Self-consistent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>k</mml:mtext><mml:mo>·</mml:mo><mml:mtext>p</mml:mtext></mml:mrow></mml:math>calculations for gated thin layers of three-dimensional topological insulators

Baum, Yuval; Böttcher, J.; Brüne, C.; Thienel, Cornelius; Molenkamp, L. W.; Stern, Ady; Hankiewicz, Ewelina M.

doi:10.1103/physrevb.89.245136

Cited by 11 publications

(6 citation statements)

References 23 publications

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“…1d and the Supplementary Figure S5d. A similar equivalent circuit has been recently suggested for the same system but a slightly different configuration [21]. The four capacitors drawn in Supplementary Figure S5d represent either geometrical (C gt and C tb ) or quantum (Ae 2 D t and Ae 2 D b ) capacitances.…”

Section: The Equivalent Circuitmentioning

confidence: 74%

Probing Quantum Capacitance in a 3D Topological Insulator

et al. 2016

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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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Section: The Equivalent Circuitmentioning

confidence: 74%

Probing Quantum Capacitance in a 3D Topological Insulator

et al. 2016

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“…It is obtained similar to ref. 19 within the tight binding approximation of the 6 × 6—Kane Hamiltonian2728. Due to reduced point symmetry at the boundary between the Cd 0.7 Hg 0.3 Te and HgTe layers, an additional interface potential is allowed in the Hamiltonian29.…”

Section: Resultsmentioning

confidence: 99%

Observation of the universal magnetoelectric effect in a 3D topological insulator

et al. 2017

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The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

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“…We simulate the evolution of the charge distribution as a function of the orbital field by solving the time-dependent Schrödinger equation. As in typical experiments, we keep the total charge (not chemical potential) constant in our simulations [25,[42][43][44]. In particular, we consider a vector potential…”

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confidence: 99%

Survival of the Quantum Anomalous Hall Effect in Orbital Magnetic Fields as a Consequence of the Parity Anomaly

et al. 2019

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Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates the Onsager relation, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with σxy = −e 2 /h to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.

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Self-consistentk·pcalculations for gated thin layers of three-dimensional topological insulators

Cited by 11 publications

References 23 publications

Probing Quantum Capacitance in a 3D Topological Insulator

Probing Quantum Capacitance in a 3D Topological Insulator

Observation of the universal magnetoelectric effect in a 3D topological insulator

Survival of the Quantum Anomalous Hall Effect in Orbital Magnetic Fields as a Consequence of the Parity Anomaly

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