Since the advent of graphene, a variety of studies have been performed to elucidate its fundamental physics, or to explore its practical applications. Gate-tunable resistance is one of the most important properties of graphene and has been studied in 1–3 layer graphene in a number of efforts to control the band gap to obtain a large on-off ratio. On the other hand, the transport property of multilayer graphene with more than three layers is less well understood. Here we show a new aspect of multilayer graphene. We found that four-layer graphene shows intrinsic peak structures in the gate voltage dependence of its resistance at zero magnetic field. Measurement of quantum oscillations in magnetic field confirmed that the peaks originate from the specific band structure of graphene and appear at the carrier density for the bottoms of conduction bands and valence bands. The intrinsic peak structures should generally be observed in AB-stacked multilayer graphene. The present results would be significant for understanding the physics of graphene and making graphene FET devices.

Monolayer graphene and bilayer graphene have strikingly different properties. One such difference is the shape of the Fermi surface. Although anisotropic band structures can be detected in optical measurements, they have so far been difficult to detect in transport experiments on twodimensional materials. Here we describe a ballistic transport experiment using high-quality graphene that revealed Fermi surface anisotropy in the magnetoresistance. The shape of the Fermi surface is closely related with the cyclotron orbit in real space. Electron trajectories in samples with triangular lattices of holes depend on the anisotropy of the Fermi surface. We found that this results in the magnetoresistance which are dependent on crystallographic orientation of the antidot lattice, which indicates the anisotropic Fermi surface of bilayer graphene which is a trigonally-warped circle in shape. While in monolayer, shape of magnetoresistance was approximately independent of the orientation of antidot lattice, which indicates that the Fermi surface is a circle in shape. The ballistic transport experiment is a new method of detecting anisotropic electronic band structures in two-dimensional electron systems.

The intrinsic peaks due to the topological transition of the Fermi surface shape, which appear in the resistivity as a function of carrier density and perpendicular electric field, were studied in AB-stacked hexlayer graphene as a system with three bilayer-like bands. By the Landau level structure measured in low temperature magnetotransport experiments, and by band structure calculations, it is shown that the ridge structures correspond one-to-one with the characteristic positions in the dispersion relations. Some ridges originated from electronic states near the bottoms of the bilayer-like bands that appears at the carrier density of the zero-mode Landau levels. Some ridges originated from the mini-Dirac cones formed in the perpendicular electric field because of hybridization of bilayer-like bands.

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