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Interference transport in mesoscopic samples of a two-dimensional topological insulator in CdHgTe quantum wells is studied for the first time. It is established that quasi-ballistic edge transport in such an insulator exists at lengths up to 10 µm. In this transport regime, almost periodic Aharonov–Bohm oscillations caused by the formation of closed loops with a characteristic size of about 200 nm by edge states are found. The phase coherence length in the two-dimensional topological insulator is determined for the first time from the measured temperature dependence of their amplitude.

An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022340045

The transport response of a CdHgTe quantum well with a thickness of 11.5 nm is investigated. The behavior of the local and nonlocal resistance in the temperature range from 0.1 to 20 K is examined. It is shown that the system under study is a two-dimensional topological insulator. In comparison with traditional two-dimensional topological insulators implemented in 8-nm-thick HgTe quantum wells, the investigated one is characterized by a significantly smaller energy gap and, at the same time, a higher carrier mobility. The data are analyzed using computer simulations taking into account the actual geometry of the sample, as well as scattering between edge and bulk carrier states. It is shown that the backscattering probability of topological electrons within the edge states is nearly independent of temperature. In contrast, the probability of scattering from the edge channels into the bulk depends exponentially on the temperature, and fitting this dependence with a standard activation formula is the most accurate way to determine the mobility gap in the system under study. Even at the highest temperature, the probability of scattering between the counter-propagating states of the same edge exceeds the probability of scattering into the bulk by an order of magnitude. Therefore, this mechanism is dominant and determines the mean free path of edge electrons.

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 300 × 10 3 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.

We demonstrate that long-debated immunity of microwave-induced resistance oscillations (MIRO) to the sense of circular polarization is not a generic property of this phenomenon in solid-state two-dimensional electron systems. Using a large-area GaAs-based heterostructure we detect up to 30 times larger MIRO signal for the cyclotron resonance (CR) active helicity, fully consistent with the concurrently measured transmission and the deduced CR shape of the Drude absorption. We further elaborate conditions to avoid extrinsic factors capable of producing an apparent immunity of the photoresponse.

The low-frequency microwave photoconductance of a short (100 nm) quantum point contact based on a high-mobility two-dimensional electron gas in the frequency range of 2–3 GHz is investigated for the first time. The giant photoconductance in the tunneling regime and the negative photoconductance in the open regime are observed. It is shown by numerical simulations that such response to microwave irradiation is caused by the forced oscillations of the saddle-point potential in the quantum point contact and of the probe voltage applied to the contact.

An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022390023

We report on a detailed experimental study of the electron transport anisotropy in HgTe (013) quantum well of 22 nm width in the directions $[100]$ and $[03\bar{1}]$ as the function of the electron density $n$. The anisotropy is absent at minimal electron density near the charge neutrality point. The anisotropy increases with the increase of n and reaches about 10% when the Fermi level is within the first subband H1. There is a sharp increase of the anisotropy (up to 60%) when the Fermi level reaches the second subband E2. We conclude that the first effect is due to the small intra-subband anisotropic interface roughness scattering, and the second one is due to the strongly anisotropic inter-subband roughness scattering, but the microscopical reason of such a strong change in the anisotropy remains unknown., 4 pages, 5 figures, published in Applied Physics Letters

Studies of photon-stimulated transport through a quantum point contact based on a high-mobility two-dimensional electron gas in a GaAs quantum well are reviewed. This review includes a brief historical introduction, experimental results on giant terahertz and microwave photoconductance of the quantum point contact in the tunneling regime, and the analysis of its behavior within a developed theoretical model of photon-stimulated tunneling. Prospects of further studies and production of a new class of terahertz and microwave detectors are discussed in closing.

Experimental studies of photo- and thermoelectric phenomena in two-dimensional topological insulators and semimetals based on HgTe quantum wells have been briefly reviewed.

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 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., 18 pages, 24 figures

The electronic analog of the Poiseuille flow is the transport in a narrow channel with disordered edges that scatter electrons in a diffuse way. In the hydrodynamic regime, the resistivity decreases with temperature, referred to as the Gurzhi effect, distinct from conventional Ohmic behaviour. We studied experimentally an electronic analog of the Stokes flow around a disc immersed in a two-dimensional viscous liquid. The circle obstacle results in an additive contribution to resistivity. If specular boundary conditions apply, it is no longer possible to detect Poiseuille type flow and the Gurzhi effect. However, in flow through a channel with a circular obstacle, the resistivity decreases with temperature. By tuning the temperature, we observed the transport signatures of the ballistic and hydrodynamic regimes on the length scale of disc size. Our experimental results confirm theoretical predictions., Comment: 10 pages, 5 figures

