Probing Quantum Capacitance in a 3D Topological Insulator

Abstract

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...

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