Disparate Exciton-Phonon Couplings for Zone-Center and Boundary Phonons in Solid-State Graphite

Xuefei Feng, Shawn Sallis, Yu-Cheng Shao, Ruimin Qiao, Yi-Sheng Liu, Li Cheng Kao, Anton S. Tremsin, Zahid Hussain, Wanli Yang, Jinghua Guo, and Yi-De Chuang

Phys. Rev. Lett. 125, 116401 – Published 8 September 2020

Abstract

The exciton-phonon coupling in highly oriented pyrolytic graphite is studied using resonant inelastic x-ray scattering (RIXS) spectroscopy. With $\sim 70 meV$ energy resolution, multiple low energy excitations associated with coupling to phonons can be clearly resolved in the RIXS spectra. Using resonance dependence and the closed form for RIXS cross section without considering the intermediate state mixing of phonon modes, the dimensionless coupling constant $g$ is determined to be 5 and 0.35, corresponding to the coupling strength of $0.42 eV + / - 20 meV$ and $0.20 eV + / - 20 meV$ , for zone center and boundary phonons, respectively. The reduced $g$ value for the zone-boundary phonon may be related to its double resonance nature.

Received 28 January 2020
Revised 26 April 2020
Accepted 28 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.116401

Physics Subject Headings (PhySH)

Electron-phonon coupling Optical phonons

Graphite

Resonant inelastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xuefei Feng ^1,†, Shawn Sallis ^1,†, Yu-Cheng Shao^1,2, Ruimin Qiao¹, Yi-Sheng Liu¹, Li Cheng Kao ¹, Anton S. Tremsin ³, Zahid Hussain ⁴, Wanli Yang ¹, Jinghua Guo ¹, and Yi-De Chuang ^1,*

¹Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
²Department of Physics, University of Houston, Houston, Texas 77204, USA
³Space Science Laboratory, University of California, Berkeley, California 94720, USA
⁴Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*To whom all correspondence should be addressed. ychuang@lbl.gov
^†These authors contributed equally to this work.

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Vol. 125, Iss. 11 — 11 September 2020

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Images

Figure 1
(a) Schematic illustration of the Frank-Condon picture showing the transition from vibrationally excited states to the ground state. (b) Total electron yield mode of the XAS spectrum at the C $K$ edge recorded with sample surface normal at 55° angle at room temperature. (c) RIXS map of HOPG at room temperature. The broadening of the elastic peak is observed at excitation energies between 291 eV and 292 eV (light yellow box). Reprinted from Ref. [50] with the permission of AIP Publishing.
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Figure 2
(a) Room temperature RIXS spectra recorded with excitation energies around the $σ^{*}$ resonance (291.80 eV). The definition of sample and spectrometer angles are shown in Fig. 3. (b) RIXS spectra recorded at 298 (top, black markers) and 80 K (bottom, red markers) with the geometry listed in Fig. 2. The excitation photon energy is 291.80 eV. The lines are the Voigt function fitting. The elastic peak and phonons are labeled as peak No. 0 and peaks No. 1–No. 6, respectively. (c) Energy position of the peaks with the elastic peak set to 0 eV. The blue shaded area shows the possible energy position by connecting the peak No. 0 to the maximum and minimum of peak No. 1 (the error bar). (d) The energy difference between the adjacent peaks from panel (c). (e) FWHM of the peaks from the fitting shown in panel (b). (f) Comparison of the intensities of peaks at 80 (red) and 298 K (black). The intensity of peak No. 1 is set to 1.0.
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Figure 3
(a) Schematic diagram of experimental geometry. (b)–(d) Room temperature RIXS spectra with excitation photon energy 291.80 eV and experimental geometry shown in panel (a). The sample and spectrometer angles defined in panel (a) are listed in each figure. (e) The peak energy positions from fitting the spectra in panels (b)–(d) with Voigt functions. (f) The normalized intensities of the peaks from the fitting. The intensity of the first peak is set to 1.0. The symbol color scheme in panels (e) and (f) adopts the trace color scheme in panels (b)–(d). The black symbols in (e) and (f) are from Figs. 2 and 2 as the reference.
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Figure 4
(a) Top: overlay of experimental (markers) and simulated RIXS spectra for the $G$ mode with $g = 5$ (blue curve; sum of fundamental up to 5th order; for details, see Ref. [54]). The red curve is the fitted elastic peak. Bottom: difference between the experimental spectrum and the sum of the $G$ mode contribution and the elastic peak. The green line shows the simulated $2 D$ mode with $g = 0.35$ . (b) Overlay of normalized XAS spectrum (shaded area), $E_{2 g}$ ( $G$ mode) peak intensity (filled blue circles), ${2 * A}_{1 g}$ ( $2 D$ mode) peak intensity (filled green squares) and the least square fitted curves using Eq. (2). The parameters $ω_{0} = 0.190 eV$ for the $G$ mode, $ω_{0} = 0.335 eV$ for the $2 D$ mode, and $Γ = 0.414 eV$ ( $\sim 10 fs$ ) are used in the equation [63]. The justification for the normalization of the $G$ mode intensity is discussed in the Supplemental Material [54].
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