Electromagnetic fields bound tightly to charge carriers in a two-dimensional sheet, namely surface plasmons, are shielded by metallic plates that are a part of a device. It is shown that for epitaxial graphenes, the propagation velocity of surface pl
asmons is suppressed significantly through a partial screening of the electron charge by the interface states. On the basis of analytical calculations of the electron lifetime determined by the screened Coulomb interaction, we show that the screening effect gives results in agreement with those of a recent experiment.
When graphene is deformed in a dynamical manner, a time-dependent potential is induced for the electrons. The potential is antisymmetric with respect to valleys, and some straightforward applications are found for Raman spectroscopy. We show that a v
alley-antisymmetric potential broadens Raman $D$ band but does not affect $2D$ band, which is already observed by recent experiments. The space derivative of the valley antisymmetric potential gives a force field that accelerates intervalley phonons, while it corresponds to the longitudinal component of the previously discussed pseudoelectric field acting on the electrons. Effects of a pseudoelectric field on the electron is quite difficult to observe due to the valley-antisymmetric coupling constant, on the other hand, such obstacle is absent for intervalley phonons with $A_{1g}$ symmetry that constitute the $D$ and $2D$ bands.
In Raman spectroscopy of graphite and graphene, the $D$ band at $sim 1355$cm$^{-1}$ is used as the indication of the dirtiness of a sample. However, our analysis suggests that the physics behind the $D$ band is closely related to a very clear idea fo
r describing a molecule, namely bonding and antibonding orbitals in graphene. In this paper, we review our recent work on the mechanism for activating the $D$ band at a graphene edge.
By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$$ Raman bands with changes in doping ($mu$) and light excitation energy ($E_L$). Comparing the se
lf-energy with the observed $mu$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $hbar vqsimeq E_L/1.6$ ($v$ is electrons Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an image of shifted Dirac cones in which the resonance decay of a phonon satisfying $q > omega/v$ ($omega$ is the phonon frequency) into an electron-hole pair is suppressed when $mu < (vq-omega)/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=omega/v$ is strongly suppressed by electron-phonon coupling at an arbitrary $mu$. This feature is in contrast to the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.
By analytically constructing the matrix elements of an electron-phonon interaction for the $D$ band in the Raman spectra of armchair graphene nanoribbons, we show that pseudospin and momentum conservation result in (i) a $D$ band consisting of two co
mponents, (ii) a $D$ band Raman intensity that is enhanced only when the polarizations of the incident and scattered light are parallel to the armchair edge, and (iii) the $D$ band softening/hardening behavior caused by the Kohn anomaly effect is correlated with that of the $G$ band. Several experiments are mentioned that are relevant to these results. It is also suggested that pseudospin is independent of the boundary condition for the phonon mode, while momentum conservation depends on it.
The universality of $k$-dependent electron-photon and electron-phonon matrix elements is discussed for graphene nanoribbons and carbon nanotubes. An electron undergoes a change in wavevector in the direction of broken translational symmetry, dependin
g on the light polarization direction. We suggest that this phenomenon originates from a microscopic feature of chirality.
Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($Delta n$) and pseudospin are the necessary elements if we are to underst
and the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($Delta n=pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggested that the absorption of low-energy light is sensitive to the position of the Fermi energy, direction of light polarization, and irregularities in the edge. The effect of depolarization on the absorption peak is briefly discussed.
The wavefunction of a massless fermion consists of two chiralities, left-handed and right-handed, which are eigenstates of the chiral operator. The theory of weak interactions of elementally particle physics is not symmetric about the two chiralities
, and such a symmetry breaking theory is referred to as a chiral gauge theory. The chiral gauge theory can be applied to the massless Dirac particles of graphene. In this paper we show within the framework of the chiral gauge theory for graphene that a topological soliton exists near the boundary of a graphene nanoribbon in the presence of a strain. This soliton is a zero-energy state connecting two chiralities and is an elementally excitation transporting a pseudospin. The soliton should be observable by means of a scanning tunneling microscopy experiment.
A phonon frequency shift of the radial breathing mode for metallic single wall carbon nanotubes is predicted as a function of Fermi energy. Armchair nanotubes do not show any frequency shift while zigzag nanotubes exhibit phonon softening, but this s
oftening is not associated with the broadening. This chirality dependence originates from a curvature-induced energy gap and a special electron-phonon coupling mechanism for radial breathing modes. Because of the particle-hole symmetry, only the off-site deformation potential contributes to the frequency shift. On the other hand, the on-site potential contributes to the Raman intensity, and the radial breathing mode intensity is stronger than that of the $G$ band. The relationship between the chirality dependence of the frequency shift of the radial breathing mode and the $Gamma$ point optical phonon frequency shift is discussed.
The quantum corrections to the frequencies of the $Gamma$ point longitudinal optical (LO) and transverse optical (TO) phonon modes in carbon nanotubes are investigated theoretically. The frequency shift and broadening of the TO phonon mode strongly d
epend on the curvature effect due to a special electron-phonon coupling in carbon nanotubes, which is shown by the Fermi energy dependence of the frequency shift for different nanotube chiralities. It is also shown that the TO mode near the $Gamma$ point decouples from electrons due to local gauge symmetry and that a phonon mixing between LO and TO modes is absent due to time-reversal symmetry. Some comparison between theory and experiment is presented.
