Chiun Yan Lin

Magneto-electronic properties of multilayer graphenes.

This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.

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.

Energy spectra of ABC-stacked trilayer graphene in magnetic and electric fields

We have developed the generalized tight-binding model to understand how the electronic structures of ABC-stacked trilayer graphene can be modulated by external fields. A band-like Hamiltonian matrix is used to obtain the electronic properties efficiently. A uniform perpendicular magnetic field gives rise to three groups of Landau levels that can be distinguished from one another by the subenvelope functions of the distinct sublattices. Intergroup Landau-level anticrossings occurring between any two groups and intragroup anticrossings coming from the second group are revealed in the magnetic field-dependent energy spectrum. Such anticrossings are induced by specific interlayer atomic interactions. In the presence of an electric field, each Landau-level group will split into two subgroups, which are characterized by the two different localization centers. The anticrossings in the second group can be suppressed or produced by varying the electric field strength, the reason being the significant modification of the band structures. Furthermore, the intragroup anticrossings arise in two split subgroups of the first group.

The effect of perpendicular electric field on temperature-induced plasmon excitations for intrinsic silicene

We use the tight-binding model and the random-phase approximation to investigate the intrinsic plasmon in silicene. At finite temperatures, an undamped plasmon is generated from the interplay between the intraband and the interband-gap transitions. The extent of the plasmon existence range in terms of momentum and temperature, which is dependent on the size of the single-particle-excitation gap, is further tuned by applying a perpendicular electric field. The plasmon becomes damped in the interband-excitation region. A low damped zone is created by the field-induced spin split. The field-dependent plasmon spectrum shows a strong tunability in the plasmon intensity and spectral bandwidth. This could make silicene a very suitable candidate for plasmonic applications.

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

We developed the generalized tight-binding model to study the magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of Landau levels (LLs) are characterized by the dominating subenvelope function on distinct sublattices. Each LL group could be further divided into two sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6) and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied conduction and the occupied valence LLs in each sub-group behave similarly. For the first group, there exist certain important differences between the two sub-groups, including the LL energy spacings, quantum numbers, spatial distributions of the LL wavefunctions, and the field-dependent energy spectra. The LL crossings and anticrossings occur frequently in each sub-group during the variation of field strengths, which thus leads to the very complex energy spectra and the seriously distorted wavefunctions. Also, the density of states (DOS) exhibits rich symmetric peak structures. The predicted results could be directly examined by experimental measurements. The magnetic quantization is quite different among the AAB-, AAA-, ABA-, and ABC-stacked configurations.

Rich magneto-absorption spectra of AAB-stacked trilayer graphene

A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.

Electric-field-induced rich magneto-absorption spectra of ABC-stacked trilayer graphene

The magneto-optical spectra of ABC-stacked trilayer graphene are enriched by the electric field. A lot of prominent absorption peaks, which arise from the inter- Lnadau-level transitions, gradually change from the twin-peak structures into the double-peak ones with the increasing electric-field strength. This comes from the de- struction in mirror symmetry of xy-plane and the non-equivalence for two sublattices with the identical projections. Specially, a single threshold peak becomes a double- peak structure, owing to the Fermi-Dirac distribution. The absorption frequencies continuously grow or decline except for the anti-crossings of Landau levels. Also, such anti-crossings can induce extra double-peak structures.The magneto-optical spectra of ABC-stacked trilayer graphene are enriched by an electric field. A lot of prominent absorption peaks, which arise from the inter-Landau-level transitions, gradually change from twin-peak structures into double-peak ones with increasing electric-field strength. This comes from the destruction in mirror symmetry of the xy-plane and the non-equivalence of two sublattices with identical projections. Specially, a single threshold peak becomes a double-peak structure, owing to the Fermi–Dirac distribution. The absorption frequencies continuously grow or decline except for those caused by the anti-crossings of Landau levels. Also, such anti-crossings can induce extra double-peak structures.