Shubnikov de Haas resistance oscillations of highly mobile two dimensional helical electrons propagating on a conducting surface of strained HgTe 3D topological insulator are studied in magnetic fields B tilted by angle θ from the normal to the conducting layer. Strong decrease of oscillation amplitude A is observed with the tilt: $${\boldsymbol{A}}\sim {\boldsymbol{e}}{\boldsymbol{x}}{\boldsymbol{p}}(\,-\,{\boldsymbol{\xi }}/{\boldsymbol{c}}{\boldsymbol{o}}{\boldsymbol{s}}({\boldsymbol{\theta }}))$$A∼exp(−ξ/cos(θ)), where ξ is a constant. Evolution of the oscillations with temperature T shows that the parameter $${\boldsymbol{\xi }}$$ξ contains two terms: $${\boldsymbol{\xi }}={{\boldsymbol{\xi }}}_{1}+{{\boldsymbol{\xi }}}_{2}{\boldsymbol{T}}$$ξ=ξ1+ξ2T. The temperature independent term, $${{\boldsymbol{\xi }}}_{{\bf{1}}}$$ξ1, signals possible reduction of electron mean free path $${l}_{q}$$lq and/or enhancement of in-homogeneous broadening of the oscillations in magnetic field B. The temperature dependent term, $${{\boldsymbol{\xi }}}_{{\bf{2}}}{\boldsymbol{T}}$$ξ2T, indicates increase of the reciprocal velocity of 2D helical electrons: $$\delta ({v}_{F}^{-1})\sim B$$δ(vF−1)∼B suggesting modification of the electron spectrum in magnetic fields. Results are found in good agreement with proposed phenomenological model.

The microwave photoresistance of a two-dimensional topological insulator in a HgTe quantum well with an inverted spectrum has been experimentally studied under irradiation at frequencies of 110-169 GHz. Two mechanisms of formation of this photoresistance have been revealed. The first mechanism is due to transitions between the dispersion branches of edge current states, whereas the second mechanism is caused by the action of radiation on the bulk of the quantum well., Comment: 4 pages, 4 figures

Topological insulators represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D topological insulator or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe quantum wells near the Dirac point, where the conductance is determined by a percolation along the zero-gap lines. The experimental results confirm the presence of percolating conducting channels of a finite width. Our work establishes the critical width HgTe QW as a promising platform for the study of the interplay between topology and localization., 7 pages, 5 figures

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., 8 pages, 5 figures

The magnetotransport properties of massless Dirac fermions in a gapless HgTe quantum well are investigated. In samples with narrow channels, a large negative magnetoresistance with a Lorentzian profile is observed, which is interpreted as a manifestation of electron viscosity due to electron-electron interaction. Comparison of experiment with theory yields the shear stress relaxation time of the Dirac fermions caused by electron-electron scattering., 8 pages , 9 figures

The theory of coherent photon-assisted electron transmission through a one-dimensional smooth barrier is successfully used to model the results of measuring the terahertz photoconductivity of a tunneling point contact in a two-dimensional electron gas. For this barrier in a deeper tunneling mode, photon steps in the curve of the transmission coefficient versus initial electron energy were found. Their position is determined by the terahertz photon energy.

We present experimental results of non-linear transport in HgTe-based 2D topological insulators, where the conductance is dominated by Dirac-like helical edge states when the Fermi level is pinned to the bulk insulating gap. We find that hot carrier's energy relaxation is faster close to the charge neutrality point (CNP) which can be attributed to localized nature and incompressibility of charge puddles resulting from inhomogeneous charge distribution near CNP. The tunnel-coupling of these puddles (quantum dots) to 1D edge channels can randomize phase memory leading to incoherent inelastic processes. Hot edge carriers, excited by the electric field, relax to equilibrium via thermalization in multiple puddles resulting in the emission of phonons in the puddles. At relatively low temperature (T ≤ 10 K), the energy relaxation time shows strong temperature dependence (τe ∝ (Te−5)), which is interpreted as small angle scattering, consistent with resistance saturation at low temperatures.

