HgTe Films Research Articles

Transport properties of a 1000 nm HgTe film: the interplay of surface and bulk carriers

We report on systematic study of transport properties of a 1000 nm HgTe film. Unlike thinner and strained HgTe films, which are known as high-quality three-dimensional topological insulators, the film under study is much thicker than the limit of pseudomorphic growth of HgTe on a CdTe substrate. Therefore, the 1000 nm HgTe film is expected to be fully relaxed and has the band structure of bulk HgTe, i.e. a zero gap semiconductor. Additionally, the system is characterized by the bands inversion, so that the two-dimensional topological surface states (TSSs) are expected to exist. To check this claim we studied classical and quantum transport response of the system. We demonstrate that by tuning the top-gate voltage one can change the electron-dominating transport to the hole one. The highest electron mobility is found to be more than cm2 Vs−1. The system exhibits Shubnikov-de Haas (SdH) oscillations with a complicated pattern and shows up to five independent frequencies in corresponding Fourier spectra. These Fourier peaks are attributed to the TSSs, Volkov-Pankratov states and spin-degenerate bulk states in the accumulation layer near the gate. The observed peculiarities of the quantum transport are the strong SdH oscillations of the Hall resistance, and the suppressed oscillatory response of the TSSs.

Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission

HgTe is a prime example of a topological material that exhibits a range of topological phases based on its dimensionality and lattice strain. The key to its topological properties lies in the band inversion between the Hg 6$s$ and Te 5$p$ valence levels, leading to the emergence of surface states. In this study, the authors present an in-depth examination of the electronic structure of strained HgTe films using angle-resolved photoelectron spectroscopy and density functional theory. The results offer a direct visualization of the topological band inversion and surface states present in HgTe.

Pressure-Induced Superconductivity in HgTe Single-Crystal Film.

HgTe film is widely used for quantum Hall well studies and devices, as it has unique properties, like band gap inversion, carrier‐type switch, and topological evolution depending on the film thickness modulation near the so‐called critical thickness (63.5 Å), while its counterpart bulk materials do not hold these nontrivial properties at ambient pressure. Here, much richer transport properties emerging in bulk HgTe crystal through pressure‐tuning are reported. Not only the above‐mentioned abnormal properties can be realized in a 400 nm thick bulk HgTe single crystal, but superconductivity is also discovered in a series of high‐pressure phases. Combining crystal structure, electrical transport, and Hall coefficient measurements, a p‐n carrier type switching is observed in the first high‐pressure cinnabar phase. Superconductivity emerges after the semiconductor‐to‐metal transition at 3.9 GPa and persists up to 54 GPa, crossing four high‐pressure phases with an increased upper critical field. Density functional theory calculations confirm that a surface‐dominated topologic band structure contributes these exotic properties under high pressure. This discovery presents broad and efficient tuning effects by pressure on the lattice structure and electronic modulations compared to the thickness‐dependent critical properties in 2D and 3D topologic insulators and semimetals.

Thermoelectric Transport in a Three-Dimensional HgTe Topological Insulator.

The thermoelectric response of 80 nm-thick strained HgTe films of a three-dimensional topological insulator (3D TI) has been studied experimentally. An ambipolar thermopower is observed where the Fermi energy moves from conducting to the valence bulk band. The comparison between theory and experiment shows that the thermopower is mostly due to the phonon drag contribution. In the region where the 2D Dirac electrons coexist with bulk hole states, the Seebeck coefficient is modified due to 2D electron–3D hole scattering.

