C. L. Lu

Low-energy electronic properties of the AB-stacked few-layer graphites

In the presence of a perpendicular electric field, the low-energy electronic properties of the AB-stacked N-layer graphites with layer number N = 2, 3, and 4, respectively, are examined through the tight-binding model. The interlayer interactions, the number of layers, and the field strength are closely related to them. The interlayer interactions can significantly change the energy dispersions and produce new band-edge states. Bi-layer and four-layer graphites are two-dimensional semimetals due to a tiny overlap between the valence and conduction bands, while tri-layer graphite is a narrow-gap semiconductor. The electric field affects the low-energy electronic properties: the production of oscillating bands, the cause of subband (anti)crossing, the change in subband spacing, and the increase in band-edge states. Most importantly, the aforementioned effects are revealed completely in the density of states, e.g. the generation of special structures, the shift in peak position, the change in peak height, and the alteration of the band gap.

Electronic properties of AA- and ABC-stacked few-layer graphites

The low-energy electronic properties of a few graphite layers with AA and ABC stacking under application of the electric field (F), perpendicular to the layers, are explored through the tight-binding model. They strongly depend on the interlayer interactions, the stacking sequences, the layer numbers, and the field strength. In the absence or presence of F, the AA-stacked N-layer graphites (N ¼ 3 and 4) exhibit the linear bands near the Fermi energy. The interlayer interactions and electric field chiefly shift the Fermi momenta and the state energies. The ABC-stacked N-layer graphites are characterized by the complicated low-energy bands due to the stacking effect, on which F has a great influence—the change of the state energies and the subband spacing, the opening of a band gap, the production of the oscillating bands, and the increase of the band-edge states. As a result, the two kinds of special structure, whose positions and heights are modulated by F, are found in the density of states (DOS) in contrast to the featureless DOS of the AA systems. The comparison with the AB-stacked few-layer graphites is also made.

Optical properties of simple hexagonal and rhombohedral few-layer graphenes in an electric field

The influence of a perpendicular electric field (F) on the optical properties of simple hexagonal and rhombohedral few-layer graphenes is studied through the tight-binding model. The electric-field-modulated absorption spectra depend on the stacking sequence. The low-energy absorption spectra of simple hexagonal few-layer graphenes exhibit the jumping structures in the absence or presence of an electric field. On the other hand, absorption spectra of rhombohedral few-layer graphenes show discontinuities and sharp peaks at F=0. Besides, the application of F affects the absorption spectra, generates new peaks, and changes peak position and peak height. The frequency of the peak is predicted to be closely associated with the stacking sequences and the field strength. Above all, the predicted absorption spectra could be verified by optical measurements.

Absorption spectra of trilayer rhombohedral graphite

Absorption spectra of trilayer rhombohedral graphite are studied with the tight-binding model. The interlayer interactions cause a tiny energy gap and band-edge states in electronic structures. The band-edge states exhibit logarithmic divergences and discontinuities in the density of states. The frequencies of the absorption peaks correspond to the vertical transition energies of the band-edge states. Optical spectra of trilayer simple hexagonal and orthorhombic graphites are also investigated. The stacking effects on the density of states and absorption spectra are presented and discussed in detail.