Low-energy band structure in Bernal stacked six-layer graphene: Landau fan diagram and resistance ridge

Abstract

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.

Intrinsic resistance peaks in AB-stacked multilayer graphene with odd number of layers

“…The resistivity of the main peak increases with |𝑉 𝑡𝑔 |, until it saturates and then slightly decreases for large |𝑉 𝑡𝑔 |. This behavior is reminiscent that of AB-stacked 4-layer [31,33] and 6-layer graphene [36] and is strikingly different from the behavior of bilayer [46][47][48][49] or AB-stacked trilayer graphene [49][50][51][52][53]. Bilayer graphene shows insulating behavior as the top gate voltage increases, while trilayer graphene shows the opposite behavior; the resistivity of the peaks appearing near the charge neutrality point decreases with increasing top gate voltage.…”

“…Recently, high-quality multilayer graphene was found to show intrinsic resistance peaks in its carrier density dependence [31,33,36]. Detailed measurements using graphene samples with top and bottom gate electrodes have uncovered intrinsic resistance ridges structure specific to the band structure of AB-stacked 4-layer [31,33] and 6-layer graphene [36]. These intrinsic resistance ridges are considered to be a promising means of probing the band structure of two-dimensional materials.…”

“…The ridges (or peaks) are related to the topological changes in the Fermi surface [31]; the complicated dispersion relations of multilayer graphene are tunable with a perpendicular electric field, and the resultant shape of the Fermi surface (energy contour of the dispersion relations) varies depending on the chemical potential. The ridges in AB-stacked graphene with even number of layers graphene are principally due to two reasons [33,36]. One is the nearly flat band structure created at the bottoms of the bilayer-like band by the perpendicular electric field; the field opens a band gap at the bottoms of these bands, and make them approximately flat.…”

“…Conspicuous split ridges appear on the map of resistivity as a function of carrier density and perpendicular electric flux density. The other reason is formation of mini-Dirac cones [41], which are created by the perpendicular electric field [31,33,36]. Trigonal warping locally closes the energy gap created by the perpendicular electric field, and thereby, mini-Dirac cones are created.…”

“…Mini-Dirac points appear as sharp resistance ridges. In AB-stacked 4-layer graphene, they appear at the charge neutrality point [31,33], while and in AB-stacked 6layer graphene, they appear not only at the charge neutrality point but also at non-zero carrier densities [36]. In this paper we will examine the intrinsic resistance peak structure of AB-stacked multilayer graphene with odd numbers of layers.…”