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Selective area growth is employed in the vapor-liquid-solid molecular beam epitaxy of ZnTe nanowire arrays. Full control over the location of the individual nanowires is achieved by defined positioning of the growth catalyst. This study addresses the influence of substrate material and growth temperature on the yield of vertical nanowires. The optimized procedure provides arrays of single-crystalline free-standing nanowires with a high ensemble uniformity. The nanowires exhibit a uniform shape with a diameter of about 80 nm and reach a length of more than 3μm, which makes them suitable as substrates for core-shell nanowires of the topological insulator material HgTe. ©2020 American Physical Society

The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature however deeply influences the properties of the supercurrent. Detailed studies of Josephson junctions can reveal microscopic properties of the superconducting pairing (spin-triplet correlations, $d$-wave symmetry) or of the electronic transport (quantum dot, ballistic channels). In recent years, considerable efforts have focused on the coupling of superconductors to topological insulators, in which transport is mediated by topologically protected Dirac surface states with helical spin polarization (while the bulk remains insulating). Here, the proximity of a superconductor is predicted to give rise to unconventional induced $p$-wave superconductivity, with a doublet of topologically protected gapless Andreev bound states, whose energies varies $4\pi$-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction with a weak link of the 3D topological insulator HgTe. The response is understood as due to a $4\pi$-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet., Comment: revised version, main text : 15 pages, 4 figures, supplementary information : 34 pages, 17 figures

We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted., Comment: 5 pages, 4 figures, supp. mat

It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. In this article we report on a set of experimental observations indicating the existence of massive surface states. These states are confined at the interface and dominate equilibrium and transport properties at high energy and/or high electric field. By monitoring the AC admittance of HgTe topological insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energy and electric fields. The Dirac surface states are characterized by a compressibility minimum, a linear energy dependence and a high mobility persisting up to energies much larger than the transport bandgap of the bulk. New features are revealed at high energies with signatures such as conductance peaks, compressibility bumps, a strong charge metastability and a Hall resistance anomaly. These features point to the existence of excited massive surface states, responsible for a strong intersubband scattering with the Dirac states and the nucleation of metastable bulk carriers. The spectrum of excited states agrees with predictions of a phenomenological model of the topological-trivial semiconductor interface. The model accounts for the finite interface depth and the effect of electric fields. The existence of excited topological states is essential for the understanding of topological phases and opens a route for engineering and exploiting topological resources in quantum technology., Comment: 29 pages, 8 figures

Magnetoresistance studies are one of the simplest yet powerful tools to investigate the electronic properties of solids. The authors here report on high-field angle-dependent magnetotransport measurements on epitaxial thin films of Bi${}_{2}$Se${}_{3}$, a three-dimensional topological insulator. At low temperature, they observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. Their key observation is a strong anisotropy in the magnetoresistance in Bi${}_{2}$Se${}_{3}$ that depends on the orientation of the applied current (electric field) with respect to the applied magnetic field. When the magnetic field is applied parallel to the electric field, they find a strong negative longitudinal magnetoresistance (NLMR) that, quite strikingly, persists even up to room temperature. With this finding, the authors demonstrate that the observation of a NLMR is not unique to topological semimetals, such as Weyl semimetals, and therefore cannot by itself be taken as a diagnostic tool and as conclusive evidence for the existence of Weyl fermions. These results could pave the way towards a general understanding of the emergence of the axial anomaly that is suggested to be a universal phenomenon for generic three-dimensional metals in the presence of parallel electric and magnetic fields.

