Two-dimensional (2D) transition metal dichalcogenide (TMD) nanosheets exhibit remarkable electronic and optical properties. The 2D features, sizable bandgaps, and recent advances in the synthesis, characterization, and device fabrication of the representative MoS2, WS2, WSe2, and MoSe2 TMDs make TMDs very attractive in nanoelectronics and optoelectronics. Similar to graphite and graphene, the atoms within each layer in 2D TMDs are joined together by covalent bonds, while van der Waals interactions keep the layers together. This makes the physical and chemical properties of 2D TMDs layer dependent. In this review, we discuss the basic lattice vibrations of monolayer, multilayer, and bulk TMDs, including high-frequency optical phonons, interlayer shear and layer breathing phonons, the Raman selection rule, layer-number evolution of phonons, multiple phonon replica, and phonons at the edge of the Brillouin zone. The extensive capabilities of Raman spectroscopy in investigating the properties of TMDs are discussed, such as interlayer coupling, spin-orbit splitting, and external perturbations. The interlayer vibrational modes are used in rapid and substrate-free characterization of the layer number of multilayer TMDs and in probing interface coupling in TMD heterostructures. The success of Raman spectroscopy in investigating TMD nanosheets paves the way for experiments on other 2D crystals and related van der Waals heterostructures.

Graphene and other two-dimensional crystals can be combined to form various hybrids and heterostructures, creating materials on demand with properties determined by the interlayer interaction. This is the case even for a single material, where multilayer stacks with different relative orientation have different optical and electronic properties. Probing and understanding the interface coupling is thus of primary importance for fundamental science and applications. Here we study twisted multilayer graphene flakes with multi-wavelength Raman spectroscopy. We find a significant intensity enhancement of the interlayer coupling modes (C peaks) due to resonance with new optically allowed electronic transitions, determined by the relative orientation of the layers. The interlayer coupling results in a Davydov splitting of the C peak in systems consisting of two equivalent graphene multilayers. This allows us to directly quantify the interlayer interaction, which is much smaller compared with Bernalstacked interfaces. This paves the way to the use of Raman spectroscopy to uncover the interface coupling of two-dimensional hybrids and heterostructures.

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