We observe a large negative magnetoresistance and a decrease of resistivity with increasing temperature, known as the Gurzhi effect, in a bilayer electron (BL) system formed by a wide GaAs quantum well. A hydrodynamic model for the single fluid transport parameters in narrow channels is employed and successfully describes our experimental findings. We find that the electron-electron scattering in the bilayer is more intensive in comparison with a single-band well (SW). The hydrodynamic assumption implies a strong dependence on boundary conditions, which can be characterized by slip length, describing the behavior of a liquid near the edge. Our results reveal that slip length in a BL is shorter than in a SW, and that the BL system goes deeper into the hydrodynamic regime. This is in agreement with the model proposed where the slip length is of the order of the electron-electron mean free path., 8 pages, 8 figures

We study the effect of magnetic field on the properties of a high mobility gated two-dimensional electron gas in a field effect transistor with the Hall bar geometry. When approaching the current saturation when the drain side of the channel becomes strongly depleted, we see a number of unusual effects related to the magnetic field induced re-distribution of the electron density in the conducting channel. The experimental results obtained in the non-linear regime have been interpreted based on the results obtained in the linear regime by a simple theoretical model, which describes quite well our observations., 6 pages, 8 figures

The anomalous magnetoresistance caused by the weak antilocalization (WAL) effects in 200-nm HgTe films is experimentally studied. This system is a high quality 3D topological insulator that has much stronger spatial separation of surface states compare to previously studied thinner HgTe structures. However, in contrast to that films, the system under study is characterized by a reduced 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 positive 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 is caused by the increasing coupling between surface and bulk carriers.

From the analysis of the cyclotron resonance, we experimentally obtain the band structure of the three-dimensional topological insulator based on a HgTe thin film. Top gating was used to shift the Fermi level in the film, allowing us to detect separate resonance modes corresponding to the surface states at two opposite film interfaces, the bulk conduction band, and the valence band. The experimental band structure agrees reasonably well with the predictions of the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model. Due to the strong hybridization of the surface and bulk bands, the dispersion of the surface states is close to parabolic in the broad range of the electron energies.

The mobility and quantum time of Dirac electrons in HgTe quantum wells with near-critical thickness corresponding to the transition from the direct to inverted spectrum are experimentally and theoretically investigated. The nonmonotonic dependence of the mobility on the electron concentration is experimentally established. The theory of the scattering of Dirac electrons by impurities and irregularities of the well boundaries leading to well thickness fluctuations is constructed. The comparison of this theory with an experiment shows their good agreement and explains the observed nonmonotonic behavior by a decrease in the ratio between the de Broglie wavelength of Dirac electrons and the characteristic size of irregularities with increasing electron concentration. It is established that the transport time is larger than the quantum time by almost an order of magnitude in the case of the dominance of roughness scattering. The transition from macroscopic to mesoscopic samples is studied and an abrupt decrease in both the mobility and quantum time is observed. This behavior is attributed to the size effect on the free path length.

The photoresponse of the conductance of a tunneling quantum point contact to irradiation in the frequency range of 0.5–1.7 THz has been simulated within the theory of photon-assisted tunneling. The simulation has shown that the dependences of the conductance on the Fermi energy exhibit steps corresponding to transitions with the absorption of one, two, or three photons to channels near the top of the tunnel barrier. Under experimentally achievable conditions, the ratio of the photoconductance to the dark value on these steps can reach several orders of magnitude.

The effect of quantizing magnetic field on the electron transport is investigated in a two dimensional topological insulator (2D TI) based on a 8 nm (013) HgTe quantum well (QW). The local resistance behavior is indicative of a metal-insulator transition at $B\approx 6$ T. On the whole the experimental data agrees with the theory according to which the helical edge states transport in a 2D TI persists from zero up to a critical magnetic field $B_c$ after which a gap opens up in the 2D TI spectrum., Comment: 5 pages, 4 figures

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.

Information on the density of states of two-dimensional Dirac fermions in a 6.6-nm-thick HgTe quantum well that corresponds to a transition from the direct to inverted spectrum is obtained for the first time by means of capacitance measurements. It is found that the density of states of Dirac electrons is a linear function of the Fermi energy at EF > 30 meV with the corresponding velocity vDF = 8.2 × 105 m/s. At lower energies, this dependence deviates from the linear law, indicating a strong effect of disorder, which is associated with fluctuations of a built-in charge, on the density of states of the studied system near the Dirac point. At negative energies, a sharp increase in the density of states is observed, which is associated with the tail of the density of states of valleys of heavy holes. The described behavior is in agreement with the proposed model, which includes both the features of the real spectrum of Dirac fermions and the effect of the fluctuation potential.

We investigate the superradiance effects in three-dimensional topological insulator HgTe with conducting surface states. We demonstrate that the superradiance can be explained using the classical electrodynamic approach. Experiments using the continuous-wave spectroscopy allowed us to separate the energy losses in the system into intrinsic and radiation losses, respectively. These results demonstrate that the superradiance effects are not sensitive to the details of the band structure of the material.

