Observation of an electrically tunable band gap in trilayer graphene

Journal name:
Nature Physics
Volume:
7,
Pages:
944–947
Year published:
DOI:
doi:10.1038/nphys2102
Received
Accepted
Published online

A striking feature of bilayer graphene is the induction of a significant band gap in the electronic states by the application of a perpendicular electric field1, 2, 3, 4, 5, 6, 7. Thicker graphene layers are also highly attractive materials. The ability to produce a band gap in these systems is of great fundamental and practical interest. Both experimental8 and theoretical9, 10, 11, 12, 13, 14, 15, 16 investigations of graphene trilayers with the typical ABA layer stacking have, however, revealed the lack of any appreciable induced gap. Here we contrast this behaviour with that exhibited by graphene trilayers with ABC crystallographic stacking. The symmetry of this structure is similar to that of AB-stacked graphene bilayers and, as shown by infrared conductivity measurements, permits a large band gap to be formed by an applied electric field. Our results demonstrate the critical and hitherto neglected role of the crystallographic stacking sequence on the induction of a band gap in few-layer graphene.

At a glance

Figures

  1. Crystal structure and tight-binding diagrams for trilayer graphene with ABA and ABC stacking order.
    Figure 1: Crystal structure and tight-binding diagrams for trilayer graphene with ABA and ABC stacking order.

    a,b, Crystal structure of ABA (a) and ABC (b) trilayer graphene. The yellow and green dots represent the A and B sublattices of the graphene honeycomb structure. c,d, Tight-binding diagrams for ABA (c) and ABC (d) trilayer graphene. At the K-point, the effective intralayer coupling vanishes. The atoms in yellow then become non-bonding monomers and the atoms in blue form a trimer in the ABA trilayer and two dimers in the ABC trilayer.

  2. Comparison of optical conductivity
[sigma]([planck][omega]) of ABA and ABC graphene trilayers for different gate voltages
Vg.
    Figure 2: Comparison of optical conductivity σ(planckω) of ABA and ABC graphene trilayers for different gate voltages Vg.

    a, Schematic representation of the trilayer device used in these studies and described in the Methods section. b, Experimental results for the gate-dependent optical conductivity spectra σ(planckω) of ABC-stacked trilayer graphene. c,d, Theoretical simulations of σ(planckω) for ABC-stacked trilayer graphene under the same gating conditions as in b. c shows the predictions of the TB model for the electronic structure described in the text, whereas d is a reference calculation in which the band structure is assumed to remain unaltered with gating and only the induced population changes are taken into account. In bd, the gate voltages V g and the condition of charge neutrality (V g=V CN=−0.65V) are denoted on the spectra, which are displaced from one another by 2 units for clarity. e, The predicted band structure of ABC trilayer graphene with (red) and without (green) the presence of a perpendicular electric field, as calculated within the TB model described in the text. Transitions 1 and 2 are the strongest optical transitions near the K-point for electron doping. fh, Results corresponding to bd, for ABA-stacked trilayer graphene samples. The different spectra, from top to bottom, were obtained for gate voltages V g=0.9, 0.7, 0.5, 0.3, 0.1, −0.1, −0.3, −0.4, −0.5, −0.6, −0.65(CN)V and are displaced from one another by 0.4 units. i, The predicted band structure of ABA trilayer graphene with (red) and without (green) a perpendicular electric field, as calculated within the TB model described in the text. The arrow indicates the transition responsible for the main absorption peak at 0.5–0.6eV.

  3. Dependence of the energy gap on the induced charge doping density for ABC trilayer graphene.
    Figure 3: Dependence of the energy gap on the induced charge doping density for ABC trilayer graphene.

    The symbols are experimental data. The error bars arise primarily from uncertainties in determining the peak position of the absorption features. The results of the TB model for both the gap at the K-point ΔEK(green line) and the band gap Eg (blue line) are plotted for comparison.

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Affiliations

  1. Departments of Physics and Electrical Engineering, Columbia University, 538 West 120th Street, New York, New York 10027, USA

    • Chun Hung Lui,
    • Zhiqiang Li,
    • Kin Fai Mak &
    • Tony F. Heinz
  2. Institute for Complex Systems (ISC), CNR, via dei Taurini 19, 00185 Rome, Italy

    • Emmanuele Cappelluti
  3. Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Cantoblanco, Madrid, Spain

    • Emmanuele Cappelluti

Contributions

C.H.L. and Z.L. fabricated and characterized the samples, and carried out the measurements. K.F.M. led the design of the experiment and analysis methods. E.C., K.F.M. and C.H.L. developed the theoretical treatment and performed the simulations. All authors discussed the experiment and analysis. C.H.L. and T.F.H. wrote the manuscript.

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The authors declare no competing financial interests.

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