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 $e^2 / 2 h c $ per surface. Here, we report on the observation of this so-called topological magnetoelectric (TME) effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semi-transparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant $\alpha = e^2 / \hbar c$ 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., Comment: Submitted 13 March, 2016; 7 pages, 4 figures

Dirac fermions have been studied intensively in condensed matter physics in recent years. Many theoretical predictions critically depend on the number of valleys where the Dirac fermions are realized. In this work, we report the discovery of a two dimensional system with a single valley Dirac cone. We study the transport properties of HgTe quantum wells grown at the critical thickness separating between the topologically trivial and the quantum spin Hall phases. At high magnetic fields, the quantized Hall plateaus demonstrate the presence of a single valley Dirac point in this system. In addition, we clearly observe the linear dispersion of the zero mode spin levels. Also the conductivity at the Dirac point and its temperature dependence can be understood from single valley Dirac fermion physics., version 2: supplementary material added

Non-local transport measurements on mercury telluride quantum wells show clear signatures of the ballistic spin Hall effect. The ballistic nature of the experiment allows the observed effect to be interpreted as a direct consequence of the band structure of these semiconductor nanostructures, rather that being caused by impurity scattering.

We investigated the magnetoconductivity and the Terahertz (THz) photo-conductivity of devices with HgTe quantum wells embedded in barrier layers of HgCdTe. For the photoconductivity measurements, a THz laser system (p-Ge-Laser) is applied. This laser uses transitions between Landau levels of light holes in Ge and emits laser pulses in the wavelength range 120 μm < λ < 180 μm. The THz laser radiation is used in order to excite charge carriers over the Landau-gap. The response of the sample to the laser impulses is in 2D-samples in the quantum Hall (QH) regime measured in order to receive data of the relaxation of the charge carriers. In this presentation we present photoconduction measurements of the HgTe-quantum well in Hall bar, Corbino as well as combined Corbino-Hall bar geometry in the QH-regime. The material system HgTe/HgCdTe is characterized by a small effective mass (compared to GaAs, in our case 0.023 m0) and accordingly smaller magnetic fields for the appropriate cyclotron energy. Thus, this material combination provides the opportunity to make THz detectors using magnetic fields below 2 T for operation.

The influence of interfaces in the structure of HgTe based quantum wells (QW's), their structure as well as the necessary technological processes on their transport properties have been investigated and either reduced or optimized. The mobility (μ) of the 2-dimensional electron gas (2DEG) has been shown to increase when the separation of the 2DEG from the ionized donors is increased, and when the separation of the QW structure from both the insulator on top and the CdTe buffer interface is increased. Furthermore, replacing wet chemical etching in the Hall bar photolithography procedure with a dry plasma etch process resulted in a 2.5 fold increase in the μ. Values for μ up to 0.7 × 106 cm2/(Vs) at 4.2 K have been reproducibly achieved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We report on magneto-optical studies of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parameters: the fundamental band gap and the band velocity. In a magnetic field, this model implies a unique property---spin splitting equal to twice the cyclotron energy: ${E}_{s}=2{E}_{c}$. This explains the extensive magnetotransport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The ${E}_{s}=2{E}_{c}$ match differentiates the massive Dirac electrons in bulk ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ from those in quantum electrodynamics, for which ${E}_{s}={E}_{c}$ always holds.

We report on magneto-optical studies of Bi2Se3, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parameters: the fundamental band gap and the band velocity. In a magnetic field, this model implies a unique property-spin splitting equal to twice the cyclotron energy: Es=2Ec. This explains the extensive magnetotransport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The Es=2Ec match differentiates the massive Dirac electrons in bulk Bi2Se3 from those in quantum electrodynamics, for which Es=Ec always holds.

We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.

The terahertz (THz) photoconductivity is investigated in HgTe/HgCdTe-quantum wells (QWs) in Corbino geometry at various wavelengths of excited radiation. The radiation source is a p-Ge cyclotron laser (pulse width about 1 µs, repetition rate 1 Hz) which is tunable in the wavelength range 120 µm

We demonstrate electrical control of the room temperature Faraday effect in a 100-nm-thick film of strained HgTe, which is a topological insulator. The terahertz (THz) response of our device is dominated by the Drude response of carriers with high mobility. The electrical control is achieved by gating the carrier density in a static magnetic field, opening new perspectives for applications like high-speed amplitude and phase modulators in the THz frequency range.

Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.

This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.

