Asymmetric gaps of tetralayer graphene unveiled by thermodynamic characterization

Tetralayer graphene has shown several interesting properties such as tunable Lifshitz transitions, helical edge states and high-temperature anomalous Hall effects. The band structure that directly relates to these phenomena, so far, has predominantly relied on fitting Landau-level spectra. Here, by characterizing electronic capacitance, we show unprecedented details of its band structure: the energy shift between heavy- and light-mass band edges in the conduction band is much larger than that in the valence band. Their responses to displacement fields are also distinct: While the former increases monotonically and significantly, the latter first decreases then increases slightly. Our results suggest that the interlayer interaction and hopping parameters are more complicate than expected, calling for precise measurements of band structures in various multilayer van der Waals systems.