A two-dimensional honeycomb lattice harbours a pair of inequivalent valleys in the k-space electronic structure, in the vicinities of the vertices of a hexagonal Brillouin zone, K_±. It is particularly appealing to exploit this emergent degree of freedom of charge carriers, in what is termed 'valleytronics'. The physics of valleys mimics that of spin, and will make possible devices, analogous to spintronics, such as valley filter and valve, and optoelectronic Hall devices, all very promising for next-generation electronics. The key challenge lies with achieving valley polarization, of which a convincing demonstration in a two-dimensional honeycomb structure remains evasive. Here we show, using first principles calculations, that monolayer molybdenum disulphide is an ideal material for valleytronics, for which valley polarization is achievable via valley-selective circular dichroism arising from its unique symmetry. We also provide experimental evidence by measuring the circularly polarized photoluminescence on monolayer molybdenum disulphide, which shows up to 50% polarization.

Graphene-based materials exhibit remarkable electronic, optical, and mechanical properties, which has resulted in both high scientific interest and huge potential for a variety of applications. Furthermore, the family of graphene-based materials is growing because of developments in preparation methods. Raman spectroscopy is a versatile tool to identify and characterize the chemical and physical properties of these materials, both at the laboratory and mass-production scale. This technique is so important that most of the papers published concerning these materials contain at least one Raman spectrum. Thus, here, we systematically review the developments in Raman spectroscopy of graphene-based materials from both fundamental research and practical (i.e., device applications) perspectives. We describe the essential Raman scattering processes of the entire first- and second-order modes in intrinsic graphene. Furthermore, the shear, layer-breathing, G and 2D modes of multilayer graphene with different stacking orders are discussed. Techniques to determine the number of graphene layers, to probe resonance Raman spectra of monolayer and multilayer graphenes and to obtain Raman images of graphene-based materials are also presented. The extensive capabilities of Raman spectroscopy for the investigation of the fundamental properties of graphene under external perturbations are described, which have also been extended to other graphene-based materials, such as graphene quantum dots, carbon dots, graphene oxide, nanoribbons, chemical vapor deposition-grown and SiC epitaxially grown graphene flakes, composites, and graphene-based van der Waals heterostructures. These fundamental properties have been used to probe the states, effects, and mechanisms of graphene materials present in the related heterostructures and devices. We hope that this review will be beneficial in all the aspects of graphene investigations, from basic research to material synthesis and device applications.

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 2D TMDs from monolayer, multilayer to bulk material, 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.

Thickness is one of the fundamental parameters that define the electronic, optical, and thermal properties of two-dimensional (2D) crystals. Phonons in molybdenum disulfide (MoS₂) were recently found to exhibit unique thickness dependence due to the interplay between short and long range interactions. Here we report Raman spectra of atomically thin sheets of WS₂ and WSe₂, isoelectronic compounds of MoS₂, in the mono- to few-layer thickness regime. We show that, similar to the case of MoS₂, the characteristic A_1g and E_2g ¹ modes exhibit stiffening and softening with increasing number of layers, respectively, with a small shift of less than 3 cm⁻¹ due to large mass of the atoms. Thickness dependence is also observed in a series of multiphonon bands arising from overtone, combination, and zone edge phonons, whose intensity exhibit significant enhancement in excitonic resonance conditions. Some of these multiphonon peaks are found to be absent only in monolayers. These features provide a unique fingerprint and rapid identification for monolayer flakes.