that extends the semiclassical ansatz to include interband mixing [arXiv:2509.00166, arXiv:2506.06439].
Using the time-dependent variational principle, we derive the leading-order nonadiabatic corrections to the wave-packet Lagrangian.
These corrections introduce a nonadiabatic metric tensor in phase space, renormalizing the quantum metric by the band gap and reformulating electron motion as forced geodesic trajectories. The metric gives rise to geometric and geodesic velocities, unifying nonlinear and nonadiabatic transport beyond Berry-phase effects.
However, when perturbations vary slowly in space and time but induce interband coherence, nonadiabatic corrections beyond the adiabatic approximation are necessary.
We develop a unified framework for nonadiabatic wave-packet dynamics that extends the semiclassical ansatz to include interband mixing [arXiv:2509.00166, arXiv:2506.06439].
Using the time-dependent variational principle, we derive the leading-order nonadiabatic corrections to the wave-packet Lagrangian.
These corrections introduce a nonadiabatic metric tensor in phase space, renormalizing the quantum metric by the band gap and reformulating electron motion as forced geodesic trajectories. The metric gives rise to geometric and geodesic velocities, unifying nonlinear and nonadiabatic transport beyond Berry-phase effects.
*This research was supported by the US National Science Foundation (NSF) through the Seed Program of the University of Delaware Materials Research Science and Engineering Center, DMR-2011824.
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Publication: Y Ren, arXiv:2506.06439
Y Ren, ME Barrero, arXiv:2509.00166
Presenters
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Yafei Ren
- University of Delaware