Energy spectrum of semimetallic HgTe quantum wells

Quantum wells (QWs) based on mercury telluride (HgTe) thin films provide a large scale of unusual physical properties starting from an insulator via a two-dimensional Dirac semimetal to a three-dimensional topological insulator. These properties result from the dramatic change of the QW band structure with the HgTe film thickness. Although being a key property, these energy dispersion relations cannot be reflected in experiments due to the lack of appropriate tools. Here we report an experimental and theoretical study of two HgTe quantum wells with inverted energy spectrum in which two-dimensional semimetallic states are realized. Using magneto-optical spectroscopy at sub-THz frequencies we were able to obtain information about electron and hole cyclotron masses at all relevant Fermi level positions and different charge densities. The outcome is also supported by a Shubnikov-de Haas analysis of capacitance measurements, which allows obtaining information about the degeneracy of the active modes. From these data, it is possible to reconstruct electron and hole dispersion relations. Detailed comparative analysis of the energy dispersion relations with theoretical calculations demonstrates a good agreement, reflecting even several subtle features like band splitting, the second conduction band, and the overlaps between the first conduction and first valence band. Our study demonstrates that the cyclotron resonance experiments can be efficiently used to directly obtain the band structures of semimetallic 2D materials.

Hybridization three subbands at Dirac point in special designed strained HgTe thin films with structural inversion asymmetry

We study specially designed strained thin HgTe layers with structural inversion asymmetry (SIA) which allow us to distinguish the topological surface states (TSS) typical for a two dimensional (2D) quantum well system in a subband state. To obtain such a dispersion relation on the basis of the eight-band kp model, the theoretical investigation calculations of thin (below 25 nm wide) HgTe strained films with SIA are investigated. The numerical band-gap engineering and dispersion relation allow us to obtain a new class of materials that are characterized by a Dirac-like dispersion and hybridization of the three different charges describing two TSS and one quantum well subband at Γ-point (zero gap). This opens up many possibilities from the applications point of view. An external electric field removed this degeneration and opened a band gap between Γ6, (lh—light hole) and (hh—heavy hole) subbands characteristic for TSS and the subband characteristic for the 2D quantum well state, respectively. The width of the band gap as a function of the external electric field is also considered. Due to consideration being given to the possible applications, analysis of the dispersion relation and Landau levels (LL) energy shape with SIA is also investigated. The possibility of tuning a band gap is promising from the point of view of, for example, THz detectors and emitters. What is very important, the proposed structures allow the avoidance of the coexistence of TSS with bulk states, as very often occurs in so-called 3D strained HgTe-like materials. Analysis of the wave function as a function of the width of the investigated structure as well as the external electric field is also presented. Due to the strong correlation between both states (2D and TSS), and their very well known properties, we expect that such HgTe films can be used as optical active layers in the THz region.

Weak antilocalization in partially relaxed 200-nm HgTe films

The anomalous magnetoresistance caused by the weak antilocalization (WAL) effects in 200-nm HgTe films is experimentally studied. The film is a high quality 3D topological insulator with much stronger spatial separation of surface states than in previously studied thinner HgTe structures. However, in contrast to that films, the system under study is characterized by a reduced partial strain resulting in an almost zero bulk energy gap. It has been shown that at all positions of the Fermi level the system exhibits a WAL conductivity correction superimposed on classical parabolic magnetoresistance. Since high mobility of carriers, the analysis of the obtained results was performed using a ballistic WAL theory. The maximum of the WAL conductivity correction amplitude was found at a Fermi level position near the bulk energy gap indicating to full decoupling of the surface carriers in these conditions. The WAL amplitude monotonously decreases when the density of either bulk electrons or holes increases that results from the increasing coupling between surface and bulk carriers.

Optical absorption in the terahertz region in HgTe/HgCd(Mn)Te double quantum well structures with a topological phase and structural inversion asymmetry

On the basis of the eight-band kp model, the theoretical engineering of HgTe/HgCd(Mn)Te double quantum well (DQW) structures is presented in this study. An external magnetic field and structural inversion asymmetry are taken into account. The advantages of HgTe two-dimensional topological insulator (2D TI) layers with x-Cd or x-Mn over pure 2D TI HgTe films are theoretically and experimentally proven. All advantages, such as the larger Fermi velocity, very high mobility of the surfaces states, the larger g factor for such mixed layers together with the sharpens on the edge layers in the 2D TI structures and the structural inversion asymmetry (which can be easy realized in the 2D DQW case), mean that the presented structures are encouraging as the basis of, for example, high resolution terahertz detectors. Considering this possible application, the optical transition for the cyclotron resonance and the excitation transfer in the terahertz region is analyzed. The results of the presented investigation are very promising for the application of HgTe/HgCd(Mn)Te DQW structures in terahertz detector.

