Charge Response Function and a Novel Plasmon Mode in Graphene

Abstract

Polarizability of non-interacting 2D Dirac electrons has a 1/ √ qv − ω singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N → ∞, where N is the "color" degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the n-th order ladder term to the same order RPA contribution is ln n |qv − ω|/N n . We perform analytical summation of the infinite series of ladder diagrams which describe excitonic effect. Beyond the threshold, qv > ω, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.PACS numbers: 73.23. -b, 72.30.+q Introduction. Many properties of interacting twodimensional electrons with linear Dirac spectrum ǫ = ±vp, found in graphene monolayers, differ sharply from those with the parabolic spectrum present in conventional semiconductor heterostructures [1,2]. Vanishing density of states at the Dirac point and less effective screening of Coulomb interaction lead to electronic properties of graphene being qualitatively different.One of the distinct signatures of non-interacting 2D electrons in graphene, caused by the absence of spectrum curvature, is a divergent behavior of the polarization operator (charge susceptibility) at the threshold for the excitation of electron-hole pairs [3,4,5,6,7], Π (0) (ω, q) = −N q 2 /16 q 2 v 2 − ω 2 , where N is the degree of degeneracy (in graphene N = 4 in the absence of magnetic field). The effects of electron-electron interaction on the polarization operator are customarily accounted for by the random phase approximation (RPA) [5,8,9,10], which sums the infinite series of electron loops,

Calculation of the RamanGpeak intensity in monolayer graphene: role of Ward identities

“…In addition, the spectrum of electron-hole excitations can be modified by excitonic effects: the Coulomb attraction between the electron and the hole lowers the energy of the excitation with respect to its non-interacting value, so that the singularity in I D should be at a lower frequency. The author is aware of only one study of excitonic effects in the optical response of monolayer graphene; within the Dirac model it was shown that excitonic effects result in a weak feature at the border of the electron-hole continuum [33]. Their importance for optical excitation of electrons near the M point of the first Brillouin zone remains to be studied.…”

Electron-electron interactions in the vacuum polarization of graphene

“…Dynamical polarization properties were studied in Ref. 25, where the vertex diagrams were found to have logarithmically singular contributions near the threshold ω ∼ vq, leading to the possibility of a plasmon mode.…”

Plasmonics of 2D Nanomaterials: Properties and Applications

“…As mentioned above, this zero band gap semimetal supports significant light‐matter interaction of high efficiency, and shows undispersed absorb properties 55, 56, 57. Furthermore, the plasmonic condition can be modified by electrical and chemical doping or hybridizing graphene with other 2D materials or traditional plasmonic nanostructures 58, 59. Among several kinds of intrinsic plasmon modes in graphene, there is longitudinal mode which is also defined as transverse magnetic mode and the polarizing electric field is parallel to the wave vector q .…”