Energetics of the complex phase diagram of a tunable bilayer graphene probed by quantum capacitance

摘要

Bilayer graphene provides a unique platform to explore the rich physics in quantum Hall effect. The unusual combination of spin, valley, and orbital degeneracy leads to interesting symmetry-broken states with electric and magnetic field. Conventional transport measurements, like resistance measurements, have been performed to probe the different ordered states in bilayer graphene. However, not much work has been done to directly map the energetics of those states in bilayer graphene. Here, we have carried out the magnetocapacitance measurements with electric and magnetic field in a hexagonal boron nitride encapsulated dual-gated bilayer graphene device. At zero magnetic field, using the quantum capacitance technique we measure the gap around the charge neutrality point as a function of perpendicular electric field and the obtained value of the gap matches well with the theory. In the presence of a perpendicular magnetic field, we observe Landau-level crossing in our magnetocapacitance measurements with electric field. The gap closing and reopening of the lowest Landau level with electric and magnetic field shows the transition from one ordered state to another. Furthermore, we observe the collapsing of the Landau levels near the band edge at higher electric field ((D) over bar 0.5 Vm), which was predicted theoretically. The complete energetics of the Landau levels of bilayer graphene with electric and magnetic field in our experiment paves the way to unravel the nature of ground states of the system.