We measure the quantum capacitance and probe thus directly the electronic density of states of the high mobility, Dirac type two-dimensional electron system, which forms on the surface of strained HgTe. Here we show that observed magnetocapacitance oscillations probe-in contrast to magnetotransportprimarily the top surface. Capacitance measurements constitute thus a powerful tool to probe only one topological surface and to reconstruct its Landau level spectrum for different positions of the Fermi energy. DOI: 10.1103/PhysRevLett.116.166802 Three-dimensional topological insulators (3D TI) represent a new class of materials with insulating bulk and conducting two-dimensional surface states [1][2][3][4]. The properties of these surface states are of particular interest as they have a spin degenerate, linear Dirac-like dispersion with spins locked to their electrons' k vectors [4,5]. Strained HgTe, examined here, constitutes a 3D TI with high electron mobilities allowing the observation of Landau quantization and quantum Hall steps down to low magnetic fields [6,7]. While unstrained HgTe is a zero gap semiconductor with inverted band structure [8,9], the degenerate Γ8 states split and a gap opens at the Fermi energy E F if strained. This system is a strong topological insulator [10], explored by transport [6,7,11], angleresolved photoemission spectroscopy [12], photoconductivity, and magneto-optical experiments [13][14][15][16]; also, the proximity effect has been investigated [17]. Since these two-dimensional electron states (2DES) have high electron mobilities of several 10 5 cm 2 =V s, pronounced Shubnikov-de Haas (SdH) oscillations of the resistivity and quantized Hall plateaus commence in quantizing magnetic fields [6,7,11], stemming from both top and bottom 2DES. The oscillations stem from Landau quantization which strongly modifies the density of states (DOS). Capacitance spectroscopy allows us to directly probe the thermodynamic DOS dn=dμ (n ¼ carrier density, μ ¼ electrochemical potential), denoted as D, of a 3D TI. The total capacitance measured between a metallic top gate and a 2DES depends, besides the geometric capacitance, on the quantum capacitance e 2 D, connected in series and reflecting the finite density of states D of the 2DES [18][19][20][21][22]; e is the elementary charge. Below, the quantum capacitance of the top surface is denoted as e 2 D t , the one of the bottom layer by e 2 D b . We show that capacitance measures, in contrast to transport, the properties of a single Dirac cone in a 3D TI.The experiments are carried out on strained 80 nm thick HgTe films, grown by molecular beam epitaxy on CdTe (013). For details, see [16]. The Dirac surface electrons have high electron mobilities of order 4 × 10 5 cm 2 =V s. The cross section of the structure is sketched in Fig. 1(a). For transport and capacitance measurements, carried out on one and the same device, the films were patterned into Hall bars with metallic top gates. Several devices from the same wafer have been studied. The measurement...
Surface states of topological insulators (TIs) have been playing the central role in the majority of outstanding investigations in low-dimensional electron systems for more than 10 years. TIs based on high quality strained HgTe films demonstrate a variety of subtle physical effects. The strain leads to a bulk band gap, but limits a maximum HgTe strained film thickness, and, therefore, the majority of experiments were performed on the films with a thickness of less than 100 nm. Since a spatial separation of topological states is crucial for the study of a single surface response, the HgTe thickness is essential to be increased further. In this work, by combining transport measurements together with capacitance spectroscopy, we performed the analysis of a 200 nm partially relaxed HgTe film. The Drude fit of the classical magnetotransport revealed the ambipolar electron-hole transport with a high electron mobility. The detailed analysis of Shubnikov-de Haas oscillations, both in conductivity and capacitance, allowed us to distinguish three groups of electrons, identified as electrons on top and bottom surfaces and bulk electrons. The indirect bulk energy gap value was found to be close to zero. It was established that the significant gap decrease does not affect the surface states which are found to be well-resolved and spin non-degenerate. The presented techniques allow the investigations of other 3D TIs, regardless of the presence of bulk conductivity.
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