Landau levels of topological surface states probed by quantum capacitance*

Three-dimensional topological insulator (3D TI) is known by its unique Dirac dispersion surface states arising from band inversion of its bulk. Development of discrete Landau levels (LLs) in strong perpendicular magnetic field provides strong evidence of quantization from two-dimensional nature of the topological surface states. Density of states of the surface states’ LLs can be quantitatively determined through a quantum capacitance measurement. However, quantum capacitance in 3D TI is relatively less explored primarily due to mixing signals from the bulk or narrow bulk bandgap such as strained HgTe. In this work, we study the quantum capacitance of a truly bulk insulating 3D TI via a TI-based van der Waals heterostructures configuration. The quantum capacitance data are compared to the quantum Hall conductance in transport. By controlling the dual-gate voltages, we access the LLs from each surface states. The chemical potentials as function of charge density are extracted to quantify the LL spacings.