Triple‐resonant two‐phonon Raman scattering in graphene

2014

Phys. Rev. B

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The dynamical conductivity of interacting multiband electronic systems derived in Ref. 1 is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have demonstrated that the relaxation-time approximation can be used to describe the damping effects in weakly interacting multiband systems only if local charge conservation in the system and gauge invariance of the response theory are properly treated. Such a gauge-invariant response theory is illustrated on the common tight-binding model for conduction electrons in hole-doped graphene. The model predicts two distinctly resolved maxima in the energyloss-function spectra. The first one corresponds to the intraband plasmons (usually called the Dirac plasmons). On the other hand, the second maximum (π plasmon structure) is simply a consequence of the van Hove singularity in the single-electron density of states. The dc resistivity and the real part of the dynamical conductivity are found to be well described by the relaxationtime approximation, but only in the parametric space in which the damping is dominated by the direct scattering processes. The ballistic transport and the damping of Dirac plasmons are thus the questions that require abandoning the relaxation-time approximation.

Section: Hole-doped Graphenementioning

confidence: 99%

Damping effects in doped graphene: The relaxation-time approximation

2014

Phys. Rev. B

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“…$H_{0}^{\rm {ph}}$ is the bare phonon Hamiltonian, given in terms of the phonon field u ν q and the conjugate field p ν q (ν is the phonon branch index). The electron–phonon coupling Hamiltonian $H_{1}^{\rm {ph}}$ is shown in the following way12, 26: Here, $\delta \Delta_{\nu} (\bf{q}) = (g_{\nu}/\sqrt{N}) u_{\nu \bf{q}}$ is the product of the phonon field u ν q and the relative electron–phonon coupling function $g_{\nu}/\sqrt{N}$ . $\hat{\rho}_{\nu}({-}\bf{q})$ is the quadrupole density operator defined in a way analogous to the expressions (4), with the $q_{\nu}^{LL'} (\bf{k}_{+}, \bf{k})$ being the quadrupole vertex functions.…”

Section: Raman Scattering In Multiband Electronic Systemsmentioning

confidence: 99%

“…4 of Ref. 26. The analytical continuation gives the total intraband contribution of the form Here, is the total Raman vertex and $\gamma_{\alpha \beta}^{CC} (\bf{k})/m = (1/\hbar^{2}) \partial^{2} E_{\rm {C}} (\bf{k})/\partial k_{\alpha} \partial k_{\beta}$ is the inverse effective mass tensor, which represents by definition the static Raman vertex, as well.…”

Section: One‐phonon Raman Scatteringmentioning

confidence: 99%

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Resonant two‐magnon Raman scattering in high‐T_c cuprates

2010

J Raman Spectroscopy

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Resonance enhancement of one-phonon, two-phonon, and two-magnon Raman scattering in a general, exactly solvable, multiband model is explained in a way that is in accordance with the general analytical properties of the total optical conductivity tensor. Using this approach, the charge-transfer limit of the Emery three-band model is examined to explain resonance enhancement of the two-magnon Raman spectra of high-T c cuprates, which is found in experiments to be of 3 orders of magnitude. While previous Raman and optical conductivity analyzes of the cuprates, based on the single-band Hubbard model, are found to be consistent with the picture where one hole per one CuO 2 unit is localized on the Cu ion, the present three-band approach allows the study of the opposite, strong copper-oxygen hybridization limit, which is found to be in agreement with the results of nuclear magnetic resonance (NMR) and one-phonon Raman scattering experiments. Copyright

“…Another advantage of the present approach over the second Kubo formula is that it can also be used to determine the structure of other correlation functions of interest, such as the self-energy of acoustic and optical phonons, as well as the structure of σ αα (q,ω) at finite q. In this way, it is possible to study in detail a rich variety of phenomena characterizing the case in which the energy of external electromagnetic fields ω, the energy of in-plane optical phonons ω νq , and the energy of intraband plasmons ω pl (q) are comparable to each other [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

General theory of intraband relaxation processes in heavily doped graphene

2015

Phys. Rev. B

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The frequency and wave-vector-dependent memory function in the longitudinal conductivity tensor of weakly interacting electronic systems is calculated by using an approach based on quantum transport equations. In this paper, we show that there is a close relation between the single-electron self-energy, the electron-hole pair self-energy, and the memory function. It is also shown in which way singular long-range Coulomb interactions, together with other q ≈ 0 scattering processes, drop out of both the memory function and the related transport equations. The theory is illustrated on heavily doped graphene, which is the prototype of weakly interacting single-band electron-phonon systems. A steplike increase of the width of the quasiparticle peak in angle-resolved photoemission spectra at frequencies of the order of the frequency of in-plane optical phonons is shown to be consistent with the behavior of an intraband plasmon peak in the energy loss spectroscopy spectra. Both anomalies can be understood as a direct consequence of weak electron scattering from in-plane optical phonons.