Chiral valley phonons and flat phonon bands in moire materials

Abstract

We investigate the chirality of phonon modes in twisted bilayer WSe 2 and demonstrate distinct chiral behavior of the K / K ′ valley phonons for twist angles close to 0 ∘ and close to 60 ∘ . In particular, multiple chiral nondegenerate K / K ′ valley phonons are found for twist angles near 60 ∘ whereas no nondegenerate chiral modes are found for twist angles close to 0 ∘ . Moreover, we discover two sets of emergent chiral valley modes that originate from an inversion symmetry breaking at the moiré scale and find similar modes in moiré patterns of strain-engineered bilayers WSe 2 and MoSe 2 / WSe 2 heterostructures. At the energy gap between acoustic and optical modes, the formation of flat phonon bands for a broad range of twist angles is observed in twisted bilayer WSe 2 . Our findings are relevant for understanding electron-phonon and exciton-phonon scattering in moiré materials and also for the design of phononic analogues of flat band electrons.