Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance.

Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface states. Despite a number of studies demonstrating the quantum Hall effect (QHE) of topological surface states, quantitative evaluation of the LL energies, which serve as fundamental electronic quantities for study of the quantum states, is still limited. In this work, we explore the density of states of LLs by measuring quantum capacitance ( C _Q ) in a truly bulk insulating 3D TI via a van der Waals heterostructure configuration. By applying dual-gate voltages, we access the individual surface states' LLs and extract their chemical potentials to quantify the LL spacings of each surface. We evaluate the LLs' energies at two distinguished QH states, namely, dissipationless (ν = ±1) and dissipative (ν = 0) states in the 3D TI.