Probing Enhanced Electron-Phonon Coupling in Graphene by Infrared Resonance Raman Spectroscopy

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Probing Enhanced Electron-Phonon Coupling in Graphene by Infrared Resonance Raman Spectroscopy

Tommaso Venanzi, Lorenzo Graziotto, Francesco Macheda, Simone Sotgiu, Taoufiq Ouaj, Elena Stellino, Claudia Fasolato, Paolo Postorino, Vaidotas Mišeikis, Marvin Metzelaars, Paul Kögerler, Bernd Beschoten, Camilla Coletti, Stefano Roddaro, Matteo Calandra, Michele Ortolani, Christoph Stampfer, Francesco Mauri, and Leonetta Baldassarre

Phys. Rev. Lett. 130, 256901 – Published 21 June 2023

Abstract

We report on resonance Raman spectroscopy measurements with excitation photon energy down to 1.16 eV on graphene, to study how low-energy carriers interact with lattice vibrations. Thanks to the excitation energy close to the Dirac point at $K$ , we unveil a giant increase of the intensity ratio between the double-resonant 2D and $2 D^{'}$ peaks with respect to that measured in graphite. Comparing with fully ab initio theoretical calculations, we conclude that the observation is explained by an enhanced, momentum-dependent coupling between electrons and Brillouin zone-boundary optical phonons. This finding applies to two-dimensional Dirac systems and has important consequences for the modeling of transport in graphene devices operating at room temperature.

Received 2 December 2022
Accepted 15 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.256901

Physics Subject Headings (PhySH)

Graphene

Density functional theory GW method Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tommaso Venanzi ¹, Lorenzo Graziotto ¹, Francesco Macheda ², Simone Sotgiu ¹, Taoufiq Ouaj³, Elena Stellino ⁴, Claudia Fasolato ⁵, Paolo Postorino ¹, Vaidotas Mišeikis ^2,6, Marvin Metzelaars ⁷, Paul Kögerler ⁷, Bernd Beschoten ³, Camilla Coletti ^2,6, Stefano Roddaro ⁸, Matteo Calandra ⁹, Michele Ortolani ¹, Christoph Stampfer ³, Francesco Mauri ^1,2, and Leonetta Baldassarre ¹

¹Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, I-00185 Rome, Italy
²Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genoa, Italy
³JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany
⁴Department of Physics and Geology, University of Perugia, via Alessandro Pascoli, 06123 Perugia, Italy
⁵Institute for Complex System, National Research Council (ISC-CNR), 00185 Rome, Italy
⁶Istituto Italiano di Tecnologia, Center for Nanotechnology Innovation @NEST, Piazza San Silvestro, 12-56126 Pisa, Italy
⁷Institute of Inorganic Chemistry, RWTH Aachen University, 52074 Aachen, Germany
⁸Department of Physics, University of Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
⁹Department of Physics, University of Trento, Via Sommarive 14, 38123 Povo, Italy

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Issue

Vol. 130, Iss. 25 — 23 June 2023

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Images

Figure 1
(a) FT-Raman spectra of graphite (HOPG), hBN-encapsulated graphene ( $hBN / graphene / hBN$ ), and suspended graphene. The G, 2D and $2 D^{'}$ peaks are indentified for all the three samples. (b) 2D and (c) $2 D^{'}$ resonance Raman peaks collected at five different $ℏ ω_{L}$ (indicated in figure). Data have been normalized to 2D peak intensity and different multiplying factors have been used to enhance the visibility of $2 D^{'}$ peak. (d) Dispersion of the 2D peak as a function of laser energy $ℏ ω_{L}$ ; (e) difference between the 2D peak center frequency measured on graphene and graphite ( $Δ ω_{2 D} = ω_{2 D}^{graphene} - ω_{2 D}^{graphite}$ ), for both suspended and encapsulated samples. For clarity, the data for suspended graphene were rigidly shifted upwards of $15 {cm}^{- 1}$ . $Δ ω_{2 D}$ is fairly constant for visible laser energies, and it steepens towards 1.16 eV. The values reported in the manuscript are derived from the analysis of single spectra, acquired as the average of many repeated spectra with long integration time. Further details on the measurement and fitting procedure, and on the error bars can be found in Sec. IV of the Supplemental Material [27].
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Figure 2
(a) Ratio $A_{2 D} / A_{{2 D}^{'}}$ as a function of the laser energy and of the position of the phonon resonance along the $Γ - K$ line. The experimental data points are compared to theoretical calculations rescaled with the square of $r_{v c} (ω_{L}) \equiv ⟨ D_{K}^{2} ⟩ / 2 ⟨ D_{Γ}^{2} ⟩$ , where $r_{v c} = 1$ (dashed black line), $r_{v c} = 1.4$ (dotted black line), or $r_{v c} = r_{v c} (ω_{L})$ , defined below in Eq. (2) (solid black line). The large experimental increase of the ratio value in the infrared indicates a strong increase of the EPC at the $K$ point with respect to that at the $Γ$ point. (b) Value of $⟨ D_{K}^{2} ⟩$ in the vicinity of $K$ deduced from $r_{v c} (ω_{L})$ as explained in the text. Sketch: leading contribution to the vertex corrections in the EPC in graphene [10].
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Figure 3
(a) Raman spectra at different gate voltage values from which the FWHM of the 2D peak is extracted. We note that indeed the FWHM is minimum for gate voltages close to 0 V, indicating that our unbiased sample is undoped. (b) FWHM measured at 1.16 eV as a function of back gate voltage. (c) FWHM as a function of laser excitation energy (full markers), extracted numerically from the fitted data, compared to data from Ref. [39] (empty markers). The experimental data are compared to the result of the theoretical calculation (dotted curve) with EPC constant assumed independent of the excitation laser energy. The solid curve is obtained instead using Eq. (4), i.e., by rescaling the EPC at $K$ with $r_{v c} (ω_{L})$ . We have also rigidly shifted the latter curve by $2 {cm}^{- 1}$ to better highlight how it compares to the experimental data (thinner solid line).
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