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

Abstract

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 (CQ) 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 2 surface. We evaluate the LLs' energies at two distinguished QH states, namely dissipationless (ν= ±1) and dissipative (ν= 0) states in the 3D TI. KEYWORDStopological insulators, quantum capacitance, Landau levels, van der Waals heterostructures, quantum Hall effect The topologically-protected linearly dispersing surface states of three-dimensional topological insulators (3D TIs) offer a route for exploration of quantum phenomena such as the topological exciton superfluid, fractional charges and Majorana fermions in quantum regimes. 1-3 In a strong perpendicular magnetic field, the surface Dirac fermions localize in cyclotron orbits, forming discrete energy states known as Landau levels (LLs). This gives rise to the quantum Hall effect (QHE) in magnetotransport, where the Hall conductivity is quantized at integers as a result of halfintegers from each (top and bottom) surface. 4-6 Alternatively, quantum capacitance (CQ) can also be exploited to study the LLs electronically. 7-10 Different from quantum transport which is only sensitive to edge modes, CQ provides a probe of the charge states in the bulk of the surfaces. CQ is an ideal measure of the thermodynamic density of states (DoS) for low carrier density and gate-tunable materials. 8-10 Nevertheless, it is relatively less explored in 3D TIs in the past as compared to quantum transport primarily due to the shortcoming of a proper 3D TI candidate.Previous studies of CQ in Bi2Se3 revealed the Dirac-like surface states 11 and Shubnikov-de Haaslike quantum oscillations in magnetic field. 12 However, Bi2Se3 is known to exhibit substantial carrier doping in bulk, and extra trapped states induced by intrinsic defects. 11,13 More recently, CQ in high mobility 3D TI based on strained HgTe was reported, 14 showing more intrinsic bulk band and clear LL quantization. Yet, the narrow bulk bandgap in strained HgTe (~20 meV), which is

Controlling and visualizing Dirac physics in topological semimetal heterostructures

“…For comparison, in the compensated 3D topological insulator BiSbTeSe 2 , the zero-B capacitance looks very similar to that shown in Fig. 2 (A and B), but the zeroth Landau level appears as a peak that develops at or very near the center of the dip feature (20,21). The same is true for graphene (22), and more broadly is an obvious consequence of Eq.…”

Two-Dimensional-Dirac Surface States and Bulk Gap Probed via Quantum Capacitance in a Three-Dimensional Topological Insulator

“…At higher temperatures, D (μ) has to be replaced by the thermodynamic density of states (TDOS) at μ, ­(μ) = d n /d μ with n as the carrier density. While gating of 3D-TIs and tuning of the carrier densities of top and bottom surfaces, − and even magnetocapacitance , has been explored in the past, the analysis of quantum capacitance and the DOS in a compensated TI like BiSbTeSe 2 remained uncharted. Our measurements show that although Dirac surface states dominate low- T transport as expected the bulk provides a background that is capable of absorbing a large amount of charge carriers.…”

Anisotropic optical conductivities of model topological nodal-line semimetals

“…It is also worthy of note that for slabs of finite thickness unusual surface states, Fermi-arc surface states in Weyl semimetal [20,21], and drumhead surface states in NLSM [1,[22][23][24][25][26] are supported by TSM. So far, only bulk and surface Landau levels, together with their transport properties, have been extensively investigated for Dirac semimetal [27][28][29][30][31] and Weyl semimetal [32][33][34][35][36][37]. We emphasize that in this paper, we consider only a bulk NLSM.…”