Kohn Anomalies and Electron-Phonon Interactions in Graphite

Abstract

We demonstrate that graphite phonon dispersions have two Kohn anomalies at the Γ-E2g and K-A ′ 1 modes. The anomalies are revealed by two sharp kinks. By an exact analytic derivation, we show that the slope of these kinks is proportional to the square of the electron-phonon coupling (EPC). Thus, we can directly measure the EPC from the experimental dispersions. The Γ-E2g and K-A ′ 1 EPCs are particularly large, whilst they are negligible for all the other modes at Γ and K. PACS numbers: 63.20.Dj, 63.20.Kr, 71.15.Mb, Carbon nanotubes (CNTs) are at the core of nanotechnology research. They are prototype one dimensional conductors. Metallic nanotubes are predicted to be onedimensional quantum wires with ballistic electron transport [1]. However, high field electrical transport measurements show that the electron-phonon scattering by optical phonons at K and Γ breaks down the ballistic behavior [2]. Electron phonon coupling (EPC) is thus the fundamental bottleneck for ballistic transport. Raman spectroscopy is a most used characterization technique to identify CNTs in terms of their size and electronic properties [3]. The optical phonons at K and Γ are the phonons responsible for the Raman D and G peaks in carbons [4]. The frequency and the intensity of the Raman modes are determined by the EPC matrix elements [5]. The determination of the EPCs is necessary to settle the 35 years debate on the nature of the Raman D peak in carbons [4,5,6,7,8,9,10,11,12]. Finally, although graphite phonon dispersions have been widely studied, several contrasting theoretical dispersions were proposed [6,7,8,9,10,13,14]. In particular, the origin of the large overbending of the K-A ′ 1 branch is not yet understood and is associated to an intense EPC [4,9,10]. In principle, the electronic and vibrational properties of CNTs can be described by folding the electronic and phonon dispersions of graphite. The precise determination of the graphite EPCs is thus the crucial step to understand the properties of any carbon based material and CNTs in particular. It is then surprising that, despite the vast literature on carbon materials and CNTs, no experimental determination or first principle calculations of the graphite EPCs has been done so far, to the best of our knowledge.Here we show that in graphite the EPC matrix elements at Γ and K can be directly extracted from the phonon dispersions. We demonstrate two remarkable Kohn anomalies in the phonon dispersions at Γ and K, by an exact analytic derivation and accurate density functional theory (DFT) calculations. We prove that the slope of the anomalies is proportional to the EPC square.A key feature of graphite is the semi-metallic character of the electronic structure. In general, the atomic vibrations are partially screened by electrons. In a metal this screening can change rapidly for vibrations associated to certain q points of the Brillouin Zone (BZ), entirely determined by the shape of the Fermi surface. The consequent anomalous behavior of the phonon dispersion is called Kohn anomaly [1...

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