Vibrational properties of graphene and graphene layers

Abstract

The phonon dispersions of graphene and graphene layers are theoretically investigated within fifth-nearest-neighbor forceconstant approach. Based on their symmetry groups, the number of Raman-and infrared-active modes at the point is given. Interatomic force constants are recalculated by fitting them to experimental phonon energy dispersion curves. Wavenumbers of optically active modes are presented as a function of number of layers (n). Our calculated results reproduce well the experimental data of G peak for graphene (1587 cm −1 ) and graphite (1581.6 cm −1 ) and clearly give the relation that ω G = 1581.6 + 11/(1 + n 1.6 ).

Ultralow-frequency shear modes of 2-4 layer graphene observed in scroll structures at edges

“…[27] According to the symmetrical analysis of an n (n≥2) layer graphene, [36,37] there are n degenerate pairs of in-pane stretching modes and n-1 degenerate pairs of in-plane shear modes between neighboring layers. The former corresponds to the feature in the G-band region and the latter appears in the low frequency region.…”

“…For the 2-4LGs, in principle, there are 1, 2 and 3 degenerate pairs of the shear mode, which is consistent with the experimental observation. The force-constant model [36] is adopted to calculate the frequency of the shear mode and the G band, in which 15 parameters are used to describe fifth-nearest neighbor force constants of intra-layer and 8 parameters for fourth-nearest-neighbor force constants i.e., E ′ mode in 3LGs, and E u and E 1 g modes in 4LGs, match well with those of additional modes observed in 3-4LSs in Figures 2(d1) and 3(a). All the graphene layers in 2-4L scrolls is hard to keep the commensurate bernal stacking structure, which is hard to be kept in the incidental rolling process to form the scroll structures.…”

Graphene versus MoS2: A short review

“…In the top panel, the three acoustic phonon modes have zero frequency, indicating that the interatomic potential did not vary during rigid translational motion. In the bottom panel, the two in-plane optical phonon modes have almost the same frequency, revealing the isotropic phonon properties for the two inplane directions in graphene [45]. Figure 4 shows the phonon dispersion of SLMoS 2 along the high-symmetry ΓKM lines in the first Brillouin zone.…”

Raman Spectroscopy of Graphene

“…它们对称性的主要区别在于偶 数层的石墨烯没有水平镜像平面对称性, 而奇数层的石 墨烯缺少反演对称操作 [103] . 少层石墨烯每个原胞中含 有 2n (n 为层数)个原子, 有 6n 个振动模, 不可约表 示 [100,102] 为: [99,100,102,105,106] .…”