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Strong electron-phonon coupling in the σ band of graphene

Federico Mazzola, Thomas Frederiksen, Thiagarajan Balasubramanian, Philip Hofmann, Bo Hellsing, and Justin W. Wells
Phys. Rev. B 95, 075430 – Published 24 February 2017
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  • INTRODUCTION
  • CALCULATIONS
  • MEASUREMENTS
  • SELF-ENERGY ANALYSIS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    First-principles studies of the electron-phonon coupling in graphene predict a high coupling strength for the σ band with λ values of up to 0.9. Near the top of the σ band, λ is found to be ≈0.7. This value is consistent with the recently observed kinks in the σ band dispersion by angle-resolved photoemission. While the photoemission intensity from the σ band is strongly influenced by matrix elements due to sublattice interference, these effects differ significantly for data taken in the first and neighboring Brillouin zones. This can be exploited to disentangle the influence of matrix elements and electron-phonon coupling. A rigorous analysis of the experimentally determined complex self-energy using Kramers-Kronig transformations further supports the assignment of the observed kinks to strong electron-phonon coupling and yields a coupling constant of 0.6(1), in excellent agreement with the calculations.

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    • Received 5 July 2016
    • Revised 18 October 2016

    DOI:https://doi.org/10.1103/PhysRevB.95.075430

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electron-phonon couplingElectronic structureFirst-principles calculations
    1. Physical Systems
    Graphene
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Federico Mazzola1, Thomas Frederiksen2,3, Thiagarajan Balasubramanian4, Philip Hofmann5, Bo Hellsing2,6, and Justin W. Wells1,*

    • 1Department of Physics, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway
    • 2Donostia International Physics Center (DIPC) — UPV/EHU, E-20018 San Sebastián, Spain
    • 3IKERBASQUE, Basque Foundation for Science, E-48013, Bilbao, Spain
    • 4MAX IV Laboratory, PO Box 118, S-22100 Lund, Sweden
    • 5Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Denmark
    • 6Material and Surface Theory Group, Department of Physics, University of Gothenburg, Sweden

    • *justin.wells@ntnu.no

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    Issue

    Vol. 95, Iss. 7 — 15 February 2017

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    Images

    • Figure 1
      Figure 1

      (a) Electronic band structure of graphene with the π (σ) bands in red (blue). (b) Phonon band structure of graphene. The optical (acoustic) bands are shown by red (blue) lines. (c) Electronic DOS (black lines) and EPC strength λσ/π (blue points) for a photohole generated in either a σ band (top) or π band (bottom). Near the top of the σ band λσ≈0.7. (d) Anisotropic momentum-resolved EPC matrix elements |gν(q)| for the LO and TO modes for electrons scattered from any of the two degenerate σ states at Γ¯ (black cross) to either the inner or the outer σ band. White circles of radius 0.14 (0.20) Å−1 indicate states 200 meV below the σ-band maximum, i.e., final states that satisfy energy conservation. The weak anisotropy cancels out if one considers the sum over LO and TO modes as shown in Fig. S1 [15].

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    • Figure 2
      Figure 2

      Effect of SLI and EPC near the top of the σ band. The left axis (EB−Eσ) indicates binding energy relative to the top of the σ band. The right (blue) axis indicates absolute binding energy. (a)–(e) Spectra relative to the first Brillouin zone (first BZ) center. (f)–(j) Spectra relative to the center of the first neighboring Brillouin zone (NBZ). (a) and (f) Spectral function determined using a tight-binding approach and a constant ℑΣ (with ℜΣ=0). (b) and (g) Expected ARPES intensity without EPC, i.e., spectral function times calculated matrix elements to account for SLI. (c) and (h) Expected ARPES intensity with EPC but without SLI. (d) and (i) Expected ARPES intensity including both EPC and SLI. (e) and (j) Measured ARPES intensities. (k) and (l) Calculated ARPES intensity at a constant energy below the band maximum in the first and neighboring BZs, respectively, not including EPC. (m) Experimental ARPES intensity in the NBZ.

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    • Figure 3
      Figure 3

      Analysis of the real and imaginary parts of the quasiparticle self-energy, ℜΣ and ℑΣ. (a) ARPES data with the bare band and experimentally determined dispersion. The left axis (EB−Eσ) indicates binding energy relative to the top of the σ band. The right (blue) axis indicates absolute binding energy. (b) ℜΣ (black) plotted alongside the KK-transformed ℑΣ (green); (c) ℑΣ (black), alongside the KK-transformed ℜΣ (green). (d) Comparison between the calculated and experimentally determined spectral intensity (i.e., MDC peak height) as function binding energy: the black curve is extracted from the experiment (a), the yellow curve from a simulated spectrum with inclusion of SLI, but zero EPC and the purple curve is extracted from a simulated spectrum with inclusion of both SLI and EPC.

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