We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime., Comment: 8 pages, 4 figures

We report on a strong nonlinear behavior of the photogalvanics and photoconductivity under excitation of HgTe quantum wells (QWs) by intense terahertz (THz) radiation. The increasing radiation intensity causes an inversion of the sign of the photocurrent and transition to its superlinear dependence on the intensity. The photoconductivity also shows a superlinear raise with the intensity. We show that the observed photoresponse nonlinearities are caused by the band-to-band light impact ionization under conditions of a photon energy less than the forbidden gap. The signature of this kind of impact ionization is that the angular radiation frequency $\ensuremath{\omega}=2\ensuremath{\pi}f$ is much higher than the reciprocal momentum relaxation time. Thus the impact ionization takes place solely because of collisions in the presence of a high-frequency electric field. The effect has been measured on narrow HgTe/CdTe QWs of 5.7 nm width; the nonlinearity is detected for linearly and circularly polarized THz radiation with different frequencies ranging from $f=0.6$ to 1.07 THz and intensities up to hundreds of kW/${\mathrm{cm}}^{2}$. We demonstrate that the probability of the impact ionization is proportional to the exponential function, $exp(\ensuremath{-}{E}_{0}^{2}/{E}^{2})$, of the radiation electric field amplitude $E$ and the characteristic field parameter ${E}_{0}$. The effect is observable in a wide temperature range from 4.2 to 90 K, with the characteristic field increasing with rising temperature.

Recent topological band theory distinguishes electronic band insulators with respect to various symmetries and topological invariants, most commonly, the time reversal symmetry and the $\rm Z_2$ invariant. The interface of two topologically distinct insulators hosts a unique class of electronic states -- the helical states, which shortcut the gapped bulk and exhibit spin-momentum locking. The magic and so far elusive property of the helical electrons, known as topological protection, prevents them from coherent backscattering as long as the underlying symmetry is preserved. Here we present an experiment which brings to light the strength of topological protection in one-dimensional helical edge states of a $\rm Z_2$ quantum spin-Hall insulator in HgTe. At low temperatures, we observe the dramatic impact of a tiny magnetic field, which results in an exponential increase of the resistance accompanied by giant mesoscopic fluctuations and a gap opening. This textbook Anderson localization scenario emerges only upon the time-reversal symmetry breaking, bringing the first direct evidence of the topological protection strength in helical edge states., Comment: version accepted by Phys. Rev. Lett

Topological states of matter have attracted a lot of attention due to their many intriguing transport properties. In particular, two-dimensional topological insulators (2D TI) possess gapless counter propagating conducting edge channels, with opposite spin, that are topologically protected from backscattering. Two basic features are supposed to confirm the existence of the ballistic edge channels in the submicrometer limit: the 4-terminal conductance is expected to be quantized at the universal value $2e^{2}/h$, and a nonlocal signal should appear due to a net current along the sample edge, carried by the helical states. On the other hand for longer channels the conductance has been found to deviate from the quantized value. This article reviewer the experimental and theoretical work related to the transport in two-dimensional topological insulators (2D-TI), based on HgTe quantum wells in zero magnetic field. We provide an overview of the basic mechanisms predicting a deviation from the quantized transport due to backscattering (accompanied by spin-flips) between the helical channels. We discuss the details of the model, which takes into account the edge and bulk contribution to the total current and reproduces the experimental results., Comment: 13 pages, 12 figures

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., Comment: 11 pages, 8 figures

The thermoelectric response of HgTe quantum wells in the state of two-dimensional topological insulator (2D TI) has been studied experimentally. Ambipolar thermopower, typical for an electron-hole system, has been observed across the charge neutrality point, where the carrier type changes from electrons to holes according to the resistance measurements. The hole-type thermopower is much stronger than the electron-type one. The thermopower linearly increases with temperature. We present a theoretical model which accounts for both the edge and bulk contributions to the electrical conductivity and thermoelectric effect in a 2D TI, including the effects of edge to bulk leakage. The model, contrary to previous theoretical studies, demonstrates that the 2D TI is not expected to show anomalies of thermopower near the band conductivity threshold, which is consistent with our experimental results. Based on the experimental data and theoretical analysis, we conclude that the observed thermopower is mostly of the bulk origin, while the resistance is determined by both the edge and bulk transport., Comment: 21 pages, 7 figures

The terahertz resistive response of a two-dimensional topological insulator in a HgTe quantum well in the quasiballistic transport regime is studied. The photoresistance appearing only near the charge neutrality point is detected. The application of the magnetic field up to 4 T in the plane of the quantum well results in an increase in the photoresistance in the peak and in the expansion of the region near the charge neutrality point where it exists. The reported results imply that the observed photoresistance is due to transitions involving edge dispersion branches of the two-dimensional topological insulator.