HgTe/Hg${}_{x}$Cd${}_{1\ensuremath{-}x}$Te quantum wells with the inverted band structure have been probed using far-infrared magnetospectroscopy. Realistic calculations of Landau level diagrams have been performed to identify the observed transitions. Investigations have been greatly focused on the magnetic field dependence of the peculiar pair of ``zero-mode'' Landau levels, which characteristically split from the upper conduction and bottom valence bands, and merge under the applied magnetic field. The observed avoided crossing of these levels is tentatively attributed to the bulk inversion asymmetry of zinc-blende compounds.

We report transport studies on a three dimensional, 70 nm thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semi-metallic HgTe, which thus becomes a three dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states., 7 pages, 6 figures

In this study we present measurements of the Terahertz (THz) photoconductivity of 2D electron system realized at HgTe∕HgCdTe and AlInSb∕InSb∕AlInSb quantum wells (QWs) in Corbino geometry (inner and outer radius: 500 μm and 1500 μm) with different mobilities and electron densities. To characterize the devices, the Shubnikov‐de Haas (SdH) effect up to magnetic fields B of 7T and current‐voltage (I‐V) characteristics at various magnetic fields were measured. The THz radiation is provided by a p‐Ge laser which operates with a magnetic field and a high voltage for the electrical pumping. The stimulated emission is caused by transistions between Landau levels of light holes [1]. The laser is tunable in the range between 1.7 to 2.5 THz (corresponding to wavelengths between 120 to 180 μm or energies of 7 to 12 meV). The laser is pulsed with a pulse rate of 1 Hz and pulse lengths of about 1 μs with low switching times (about 20 ns). The monochromatic THz radiaton is tranferred to our samples via a 0.32m long brass waveguide immersed in liquid Helium. The detection of a change in the conductivity of the sample due to absorption of THz‐radiation (photoresponse) requires a low‐noise circuit. For the Corbino‐shaped samples the photoresponse (PR) is measured via a resistor RV of 1 kΩ. The signal is transferred via in a high‐frequency cable and detected with a digital oscilloscope.

We present a survey of photoresponse (PR) measurements of various devices containing quantum wells (QWs) of HgTe of various widths dQW and of InSb. By varying dQW for HgTe, the material properties of the QW material change from semiconducting to semimetallic as dQW is increased above a value of about 6nm. We have studied the PR of devices made from CdxHg1−xTe/HgTe/CdxHg1−xTe wafers with values of the QW width in the range of 6 nm ≤ dQW ≤ 21 nm. Only for samples with semimetallic HgTe QWs, a measurable PR could be detected. However, our investigations of samples made from AlxIn1−xSb/InSb/AlxIn1−xSb wafers gave evidence that a measurable PR also can appear from devices with a semiconducting QW. Both cyclotron-resonant (CR) and nonresonant (bolometric, BO) interaction mechanisms can contribute to the PR signal. Whereas the CR contribution is dominant in AlxIn1−xSb/InSb/AlxIn1−xSb samples, in CdxHg1−xTe/HgTe/CdxHg1−xTe samples the behavior is more complex. In a sample with dQW = 8 nm, the PR is clearly dominated by the BO contribution. In the PR of another sample of dQW = 12 nm, both contributions (BO and CR) are present. The sample of dQW = 21 nm shows a PR with not clearly separable BO and CR contributions.

We report the observation of a giant Faraday effect, using terahertz (THz) spectroscopy on epitaxial HgTe thin films at room temperature. The effect is caused by the combination of the unique band structure and the very high electron mobility of HgTe. Our observations suggest that HgTe is a high-potential material for applications as optical isolator and modulator in the THz spectral range.

The density-dependent mobility of n-type HgTe quantum wells with inverted band ordering has been studied both experimentally and theoretically. While semiconductor heterostructures with a parabolic dispersion exhibit an increase in mobility with carrier density, high quality HgTe quantum wells exhibit a distinct mobility maximum. We show that this mobility anomaly is due to backscattering of Dirac fermions from random fluctuations of the band gap (Dirac mass). Our findings open new avenues for the study of Dirac fermion transport with finite and random mass, which so far has been hard to access., Comment: version as published in Phys. Rev. Lett. 106, 076802 (2011)

Terahertz-frequencies in semiconductor quantum wells are of interest due to the opportunity for making devices that operate at THz frequencies. In this study we present magnetotransport and magnetooptical data obtained in the magnetic field range 0 < B < 7T at QH detectors patterned as Corbino rings on AlInSb/InSb/AlInSb and HgCdTe/HgTe/HgCdTe quantum well wafers.

