Atom-Dependent Edge-Enhanced Second-Harmonic Generation on MoS2 Monolayers.

Edge morphology and lattice orientation of single-crystal molybdenum disulfide (MoS2) monolayers, a transition metal dichalcogenide (TMD), possessing a triangular shape with different edges grown by chemical vapor deposition are characterized by atomic force microscopy and transmission electron microscopy. Multiphoton laser scanning microscopy is utilized to study one-dimensional atomic edges of MoS2 monolayers with localized midgap electronic states, which result in greatly enhanced optical second-harmonic generation (SHG). Microscopic S-zigzag edge and S-Mo Klein edge (bare Mo atoms protruding from a S-zigzag edge) terminations and the edge-atom dependent resonance energies can therefore be deduced based on SHG images. Theoretical calculations based on density functional theory clearly explain the lower energy of the S-zigzag edge states compared to the corresponding S-Mo Klein edge states. Characterization of the atomic-scale variation of edge-enhanced SHG is a step forward in this full-optical and high-yield technique of atomic-layer TMDs.

Magneto-optical properties of ABC-stacked trilayer graphene.

The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene. The absorption peaks can be classified into nine categories of inter-Landau-level optical excitations, including three intra-group and six inter-group ones. Most of them belong to the twin-peak structures because of the asymmetric Landau level spectrum. The threshold absorption peak alone comes from a certain excitation channel, and its frequency is associated with a specific interlayer atomic interaction. The Landau-level anticrossings cause extra absorption peaks. Moreover, a simple relationship between the absorption frequency and the field strength is absent. The magneto-optical properties of ABC-stacked trilayer graphene are totally different from those of AAA- and ABA-stacked ones, such as the number, intensity and frequency of absorption peaks.

Feature-rich magnetic quantization in sliding bilayer graphenes.

The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.

Magneto-optical Selection Rules in Bilayer Bernal Graphene.

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

Effects of a modulated electric field on the optical absorption spectra in a single-layer graphene.

The optical absorption spectra of a graphene monolayer in the presence of a modulated electric field are investigated by the gradient approximation with tight-binding model. Such a field could strongly affect the low-energy electronic and optical properties. The low-energy bands exhibit two kinds of band-edge states (micro and upsilon), which lead to many prominent asymmetric peaks in the density of states (DOS). The finite DOS at omega = 0 implies that a single layer graphene in the presence of modulated electric fields would become a semimetallic one. The low-frequency optical absorption spectra display rich peaks and they vanish at omega = 0. Such absorption peaks mainly result from the two kinds of band-edge states and could be divided into two groups. However, they could not be ascribed to an obvious selection rule. It is worth noting that the optical absorption spectra could show anisotropic features in different modulated directions. The predicted results could be verified by the experimental measurements.