Terahertz photoresistivity of a high-mobility 3D topological insulator based on a strained HgTe film

We report on a detailed study of terahertz (THz) photoresistivity in a strained HgTe three-dimensional topological insulator (3D TI) for all Fermi level positions: inside the conduction and valence bands and in the bulk gap. In the presence of a magnetic field, we detect a resonance corresponding to the cyclotron resonance (CR) in the top surface Dirac fermions (DFs) and examine the nontrivial dependence of the surface state cyclotron mass on the Fermi level position. We also detect additional resonant features at moderate electron densities and demonstrate that they are caused by the mixing of surface DFs and bulk electrons. At high electron densities, we observe THz radiation-induced 1/B-periodic low-field magneto-oscillations coupled to harmonics of the CR and demonstrate that they have a common origin with microwave-induced resistance oscillations previously observed in high mobility GaAs-based heterostructures. This observation attests the superior quality of a 2D electron system formed by helical surface states in strained HgTe films.

Topological insulators based on HgTe

The most interesting experimental results obtained in studies of 2D and 3D topological insulators (TIs) based on HgTe quantum wells and films are reviewed. In the case of 2D TIs, these include the observation of nonlocal ballistic and diffusion transport, the magnetic breakdown of 2D TIs, and an anomalous temperature dependence of edge-channel resistance. In 3D TIs, a record-setting high mobility (up to 5 × 105 cm2 V−1 s−1) of surface two-dimensional Dirac fermions (DFs) has been attained. This enabled determining all the main TI parameters (the bulk gap and the density of DFs on both of its surfaces) and provided information on the phase of the Shubnikov–de Haas oscillations of DFs, which indicates the rigid topological coupling between the fermion spin and momentum. Prospects for further research are discussed in the conclusion.

MBE Growth and Characterization of Strained HgTe (111) Films on CdTe/GaAs**Supported by the National Natural Science Foundation of China (Grant Nos. 11634009, 61874069, 1177041280 and 11574336), and Shanghai Science and Technology Foundation (Grant No.18JC1420401).

Strained HgTe thin films are typical three-dimensional topological insulator materials. Most works have focused on HgTe (100) films due to the topological properties resulting from uniaxial strain. In this study, strained HgTe (111) thin films are grown on GaAs (100) substrates with CdTe (111) buffer layers using molecular beam epitaxy (MBE). The optimal growth conditions for HgTe films are determined to be a growth temperature of 160°C and an Hg/Te flux ratio of 200. The strains of HgTe films with different thicknesses are investigated by high-resolution x-ray diffraction, including reciprocal space mapping measurements. The critical thickness of HgTe (111) film on CdTe/GaAs is estimated to be approximately 284 nm by Matthews’ equations, consistent with the experimental results. Reflection high-energy electron diffraction and high-resolution transmission electron microscopy investigations indicate that high-quality HgTe films are obtained. This exploration of the MBE growth of HgTe (111) films provides valuable information for further studies of HgTe-based topological insulators.