This study concerns the experimental investigation of the Terahertz ‐(THz‐) photoresponse in systems under quantum‐Hall‐(QH‐) conditions. These investigations are interesting regarding a potential application of QH‐systems as fast and spectrally sensitive THz‐detectors. The measurements of the THz‐photoresponse (PR) of devices with HgTe quantum wells (QWs) embedded in CdHgTe barriers are aimed at obtaining photosignals at smaller magnetic fields in comparison to detectors made of GaAs/AlGaAs wafers. This can be realized by changing the electron density (application of a gate electrode). The QWs have a thickness of dQW between 7 nm and 12 nm, so that the material HgTe of the QW possesses a semimetallic band structure. We found a cyclotron mass of about mc = 0.026 m0 for our samples from cyclotron resonance measurements (also approximately determined from our PR). As this cyclotron mass is by about a factor 3 smaller than the one of electrons in GaAs, the same Landau level splitting is reached at about 1/3 of the magnetic field as in GaAs.

We report on the observation of nonlinear magneto-gyrotropic photogalvanic effect in HgTe/HgCdTe quantum wells. The interband absorption of mid-infrared radiation as well as the intrasubband absorption of terahertz radiation in the heterostructures is shown to cause a dc electric current in the presence of an in-plane magnetic field. A cubic in magnetic field component of the photocurrent is observed in quantum wells with the inverted band structure only. The experimental data are discussed in terms of both the phenomenological theory and microscopic models., Comment: 10 pages, 9 figures

HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magneto-photoresponse (PR) and magneto-transport measurements. The QW sample has the conventional band alignment with the well thickness (6.1 nm) slightly smaller than the critical thickness for the topological phase transition. The effective gap of this structure is roughly 10 meV, and the large sheet density ([Formula: see text] m-2) of the two-dimensional electron gas (2DEG) results in a very large Fermi energy ([Formula: see text] meV). We have found several interesting effects at these high densities. In this paper we focus on an observed beating of quantum oscillations in the PR signal (at 1.83 THz) and compare it with direct measurements of oscillations in the longitudinal magneto-resistance (Rxx). The mechanism for the PR is cyclotron resonance absorption heating of the electrons (an electron bolometric effect). We attribute the beating to Rashba splitting of the spin states, which is barely observable in direct Rxx measurements under strong gate-induced electric fields.

We present a fabrication process for devices on HgTe quantum wells through which the quantum spin Hall regime can be reached without the use of a top-gate electrode. We demonstrate that a nominally undoped HgTe quantum well can be tuned from p-type to n-type, crossing through the quantum spin Hall regime, using only a back-gate hundreds of microns away. Such structures will enable scanning probe investigations of the quantum spin Hall effect that would not be possible in the presence of a gate electrode on the surface of the wafer. All processes are kept below 80 °C to avoid degradation of the heat-sensitive HgTe quantum wells.

Thin films of HgTe have been systematically investigated using continuous frequency terahertz spectroscopy in external magnetic fields. In these experiments, full control of the polarization state can be achieved including Faraday rotation and ellipticity. We present the details of the experimental procedure and of the data analysis. Besides the cyclotron resonance, an additional mode is observed in the zero-gap sample. The results at high temperatures can be well understood within the classical Drude model of the dynamic conductivity. Possible dimensionality of the charge dynamics at low temperatures is discussed.

We present a magneto-optical study of the three-dimensional topological insulator, strained HgTe using a technique which capitalizes on advantages of time-domain spectroscopy to amplify the signal from the surface states. This measurement delivers valuable and precise information regarding the surface state dispersion within, Published version, online Sept 23, 2011

This corrects the article DOI: 10.1103/PhysRevLett.117.086403.