Line Width-Activated Interband Contribution to Thermally Driven Phonon Angular Momentum

Temperature gradients can generate phonon angular momentum, yet most quantitative descriptions rely on semiclassical intraband transport. Here we show that finite line widths can activate an interband channel once neighboring phonon branches develop spectral overlap. Within a self-energy-broadened Green's-function (bubble) framework, we derive compact intraband/interband expressions and identify an activation criterion, (Γ_n + Γ_m)/2 ∼ |ω_n - ω_m|. Using first-principles phonon dispersions and eigenvectors together with temperature-dependent, mode-resolved line widths, we compare three materials spanning distinct phonon landscapes: chiral Te as an intraband-dominant baseline, multibranch LiNbO₃ as an activated but overbroadening-limited case, and strongly anharmonic Rb₂Se₃, where dense low-frequency manifolds make the interband contribution dominant at elevated temperatures. We further introduce a minimal nanoribbon model showing that subband crowding and finite line widths can also promote interband contributions in nanostructures. These results identify line width broadening as a design knob and provide practical guidelines for searching for larger interband thermal Edelstein responses in complex crystals and nanostructures.