Shubnikov—de Haas Oscillations in a Three-Dimensional Topological Insulator Based on a Strained HgTe Film in an Inclined Magnetic Field

Specific features in the formation of Landau levels in a three-dimensional topological insulator based on an 80-nm-thick strained mercury telluride film in an inclined magnetic field are studied. The magnetoresistance in the Hall bar geometry with a gate is measured at a temperature 1.9 K and in an applied magnetic field up to 10 T. The gate allows varying the Fermi level position from the valence to conduction band, passing through the bulk band gap. The samples are mounted on a rotating platform that makes it possible to change arbitrarily the angle between the magnetic field direction and the normal to the sample plane within the range of 0°–90°. It is found that the Shubnikov–de Haas oscillations are formed if the perpendicular magnetic field component exceeds 0.4 T, independent of the applied gate voltage. However, the sensitivity of the system to the parallel magnetic field component exhibits a pronounced dependence on the applied gate voltage. Namely, if the Fermi level is in the bulk band gap and the conductivity is determined by the surface states, the amplitude and position of Shubnikov–de Haas oscillations remain independent of the perpendicular magnetic field component even in the situation where the parallel component is twice as large as the perpendicular one. At high magnetic fields, the amplitude of oscillations is suppressed by the parallel field component. On the contrary, if the Fermi level is in the valence or conduction band, the parallel field component not only affects the amplitude of oscillations but also results even in their qualitative changes, e.g., giving rise to new minima related to Zeeman splitting. The observed behavior of the system is in agreement with the modern concepts concerning the spin polarization of the surface state in three-dimensional topological insulators and the spin degeneracy of charge carriers in the bulk.

Cyclotron-resonance-induced photogalvanic effect in surface states of 200-nm-thick strained HgTe films

We report on the study of magneto-photogalvanic and magnetotransport phenomena in 200 nm partially strained HgTe films. This thickness is slightly larger than the estimated critical thickness of lattice relaxation leaving the film partially relaxed with the value of the energy gap close to zero. We show that illumination of HgTe films with monochromatic terahertz laser radiation results in a giant resonant photocurrent caused by the cyclotron resonance in the surface states. The resonant photocurrent is also detected in the reference fully strained 80 nm HgTe films previously shown to be fully gapped 3D topological insulators. We show that the resonance positions in both types of films almost coincide demonstrating the existence of topologically protected surface states in thick HgTe films. The conclusion is supported by magnetotransport experiments.

Topological surface states in thick partially relaxed HgTe films

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 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, it is essential to increase the HgTe thickness further. In this work, by combining transport measurements together with capacitance spectroscopy, we perform an analysis of a 200-nm partially relaxed HgTe film. The Drude fit of the classical magnetotransport reveals the ambipolar electron-hole transport with a high electron mobility. A detailed analysis of Shubnikov-de Haas oscillations in both conductivity and capacitance allows us to distinguish three groups of electrons, identified as electrons on top and bottom surfaces and bulk electrons. The indirect bulk energy gap value is found to be close to zero. It is established that the significant gap decrease does not affect the surface states, which are found to be well resolved and spin nondegenerate. The presented techniques allow investigations of other three-dimensional TIs, regardless of the presence of bulk conductivity.

Transmission Spectra of HgTe-Based Quantum Wells and Films in the Far-Infrared Range

Strained 80-nm-thick HgTe films belong to a new class of materials referred to as three-dimensional topological insulators (i.e., they have a bulk band gap and spin-nondegenerate surface states). Though there are a number of studies devoted to analysis of the properties of surface states using both transport and magnetooptical techniques in the THz range, the information about direct optical transitions between bulk and surface bands in these systems has not been reported. This study is devoted to the analysis of transmission and reflection spectra of HgTe films of different thicknesses in the far-infrared range recorded in a wide temperature range in order to detect the above interband transitions. A peculiarity at 15 meV, which is sensitive to a change in the temperature, is observed in spectra of both types. Detailed analysis of the data obtained revealed that this feature is related to absorption by HgTe optical phonons, while the interband optical transitions are suppressed.

