Kohn anomaly and interplay of electron-electron and electron-phonon interactions in epitaxial graphene

S. Y. Zhou, D. A. Siegel, A. V. Fedorov, and A. Lanzara

Phys. Rev. B 78, 193404 – Published 20 November 2008

Abstract

The interplay of electron-phonon (el-ph) and electron-electron (el-el) interactions in epitaxial graphene is studied by directly probing its electronic structure. We found a strong coupling of electrons to the soft part of the $A_{1 g}$ phonon evident by a kink at $150 \pm 15 meV$ , while the coupling of electrons to another expected phonon $E_{2 g}$ at 195 meV can only be barely detected. The possible role of the el-el interaction to account for the enhanced coupling of electrons to the $A_{1 g}$ phonon, and the contribution of el-ph interaction to the linear imaginary part of the self-energy at high binding energy are also discussed. Our results reveal the dominant role of the $A_{1 g}$ phonon in the el-ph interaction in graphene and highlight the important interplay of el-el and el-ph interactions in the self-energy of graphene.

Received 14 October 2008

DOI:https://doi.org/10.1103/PhysRevB.78.193404

Authors & Affiliations

S. Y. Zhou^1,2, D. A. Siegel^1,2, A. V. Fedorov³, and A. Lanzara^1,2

¹Department of Physics, University of California–Berkeley, Berkeley, California 94720, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Vol. 78, Iss. 19 — 15 November 2008

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Images

Figure 1
(Color online) (a) ARPES data taken along $K M$ direction (solid line in the inset). (b) Dispersion (black curve) extracted by fitting the raw data. The dashed line is the fit using two straight lines with different slopes. Within 20 meV below $E_{F}$ , the dispersion is affected by the resolution, and therefore we fit the dispersion only in the range between $- 250$ and $- 20 meV$ . The gray dotted line is a guide for the deviation of the low-energy dispersion from the extrapolation of the high-energy dispersion. (c) Extracted velocity as a function of energy from dispersions plotted in panel (b). The symbols are the raw data and the black solid line is a guide for the eyes. (d) Extracted real part of the self-energy as a function of energy $Re Σ (E) = E (k) - v_{b} k_{F}$ where $E (k)$ is the measured dispersion and $k_{F}$ is the Fermi wave vector. The inset shows the MDC width.Reuse & Permissions
Figure 2
(Color online) (a) Intensity maps for the neighboring $K$ and $K^{'}$ points as functions of energy and momentum. The two arrows show the el-ph interaction with the $E_{2 g}$ phonon and $A_{1 g}$ phonon, respectively. (b) Phonon dispersions for the $A_{1 g}$ near $K$ and $E_{2 g}$ near $Γ$ (Refs. 8, 9).Reuse & Permissions
Figure 3
(Color online) (a) Dispersions along various directions (labeled as $α$ , $β$ , $γ$ , and $δ$ ) shown in the Brillouin zone in the inset. The dashed lines are fits of the dispersion using two straight lines with different slopes. The dotted line is a guide to the eyes for the deviation at low binding energy. The horizontal gray shadow highlights the kink energy. (b) Corresponding $Re Σ$ extracted by subtracting the bare band dispersion from the measured dispersion. The bare band dispersion is taken as a straight line connecting the dispersions at $E_{F}$ and $- 250 meV$ .Reuse & Permissions
Figure 4
(Color online) (a)–(c) Dispersions along various directions. The inset shows the constant energy map at $- 3 eV$ , where the trigonal distortion can be clearly observed. The three lines in the inset label the three cuts shown in panels (a)–(c). (d)–(f) Extracted MDC width as a function of energy for data shown in panels (a)–(c). The gray line is a guide for the transition from a more linear behavior to a more quadratic behavior. (g)–(i) Imaginary part of the self-energy $Im Σ = \frac{1}{2} v \cdot Δ k$ , where $v$ is the velocity at each energy and $Δ k$ is the MDC width subtracted by the width at $E_{F}$ [dotted lines in panels (d)–(f)] to take care of the impurity scattering and finite experimental resolution.Reuse & Permissions

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