Magnetic oscillation of optical phonon in ABA- and ABC-stacked trilayer graphene

Chunxiao Cong, Jeil Jung, Bingchen Cao, Caiyu Qiu, Xiaonan Shen, Aires Ferreira, Shaffique Adam, and Ting Yu

Phys. Rev. B 91, 235403 – Published 5 June 2015

Abstract

We present a comparative measurement of the $G$ -peak oscillations of phonon frequency, Raman intensity, and linewidth in the magneto-Raman scattering of optical $E_{2 g}$ phonons in mechanically exfoliated ABA- and ABC-stacked trilayer graphene (TLG). Whereas in ABA-stacked TLG, we observe magnetophonon oscillations consistent with single-bilayer chiral band doublets, the features are flat for ABC-stacked TLG up to magnetic fields of 9 T. This suppression can be attributed to the enhancement of band chirality that compactifies the spectrum of Landau levels and modifies the magnetophonon resonance properties. The drastically different coupling behavior between the electronic excitations and the $E_{2 g}$ phonons in ABA- and ABC-stacked TLG reflects their different electronic band structures and the electronic Landau level transitions and thus can be another way to determine the stacking orders and to probe the stacking-order-dependent electronic structures. In addition, the sensitivity of the magneto-Raman scattering to the particular stacking order in few-layer graphene highlights the important role of interlayer coupling in modifying the optical response properties in van der Waals layered materials.

Received 11 November 2014
Revised 10 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235403

Authors & Affiliations

Chunxiao Cong¹, Jeil Jung^2,3,4, Bingchen Cao¹, Caiyu Qiu¹, Xiaonan Shen¹, Aires Ferreira^3,4,5, Shaffique Adam^3,4, and Ting Yu^1,3,4,*

¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
²Department of Physics, University of Seoul, Seoul 130-743, Korea
³Department of Physics, Faculty of Science, National University of Singapore, 117542 Singapore
⁴Graphene Research Centre, National University of Singapore, 117546 Singapore
⁵Department of Physics, University of York, YO10 5DD, United Kingdom

^*Author to whom correspondence should be addressed: yuting@ntu.edu.sg

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Vol. 91, Iss. 23 — 15 June 2015

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Images

Figure 1
(a) Optical image of trilayer graphene sheet. (b) Raman spectra of trilayer graphene taken at different domains with stacking orders of ABA and ABC. (c) White light reflectance image of trilayer graphene sheet shown in panel (a). (d) and (e) are Raman images of $G$ band intensity and $G^{'} (2 D)$ band linewidth of trilayer graphene sheet, respectively.
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Figure 2
False-color map of the Raman intensity in the energy range of the $E_{2 g}$ optical phonon as a function of the magnetic field for (a) ABA-stacked and (b) ABC-stacked trilayer graphene measured at $T = 4.2 K$ under $λ = 532 nm$ laser excitation. Magnetic field evolution of (c) $G$ peak position, (d) $G$ peak linewidth (FWHM), and (e) $G$ peak height of ABA- and ABC-stacked trilayer graphene by fitting the Raman $G$ band at different values of magnetic field as a single Lorentzian peak. (f), (g), and (h) are the amplitude of the Fourier transform of their corresponding insets, showing the $G$ peak position, $G$ peak linewidth, and $G$ peak height of ABA-stacked trilayer graphene as a function of $1 / B$ , respectively. We note that in sufficiently clean samples it is possible to observe clearly the anticrossing branches that underlie the oscillatory features observed in our experiments.
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Figure 3
Left panel: Theoretical calculations of the magnetophonon oscillations for ABA- and ABC-stacked trilayer graphene. The oscillations for ABA-stacked TLG have been modeled using the dominant monolayer Landau levels in the system. In ABC-stacked TLG, we have used the low-energy approximation for the Landau level spectrum. Because this approximation overestimates the Landau level spacing for moderately large magnetic fields we use a correction factor $ξ = 1 / 4$ which in turn leads to a suppression of the magnetophonon oscillations. We used the parameter values of $t = 0.4, 0.9 eV$ for the ABC trilayer and $t = 1.2 eV$ for the ABA trilayer to control the vertical position of the magnetophonon oscillation curves. Right panel: The first 20 Landau levels in monolayer graphene and ABC trilayer graphene. In the ABC trilayer case we plotted the full-band Landau levels in blue and the corrected low-energy form we used in our calculations. The comparison of the vertical axis energy scales between the monolayer and ABC trilayer graphene shows that the latter has more compactly bunched Landau levels due to its higher band chirality.
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Figure 4
Raman spectra of (a) ABA-stacked and (b) ABC-stacked trilayer graphene at different values of magnetic field measured at $T = 4.2 K$ under $λ = 532 nm$ laser excitation.
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Figure 5
(a) Optical image of suspended and supported trilayer graphene sheets. The Raman spectra and Raman images (not shown here) indicate that the whole piece is ABA-stacked trilayer graphene. (b) and (c) are the magnetic field evolution of the $G$ peak position and the $G$ peak linewidth, respectively, of both suspended and supported ABA-stacked trilayer graphene.
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Figure 6
(a) Optical and (b) white light reflectance images of trilayer graphene sheets. (c) and (d) are Raman images extracted from $G$ band intensity and $G^{'} (2 D)$ band linewidth, respectively. (e), (f), and (g) are magnetic field evolution of the $G$ peak position, the $G$ peak linewidth, and the $G$ peak height, respectively, of ABC-stacked trilayer graphene.
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