Observation of an electrically tunable band gap in trilayer graphene

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 field1–7. 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 theoretical9–16 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. Producing a controlled and tunable band gap in graphene is a topic of central importance1–7,17,18. In addition to the intrinsic interest of altering the electronic properties of materials, the availability of an adjustable band gap opens up the possibility of a much wider range of applications for graphene in electronics and photonics. Both singleand few-layer graphene in their unperturbed state lack a band gap19,20. However, few-layer graphene materials under the application of a symmetry-lowering perpendicular electric field may exhibit an induced gap9–16,21,22. In this regard, trilayer graphene is an attractive material system. Unlike bilayer graphene, however, trilayers, which typically exhibit Bernal (ABA) stacking order and the associated mirror symmetry (Fig. 1a), have been shown both theoretically9–16 and experimentally8 not to support the induction of a significant band gap when subjected to a perpendicular electric field. As discussed below, this behaviour follows from the mirror symmetry of the unperturbed ABA trilayer10,23. Recent research24,25 has, however, reported the existence of a new type of trilayer graphene, one with ABC (rhombohedral) stacking order between the graphene sheets (Fig. 1b). This crystal structure, like that of the bilayer, possesses inversion symmetry, but lacks mirror symmetry (Fig. 1b). The low-energy electronic structure of the ABC trilayer20,22 is accordingly more similar to that of the AB-stacked bilayer graphene. In particular, the undoped ABC trilayer has only two-fold degeneracy20 at the Fermi energy, like the graphene bilayer, rather than the four-fold degeneracy found in the ABA trilayer20,23. The two-fold degeneracy in the ABC trilayer band structure can be readily lifted by imposing different potentials on the top and bottom graphene layers by an applied electric field, which leads to the opening of a band gap9,10,13–16,21,22. Although theory has predicted the induction of a large band gap for ABC trilayer graphene, experimental confirmation has been lacking.