Interlayer bond polarizability model for interlayer phonons in van der Waals heterostructures

Raman scattering provides essential insights into phonons, electronic structures and electron-phonon coupling within solids through the intensity of Raman peaks, which cannot be easily quantified using the classical bond polarizability model. The interlayer bond polarizability model (IBPM) had been developed to understand the Raman intensity of layer-breathing modes (LBMs) in two-dimensional materials. However, the quantitative understanding of the LBM intensity of a van der Waals heterostructure (vdWH) remains challenging. Here, in polynary vdWHs comprising twisted multilayer graphene (tMLG), MoS₂ and hBN, we observed a series of LBMs, whose intensity is markedly dependent on the excitation energy and twist angle of the tMLG constituent. An improved IBPM is proposed to quantitatively understand the Raman intensity of LBMs in the tMLG-based vdWHs, including the emergence or absence of a specific LBM when the excitation energy is resonant with the electronic states of tMLG or MoS₂ constituents. This work underscores the significant potential of the improved IBPM in accurately understanding and predicting the intensity profile of LBM in polynary vdWHs, even for the case of Raman scattering with excitation energies selectively resonant with the electronic states of the corresponding specific constituents.