We experimentally investigate spin-polarized electron transport between a permalloy ferromagnet and the edge of a two-dimensional electron system with band inversion, realized in a narrow, 8 nm wide, HgTe quantum well. In zero magnetic field, we observe strong asymmetry of the edge potential distribution with respect to the ferromagnetic ground lead. This result indicates that the helical edge channel, specific for the structures with band inversion even at the conductive bulk, is strongly coupled to the ferromagnetic side contact, possibly due to the effects of proximity magnetization. This allows selective and spin-sensitive contacting of helical edge states.

The mobility of Dirac electrons (DEs) in HgTe quantum wells with the thickness close to the critical value corresponding to the transition from the direct to inverted spectrum has been studied experimentally and theoretically. The nonmonotonic dependence of this mobility on the electron density is found experimentally. The theory of DE scattering on impurities and fluctuations of the thickness of a well caused by its roughnesses is elaborated. This theory is in good agreement with experiment and explains the observed nonmonotonicity by the decrease in the ratio of the de Broglie wavelength of DEs to the characteristic size of the roughness with the increase in their concentration.

A method is presented to be used in a computational experiment aimed at studying the internal structure of nano- and mesoscopic objects, i.e., conducting subsystems and quantum phenomena in solid submicron objects, which demonstrate an individual behavior of low-temperature resistance.

We report on a detailed study of the 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 (DF) 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 DF 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 (MIRO) previously observed in high mobility GaAs-based heterostructures. This observation attests the superior quality of 2D electron system formed by helical surface states in strained HgTe films.

We report results of systematic measurements of charge transport properties of the 20.5nm wide HgTe-based quantum well in perpendicular magnetic field, performed under hydrostatic pressures up to 15.1 kbar. At ambient pressure transport is well described by the two-band semiclassical model.In contrast, at elevated pressure, we observed non-monotonic pressure dependence of resistivity at CNP. For pressures lower than $\approx9$ kbar, resistivity grows with pressure, in accord with expectations from the band structure calculations and the model incorporating effects of disorder on transport in 2D semimetals with indirect band overlap. For higher pressures, the resistivity saturates and starts decreasing upon further increase of pressure. Above $\approx14$ kbar the resistance and hopping transport character sharply change, which may indicate formation of the excitonic insulator state. The data also reveals strong influence of disorder on transport in 2D electron-hole system with a small band overlap., 11 pages, 13 figures

We report on beating appearance in Shubnikov-de Haas oscillations in conduction band of 18-22nm HgTe quantum wells under applied top-gate voltage. Analysis of the beatings reveals two electron concentrations at the Fermi level arising due to Rashba-like spin splitting of the first conduction subband H1. The difference dN_s in two concentrations as a function of the gate voltage is qualitatively explained by a proposed toy electrostatic model involving the surface states localized at quantum well interfaces. Experimental values of dN_s are also in a good quantitative agreement with self-consistent calculations of Poisson and Schrodinger equations with eight-band kp Hamiltonian. Our results clearly demonstrate that the large spin splitting of the first conduction subband is caused by surface nature of $H1$ states hybridized with the heavy-hole band., 7 pages, 7 figures

We report on the observation of the giant photoconductance of a quantum point contact (QPC) in the tunneling regime excited by terahertz radiation. Studied QPCs are formed in a GaAs/(Al, Ga) As heterostructure with a high-electron-mobility two-dimensional electron gas. We demonstrate that irradiation of strongly negatively biased QPCs by laser radiation with frequency f = 0.69 THz and intensity 50mW/cm(2) results in two orders of magnitude enhancement of the QPC conductance. The effect increases with the dark conductivity decrease. It is also characterized by a strong polarization dependence and a drastic reduction of the signal by increasing the radiation frequency to 1.63 THz. We demonstrate that all experimental findings can be well explained by the photon-assisted tunneling through the QPC. Corresponding calculations are in good agreement with the experiment.

We present both the experimental and theoretical investigation of a non-trivial electron Landau levels shift in magnetic field in wide ~20 nm HgTe quantum wells: Landau levels split under magnetic fields but become degenerate again when magnetic field increases. We reproduced this behavior qualitatively within an isotropic 6-band Kane model, then using semiclassical calculations we showed this behavior is due to the mixing of the conduction band with total spin 3/2 with the next well subband with spin 1/2 which reduces the average vertical spin from 3/2 to around 1. This change of the average spin changes the Berry phase explaining the evolution of Landau levels under magnetic field.