Stacking-dependent band gap and quantum transport in trilayer graphene

Graphene1–3 is an extraordinary two-dimensional (2D) system with chiral charge carriers and fascinating electronic, mechanical and thermal properties4,5. In multilayer graphene6,7, stacking order provides an important yet rarely explored degree of freedom for tuning its electronic properties8. For instance, Bernal-stacked trilayer graphene (B-TLG) is semi-metallic with a tunable band overlap, and rhombohedral-stacked trilayer graphene (r-TLG) is predicted to be semiconducting with a tunable band gap9–17. These multilayer graphenes are also expected to exhibit rich novel phenomena at low charge densities owing to enhanced electronic interactions and competing symmetries. Here we demonstrate the dramatically different transport properties in TLG with different stacking orders, and the unexpected spontaneous gap opening in charge neutral r-TLG. At the Dirac point, B-TLG remains metallic, whereas r-TLG becomes insulating with an intrinsic interaction-driven gap ∼6 meV. In magnetic fields, well-developed quantum Hall (QH) plateaux in r-TLG split into three branches at higher fields. Such splitting is a signature of the Lifshitz transition, a topological change in the Fermi surface, that is found only in r-TLG. Our results underscore the rich interaction-induced phenomena in trilayer graphene with different stacking orders, and its potential towards electronic applications. TLG has two natural stable allotropes: (1) ABA or Bernal stacking, where the atoms of the topmost layer lie exactly on top of those of the bottom layer; and (2) ABC or rhombohedral stacking, where one sublattice of the top layer lies above the centre of the hexagons in the bottom layer (Fig. 1a,b insets). This subtle distinction in stacking order results in a dramatic difference in band structure. The dispersion of B-TLG is a combination of the linear dispersion of single layer graphene (SLG) and the quadratic relation of bilayer graphene (BLG; Fig. 1a), whereas the dispersion of r-TLG is approximately cubic, with its conductance and valence bands touching at a point close to the highly symmetric Kand K-points (Fig. 1b; refs 9,10,12,13). These distinctive band structures are expected to give rise to different transport properties. For instance, owing to the cubic dispersion relation, r-TLG is expected to host stronger electronic interactions than B-TLG. This is because the interaction strength rs is approximately the ratio of the inter-electron Coulomb energy to the Fermi energy. In graphene, rs ∝ n−(p−1)/2, where n is charge density and p is the power of the dispersion relation; p = 1, 2, 3 for SLG, BLG and r-TLG, respectively5. Consequently, at low n, the interaction strength in r-TLG is significantly higher than that in SLG, BLG