Impact of the electron-electron correlation on phonon dispersion: Failure of LDA and GGA DFT functionals in graphene and graphite

Abstract

We compute the electron-phonon coupling ͑EPC͒ of selected phonon modes in graphene and graphite using various ab initio methods. The inclusion of nonlocal exchange-correlation effects within the GW approach strongly renormalizes the square EPC of the A 1 Ј K mode by almost 80% with respect to density-functional theory in the LDA and GGA approximations. Within GW, the phonon slope of the A 1 Ј K mode is almost two times larger than in GGA and LDA, in agreement with phonon dispersions from inelastic x-ray scattering and Raman spectroscopy. The hybrid B3LYP functional overestimates the EPC at K by about 30%. Within the Hartree-Fock approximation, the graphene structure displays an instability under a distortion following the A 1 Ј phonon at K. The electron-phonon coupling ͑EPC͒ is one of the fundamental quantities in condensed matter. It determines phonon dispersions and Kohn anomalies, phonon-mediated superconductivity, electrical resistivity, Jahn-Teller distortions, etc. Nowadays, density-functional theory ͑DFT͒ within local and semilocal approximations is considered the "standard model" to compute ab initio the electron-phonon interaction and phonon dispersions.1 Thus, a failure of DFT would have major consequences in a broad context. In GGA and LDA approximations, 2 the electron exchange-correlation energy is a local functional of the charge density, and the long-range character of the electron-electron interaction is neglected. These effects are taken into account by Green's-function approaches based on the screened electron-electron interaction W such as the GW method.3 GW is considered the most precise ab initio approach to determine electronic bands, but so far it has never been used to compute EPCs nor phonon dispersions. The semiempirical B3LYP functional 2 partially includes long-range Hartree-Fock ͑HF͒ exchange. B3LYP has been used to compute phonon frequencies but, so far, not the EPC.The EPC is a key quantity for graphene, graphite, and carbon nanotubes. It determines the Raman spectrum, which is the most common characterization technique for graphene and nanotubes 4,5 and the high-bias electron transport in nanotubes.6 Graphene and graphite are quite unique systems in which the actual value of the EPC for some phonons can be obtained almost directly from measurements. In particular, the square of the EPC of the highest optical-phonon branch ͑HOB͒ at the symmetry K point is proportional to the HOB slope near K. 7 The HOB K slope can be measured by inelastic x-ray scattering ͑IXS͒ 8,9 or by the dispersion of the D and 2D lines as a function of the excitation energy in a Raman experiment. 5,[10][11][12][13] A careful look at the most recent data suggests that the experimental phonon slopes ͑and thus the EPC͒ are underestimated by DFT. 5 The ability of DFT ͑LDA and GGA͒ in describing the EPC of graphene was also questioned by a recent theoretical work.14 Here, we show that: ͑i͒ the GW approach, which provides the most accurate ab initio treatment of electron correlation, can be used to compute the elect...

Probing carbon isotope effects on the Raman spectra of graphene with differentC13concentrations

“…The results shown in Table I correspond to the phonon velocities with wave vectors that are probed by resonance Raman scattering in the visible range. The Kohn anomaly [24][25][26] might decrease the phonon velocity in the IR range. Anyway, our results, obtained with visible laser lines, demonstrate that the slope of the phonon dispersion in the visible range does not depend on the isotopic concentration.…”

Electron-phonon coupling in a system with broken symmetry: Surface ofBe(0001)

“…A general observation is that EPC in systems without broken symmetry, such as MgB 2 , is well understood [29], but for systems with broken symmetry, such as substrate-supported graphene and Be(0001) surfaces, present theory is unsatisfactory [30,31]. It seems that the state-of-the-art theories fail to capture some essential ingredients of the EPC for systems with broken symmetry.…”

Defect characterization in graphene and carbon nanotubes using Raman spectroscopy

“…The C A parameter in equation (3.1) is a measure of the maximum possible value of the I D /I G ratio in graphene, which would occur in a hypothetical situation in which K-K wavevector mixing would be allowed everywhere, but no damage would be made to the hexagonal network of carbon atoms. C A should then be defined by the electron-phonon matrix elements, and the value C A = 4.56 is then in rough agreement with the ratio between the electron-phonon coupling for the iTO phonons evaluated between the G and K points in the Brillouin zone (Lazzeri et al 2008). The C S parameter is then the value of the I D /I G ratio in the highly disordered limit, which has not yet been addressed theoretically.…”