Optical Properties of Graphene in Magnetic and Electric Fields

Abstract

Optical properties of graphene are explored by using the generalized tight-binding model. The main features of spectral structures, the form, frequency, number and intensity, are greatly enriched by the complex relationship among the interlayer atomic interactions, the magnetic quantization and the Coulomb potential energy. Absorption spectra have shoulders, asymmetric peaks and logarithmic peaks, coming from the band-edge states of parabolic dispersions, the constant-energy loops and the saddle points, respectively. The initial forbidden excitation region is only revealed in even-layer AA stacking systems. Optical gaps and special structures can be generated by an electric field. The delta-function-like structures in magneto-optical spectra, which present the single, twin and double peaks, are associated with the symmetric, asymmetric and splitting Landau-level energy spectra, respectively. The single peaks due to the non-tilted Dirac cones exhibit the nearly uniform intensity. The AAB stacking possesses more absorption structures, compared to the other stackings. The diverse magneto-optical selection rules are mainly determined by the well-behaved, perturbed and undefined Landau modes. The frequent anti-crossings in the magneticand electric-field-dependent energy spectra lead to the increase of absorption peaks and the reduced intensities. Part of theoretical calculations are consistent with the 1 arXiv:1603.02797v2 [physics.comp-ph] 19 Jul 2016 experimental measurements, and the others need further detailed examinations.Graphene is a 2D material made up of hexagonal carbon lattices [1,2]. Since mono-and few-layer graphene sheets were first fabricated in 2004 [1,2], low-dimensional graphenerelated systems have been a great interest to experimental and theoretical studies. The stacking orders of graphene sheets include the essential sequences of AA [3,4], AB [5-9], ABC [5,[8][9][10][11] stackings. While the AA stacking configuration has only been artificially made from intercalated graphite compounds, the AB and ABC configurations are the common orders in natural graphite, respectively, with their estimated volume fractions: 80 % and 14 % [15,16]. The rest parts ∼ 6% consist of haphazardly stacked graphene sheets, called turbostratic configuration [17][18][19]. Few-layer graphene desired with a specific stacking configuration can be exfoliated from highly orientated pyrolytic graphite [1,2], and chemically and electrochemically reduced from graphene oxide [20][21][22][23][24][25][26][27]. Nevertheless, chemical vapor deposition method has the advantage of producing large-scale size of highquality graphene sheets. Recently, large area of graphene with high mobility and highly symmetric configurations, e.g., AA, AB and ABC, have been found in CVD-grown samples [28][29][30][31][32][33][34][35][36][37][38][39][40]. The improved quality is adequate for research experiments and industry applications [41][42][43][44][45][46][47][48][49][50]. In addition, the AAB stacking and intermediate bilayer configurations, with r...

Coulomb Excitations and Decays in Graphene-Related Systems

“…[29] The magnetoplasmon is discussed in this book by the development of the modified RPA and the generalized Peierls tight-binding model. [30][31][32][33] It is very suitable for studying the inter-landau-level (inter-LL), single-particle excitations and magneto-plasmon modes. [34][35][36] Moreover, electronic excitation spectra are also quite efficient decay channels by the inelastic Coulomb scatterings, being the strong effects on the energy widths of the quasiparticle states (the excited electrons or holes).…”

“…[30,93] During the continuous variation of stacking configuration, energy bands present the serious distortions and free carrier density show the drastic changes. [30,93] These are predicted to induce the novel Coulomb excitation phenomena in pristine and extrinsic systems. AAA stacking has one acoustic plasmon mode and (N − 1) optical ones, [22,23] in which the former and the latter, respectively, originate from the intraband and the interband electronic excitations.…”

“…Hamiltonian dimension is 32000 under the magnetic field strength of B z = 10 T. The huge magnetic Hamiltonian could be efficiently solved using the band-like matrix by the rearrangement of the R B tight-binding functions (details in Refs [30,31]…”

Si-doped Defect in Monolayer Graphene: Magnetic Quantization

“…Magnetic quantization is one of the mainstream topics in the physical science, such as the rich magneto-electronic properties [1][2][3] , magneto-optical selection rules, [4][5][6] and quantum Hall effects in few-layer graphene systems. [7][8][9] Diverse physical phenomena could be achieved by changing the atomic components, 10 the lattice symmetries, 11,12 the lattice geometries such as planar, buckling, rippled, and folding structures, [13][14][15] the stacking configurations, 16,17 the number of layers, 18,19 the distinct dimensionalities, 20,21 the spinorbital couplings, 2,22 the single-or multi-orbital hybridizations, 23 the electric field, 24 and the uniform or non-uniform magnetic field. 2,25 In this Letter, we aim to investigate the interesting quantization phenomena of monolayer graphene under the effect of Si-doped defect.…”

Coulomb excitations in ABC-stacked trilayer graphene

“…In response to the dynamic Coulomb potential, the real part Re[P (1) ll ′ (q, ω)] and imaginary part Im[P appear as a result of the nearly isotropic energy dispersions near the K point. 15 The others This implies that due to the interplay between interband and intraband excitations, the electronic excitation spectra can be diversified, and various plasmon modes are presented with a variation of q and E F .…”