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Spectroscopy of discrete Landau levels (LLs) in bulk-insulatingthree-dimensional topological insulators (3D TIs) in perpendicular magneticfield characterizes the Dirac nature of their surface states. Despite a numberof studies demonstrating the quantum Hall effect (QHE) of topological surfacestates, quantitative evaluation of the LL energies, which serve as fundamentalelectronic quantities for study of the quantum states, is still limited. Inthis work, we explore the density of states of LLs by measuring quantumcapacitance (CQ) in a truly bulk insulating 3D TI via a van der Waalsheterostructure configuration. By applying dual gate voltages, we access theindividual surface states' LLs and extract their chemical potentials toquantify the LL spacings of each surface. We evaluate the LLs' energies at twodistinguished QH states, namely dissipationless ({\nu}= +/-1) and dissipative({\nu}= 0) states in the 3D TI.

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