Tunable free-electron flat-band resonances for in-plane sensing.

Hyperbolic phonon polaritons offer a unique and powerful platform for enhancing directional light-matter interactions at the nanoscale, benefiting from their long lifetimes and deep subwavelength confinement. In particular, the interaction between free electrons and flat-band-like iso-frequency curves (IFCs) gives rise to strongly enhanced electromagnetic radiation, providing a novel, to the best of our knowledge, route toward compact mid-infrared optical sources without the need for complex nanostructuring. Here, we develop a general theoretical framework to describe free-electron-induced flat-band resonances in a representative graphene/α-MoO3 heterostructure. Specifically, sharp resonances with quality factors around 200 and tunable frequencies spanning a broad mid-infrared range are presented. Furthermore, we showcase their application in vibrational sensing, where strong coupling between the flat-band resonance and molecular vibrational modes is achieved. Our work thus establishes a compact and flexible strategy for tunable mid-infrared light generation and highlights its potential for in-plane sensing applications.