The phonon physics of two-dimensional materials and related heterostructures

Phonon is one of the most important elementary excitations, and is fundamental for understanding thermodynamic properties, such as heat capacity, Debye temperature, and the coefficient of thermal expansion. Furthermore, electron-phonon coupling can determine the electric conductivity and superconductivity of materials. Raman spectroscopy is the most important tool to study phonon physics, and can not only be utilized to explore the lattice structure and quality of materials but also their phonon properties, electronic band structure and electron-phonon coupling. Here, we investigate the phonon physics of two-dimensional (2D) materials and the related van der Waals heterostructures by Raman spectroscopy. First, we will introduce interlayer and intralayer phonon modes. The frequency of the interlayer phonon modes can be well reproduced by the linear chain model while their intensity can be calculated by the interlayer bond polarizability model; in addition, the splitting frequency between Davydov components in multilayer 2D materials originating from the same intralayer mode in monolayer counterpart can be well fitted by the van der Waals model. Secondly, we extend these models to 2D van der Waals heterostructures. By taking twisted multilayer graphene, MoS₂/graphene and hBN/WS₂ heterostructures as examples, we demonstrate how to calculate the frequency and Raman intensity of the interlayer modes by the linear chain and interlayer polarizability models, respectively, which can further give the strength of the interlayer coupling and electron-phonon coupling for layer-breathing modes in van der Waals heterostructures.