Detection of interlayer interaction in few-layer graphene

Zefei Wu, Yu Han, Jiangxiazi Lin, Wei Zhu, Mingquan He, Shuigang Xu, Xiaolong Chen, Huanhuan Lu, Weiguang Ye, Tianyi Han, Yingying Wu, Gen Long, Junying Shen, Rui Huang, Lin Wang, Yuheng He, Yuan Cai, Rolf Lortz, Dangsheng Su, and Ning Wang

Phys. Rev. B 92, 075408 – Published 6 August 2015

Abstract

Bernal-stacked few-layer graphene has been investigated by analyzing its Landau-level spectra through quantum capacitance measurements. We find that surface relaxation, which is insignificant in trilayer graphene, starts to manifest in Bernal-stacked tetralayer graphene. In trilayer graphene, the interlayer interaction parameters are generally similar to those of graphite. However, in tetralayer graphene, the hopping parameters of the two bulk layers are quite different from those of the two outer layers. This represents direct evidence of the surface relaxation phenomenon. Traditionally, the van der Waals interaction between the carbon layers is thought to be insignificant. However, we suggest that the interlayer interaction is an important factor in explaining the observed results, and the symmetry-breaking effects in graphene sublattice are not negligible.

Received 16 January 2015
Revised 6 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075408

Authors & Affiliations

Zefei Wu^1,*, Yu Han^1,*, Jiangxiazi Lin^1,*, Wei Zhu², Mingquan He¹, Shuigang Xu¹, Xiaolong Chen¹, Huanhuan Lu¹, Weiguang Ye¹, Tianyi Han¹, Yingying Wu¹, Gen Long¹, Junying Shen¹, Rui Huang³, Lin Wang⁴, Yuheng He¹, Yuan Cai¹, Rolf Lortz¹, Dangsheng Su⁵, and Ning Wang^1,†

¹Department of Physics and the William Mong Institute of Nano Science and Technology, Hong Kong University of Science and Technology, Hong Kong, China
²Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
³Department of Physics and Electronic Engineering, Hanshan Normal University, Chaozhou, China
⁴Department of Condensed Matter Physics, Group of Applied Physics, University of Geneva, Switzerland
⁵Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China

^*These authors contributed equally to this paper.
^†Corresponding author: phwang@ust.hk

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Vol. 92, Iss. 7 — 15 August 2015

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Images

Figure 1
Characterization of trilayer and tetralayer graphene. (a) Optical image and spatial maps of the spectral width of Raman 2D-mode feature for trilayer and tetralayer graphene samples. The scale bar is 10 μm. (b) Energetically favored stacking arrangements for graphene layers. The $α$ and $β$ sublattices in A, B, and C layers are labeled in the illustration.
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Figure 2
BN-graphene-BN heterostructure device. (a) Schematic of the BN-graphene-BN heterostructure device fabrication process. (b) Schematic and (e) optical image of a BN-graphene-BN capacitance device. The scale bar is 10 μm. (c) The sandwiched trilayer and tetralayer graphene heterostructure. (d) The BN-graphene-BN heterostructure for oxygen plasma etching. The etching window is marked by the arrows.
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Figure 3
Measured capacitance of Bernal-stacked trilayer graphene. (a) Lattice structure and its side-view picture of Bernal-stacked trilayer graphene. The dashed lines describe the interlayer hopping parameters. (b) Measured total capacitance $C_{tot}$ of trilayer graphene as a function of the top-gate voltage $V_{t g}$ at 2 K. The arrows signify the Landau-level crossing points that evolve with B fields. (c) A color map of measured $C_{tot}$ as a function of top-gate voltages and B fields. The beating patterns at higher voltages and the bifurcation near zero voltage implies LL crossings. Here, the geometric capacitance $C_{B N} \sim 1.03 \times 10^{- 1} pF$ . The theoretically predicted LL traces are plotted by the white dash lines.
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Figure 4
Calculated band structure and Landau-level (LL) spectrum of Bernal-stacked trilayer graphene. (a) The LL spectrum of trilayer graphene plotted as a function of B fields and energies. Two sets of LLs originating from SLG- and BLG-like bands cross at certain B fields. Note that the lowest six bands are twofold spin-degenerated and the rest are spin and valley degenerated. (b) The band structure in the vicinity of $K (K^{'})$ in the low-energy regime.
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Figure 5
Measured capacitance of Bernal-stacked tetralayer graphene. (a) Measured total capacitance $C_{tot}$ of tetralayer graphene as a function of the top-gate voltage $V_{t g}$ at 2 K. The arrows signify the LL crossing points that evolve with B fields. Note that the larger peak amplitudes on the electron side than on the hole side indicate a higher Fermi velocity of electrons than that of holes. (b) Lattice structure and its side-view picture of Bernal-stacked tetralayer graphene. The dashed lines describe the interlayer hopping parameters. (c) A color map of measured $C_{tot}$ plotted as a function of top-gate voltages and B fields. Here, the geometric capacitance $C_{B N} \sim 1.57 \times 10^{- 1} pF$ . The theoretically predicted LL traces are plotted by the white dashed lines.
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Figure 6
Calculated band structure and Landau-level (LL) spectrum of Bernal-stacked trilayer graphene. (a) The LL spectrum of tetralayer graphene as a function of B fields and energies. The LLs originating from two sets of bilayerlike bands are illustrated by the dashed-line arrows, respectively. Note that all LLs are spin and valley degenerated. (b) The band structure in the vicinity of $K (K^{'})$ in the low-energy regime.
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