Quantum-Geometric Raman Response in Multiorbital Flat-Band Systems

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Original abstract

Flat-band materials host rich collective phenomena, yet a complete theory of their signatures in inelastic light scattering remains lacking. While naive theories of interacting flat bands would predict that Raman scattering vertices vanish identically in the limit of vanishing dispersion, we show that this picture is incomplete upon including the multiorbital character of such systems. We show that virtual interband processes generate a finite subgap Raman vertex controlled by the quantum geometric tensor even in the strict flat-band limit. We develop a systematic perturbative theory for Raman scattering from flat bands in the limit where the photon energy is far from resonance with interband transitions. Treating interband Coulomb scattering and light-matter coupling on equal footing, we decompose the Raman scattering vertices into an interaction-independent geometric term expressible directly in terms of the quantum geometric tensor, together with effective resonant and non-resonant pieces generated by virtual interband Coulomb scattering. We then study the polarization-resolved Raman response from collective excitations of an interacting flat band with nontrivial quantum geometry, and demonstrate quantitative agreement of our framework with a full multi-orbital calculation at large photon detuning from interband transitions. These results establish quantum geometry as an intrinsic contribution to inelastic light scattering in flat-band systems, and suggest polarization-resolved Raman spectroscopy as a quantum geometry-sensitive probe of the collective excitations of correlated flat-band platforms.

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• Official / arXiv page
• PDF from original source

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