Спектры пропускания квантовых ям и пленок на основе HgTe в дальнем ИК-диапазоне

AbstractStrained 80-nm-thick HgTe films belong to a new class of materials referred to as three-dimensional topological insulators (i.e., they have a bulk band gap and spin-nondegenerate surface states). Though there are a number of studies devoted to analysis of the properties of surface states using both transport and magnetooptical techniques in the THz range, the information about direct optical transitions between bulk and surface bands in these systems has not been reported. This study is devoted to the analysis of transmission and reflection spectra of HgTe films of different thicknesses in the far-infrared range recorded in a wide temperature range in order to detect the above interband transitions. A peculiarity at 15 meV, which is sensitive to a change in the temperature, is observed in spectra of both types. Detailed analysis of the data obtained revealed that this feature is related to absorption by HgTe optical phonons, while the interband optical transitions are suppressed.

Quantum capacitance of a three-dimensional topological insulator based on HgTe

The quantum capacitance that directly characterizes the density of states of highly mobile Dirac two-dimensional states formed on the surface of a stressed HgTe film is studied experimentally. It is shown that, as opposed to the oscillations in the magnetotransport to which all the existing types of carriers contribute, the quantum oscillations observed in the magnetic capacitance correspond to electrons on the upper surface of the film. Thus, capacitance spectroscopy is a selective technique for studying the properties of an individual topological surface, even when a large number of bulk carriers are present. Because of this feature, for the first time we have obtained data on the phase shift in the Shubnikov-de Haas oscillations usually associated with the Berry phase for an isolated Dirac cone and found its dependence on the location of the Fermi level.

Terahertz properties of Dirac fermions in HgTe films with optical doping

Terahertz properties of mercury telluride (HgTe) films with critical thickness are presented and discussed. The density of the charge carriers is controlled using contact-free optical doping by visible light. In the magneto-optical response of HgTe the contribution of two types of carriers (electrons and holes) can be identified. The density of the electrons can be modified by light illumination by more than one order of magnitude. As the hole density is roughly illumination-independent, the terahertz response of the illuminated samples becomes purely electronic. In some cases, light illumination may switch the qualitative electrodynamic response from hole-like to the electron-like. The cyclotron mass of the electrons could be extracted from the data and shows a square root dependence upon the charge concentration in the broad range of parameters. This can be interpreted as a clear proof of a linear dispersion relations, i.e. Dirac-type charge carriers.

Weak antilocalization in a three-dimensional topological insulator based on a high-mobility HgTe film

The anomalous magnetoresistance (AMR) caused by the weak antilocalization effects in a three-dimensional topological insulator based on a strained mercury telluride film is experimentally studied. It is demonstrated that the obtained results are in a good agreement with the universal theory of Zduniak, Dyakonov, and Knap. It is found that the AMR in the bulk band gap is far below that expected for the system of Dirac fermions. Such a discrepancy can assumingly be related to a nonzero effective mass of Dirac fermions. The filling of energy bands in the bulk is accompanied by a pronounced increase in the AMR. This is a signature of the weak coupling between the surface and bulk charge carriers.

Cyclotron-resonance-assisted photocurrents in surface states of a three-dimensional topological insulator based on a strained high-mobility HgTe film

We report on the observation of cyclotron resonance induced photocurrents, excited by continuous wave terahertz radiation, in a 3D topological insulator (TI) based on an 80 nm strained HgTe film. The analysis of the photocurrent formation is supported by complimentary measurements of magneto-transport and radiation transmission. We demonstrate that the photocurrent is generated in the topologically protected surface states. Studying the resonance response in a gated sample we examined the behavior of the photocurrent, which enables us to extract the mobility and the cyclotron mass as a function of the Fermi energy. For high gate voltages we also detected cyclotron resonance (CR) of bulk carriers, with a mass about two times larger than that obtained for the surface states. The origin of the CR assisted photocurrent is discussed in terms of asymmetric scattering of TI surface carriers in the momentum space. Furthermore, we show that studying the photocurrent in gated samples provides a sensitive method to probe the effective masses and the mobility of 2D Dirac surface states, when the Fermi level lies in the bulk energy gap or even in the conduction band.