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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 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

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

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 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 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.

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.

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 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.

We report on the observation of terahertz radiation induced photoconductivity and of terahertz analog of the microwave-induced resistance oscillations (MIRO) in HgTe-based quantum well (QW) structures of different width. The MIRO-like effect has been detected in QWs of 20 nm thickness with inverted band structure and a rather low mobility of about 3 $\times$ 10$^5$ cm$^2$/V s. In a number of other structures with QW widths ranging from 5 to 20 nm and lower mobility we observed an unconventional non-oscillatory photoconductivity signal which changes its sign upon magnetic field increase. This effect was observed in structures characterized by both normal and inverted band ordering, as well as in QWs with critical thickness and linear dispersion. In samples having Hall bar and Corbino geometries an increase of the magnetic field resulted in a single and double change of the sign of the photoresponse, respectively. We show that within the bolometric mechanism of the photoresponse these unusual features imply a non-monotonic behavior of the transport scattering rate, which should decrease (increase) with temperature for magnetic fields below (above) the certain value. This behavior is found to be consistent with the results of dark transport measurements of magnetoresistivity at different sample temperatures. Our experiments demonstrate that photoconductivity is a very sensitive probe of the temperature variations of the transport characteristics, even those that are hardly detectable using standard transport measurements., Comment: 9 pages, 8 figures

We report non-local electrical measurements in a mesoscopic size two-dimensional (2D) electron gas in a GaAs quantum well in a hydrodynamic regime. Viscous electric flow is expected to be dominant when electron-electron collisions occur more often than the impurity or phonon scattering events. We observe a negative nonlocal resistance and attribute it to the formation of whirlpools in the electron flow. We use the different nonlocal transport geometries and compare the results with a theory demonstrating the significance of hydrodynamics in mesoscopic samples., Comment: 8 pages, 9 figures

The thermopower in a two-dimensional semimetal existing in HgTe quantum wells 18-21 nm thick has been studied experimentally and theoretically for the first time. It has been found theoretically and experimentally that the thermopower has two components - diffusion and phonon drag and that the second component is several times larger than the first. It has been concluded that the electron-hole scattering plays an important role in both mechanisms of the thermopower.

We investigate lateral $p\ensuremath{-}n$ junctions, electrostatically defined in 14-nm-wide HgTe-based quantum wells (QWs) with inverted band structure. The $p\ensuremath{-}n$ junction resistances are close to $h/2{e}^{2}$, consistent with some previous experiments on $8--10\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ QWs, and the current-voltage characteristics are highly linear, indicating the transport via ballistic helical edge states. Shot noise measurements are performed in order to further verify the underlying transport mechanism. We discuss the role of unknown inelastic relaxation rates in the leads and in the edge channels for the correct interpretation of the noise data. Although the interpretation in favor of the helical edge states seems more consistent, a definite conclusion cannot be drawn based on the present experiment. Our approach looks promising for the study of short quasiballistic edges in topological insulators in suitable geometry.

We experimentally investigate spin-polarized electron transport between two ferromagnetic contacts, placed at the edge of a two-dimensional electron system with band inversion. The system is realized in a narrow (8 nm) HgTe quantum well, the ferromagnetic side contacts are formed from a premagnetized permalloy film. In zero magnetic field, we find a significant edge current contribution to the transport between two ferromagnetic contacts. We experimentally demonstrate that this transport is sensitive to the mutual orientation of the magnetization directions of two 200 µm-spaced ferromagnetic leads. This is a direct experimental evidence on the spin-coherent edge transport over the macroscopic distances. Thus, the spin is extremely robust at the edge of a two-dimensional electron system with band inversion, confirming the helical spin-resolved nature of edge currents.

Scattering of two-dimensional electrons in wide (d = 18–22 nm) HgTe-based quantum wells has been thoroughly studied. The mobility has been found to reach a maximum and then to decrease at two-dimensional electron densities above (2–6) × 1011 cm−2 owing to scattering by roughness of the quantum well. The theory of scattering by roughness has been elaborated taking into account transformation of the wavefunction with an increase in the electron density. Good agreement of this theory with the experiment indicates the existence of surface states at the interfaces of the wide HgTe quantum well.

The specific features of the quantum Hall effect (QHE) in a system of gapless Dirac fermions in HgTe quantum wells have been studied. It has been established that the behavior of the QHE is asymmetric with respect to the Dirac point: at the lowest temperature (0.2 K), quantization of hole fermions occurs in weak magnetic fields down to 0.15 T, whereas quantization of the electron part of the Dirac cone occurs only in fields of about 0.5 T. Such an asymmetry is caused by the effect of sideband maxima in the valence band forming the heavy-hole valleys, which play the role of a reservoir and screen out the fluctuation potential. The analysis of the behavior of the dissipative component of the conductivity near the Dirac point has led to a conclusion on the existence of the zeroth Landau level at this point.

We experimentally investigate electron transport through the interface between a superconductor and the edge of a two-dimensional electron system with band inversion. The interface is realized as a tunnel NbN side contact to a narrow 8~nm HgTe quantum well. It demonstrates a typical Andreev behavior with finite conductance within the superconducting gap. Surprisingly, the conductance is modulated by a number of equally-spaced oscillations. The oscillations are present only within the superconducting gap and at lowest, below 1~K, temperatures. The oscillations disappear completely in magnetic fields, normal to the two-dimensional electron system plane. In contrast, the oscillations' period is only weakly affected by the highest, up to 14~T, in-plane oriented magnetic fields. We interpret this behavior as the interference oscillations in a helical one-dimensional edge channel due to a proximity with a superconductor., Comment: minor corrections - as published

The universal value of the Faraday rotation angle close to the fine structure constant (α≈1/137) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σ_{xy}=e^{2}/h, which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.

Among the most interesting predictions in two-dimensional materials with a Dirac cone is the existence of the zeroth Landau level (LL), equally filled by electrons and holes with opposite chirality. The gapless edge states with helical spin structure emerge from Zeeman splitting at the LL filling factor $\nu=0$ gapped quantum Hall state. We present observations of a giant nonlocal four-terminal transport in zero-gap HgTe quantum wells at the $\nu=0$ quantum Hall state. Our experiment clearly demonstrates the existence of the robust helical edge state in a system with single valley Dirac cone materials., Comment: 9 pages, 8 figures

In this chapter results are reported from a study of a new two-dimensional electron system, a two-dimensional semimetal, that is observed in wide quantum wells based on mercury telluride, which have an inverted band spectrum. Magnetotransport experiments confirm the existence of a semimetal state in quantum wells with (013) and (112) orientations, and thicknesses of 18–21 nm. These experiments show that the band overlap is Δ=3–5 meV. A comparison of the experimentally determined Δ with a theoretical calculation of the energy spectrum reveals the fundamental role of strain effects in the formation of the semimetal state. Scattering processes in the two-dimensional semimetal are studied, and it is found that the jump in the electron mobility during electronic metal-two-dimensional semimetal transitions is caused by screening of electron scattering on impurities by holes. The substantial anomalous rise in the resistivity of the two-dimensional semimetal with an increasing temperature is caused by electron–hole scattering. This is the first observation of the direct effect of interparticle scattering (Landau mechanism) on the resistivity of metals. The properties of two-dimensional semimetals in the quantum Hall effect regime are examined. Primary attention is paid to the observed suppression of strong localization under the conditions of the quantum Hall effect. It is shown that, in a strong magnetic field, the two-component electron–hole plasma has fundamentally different topological properties from those of ordinary single-component (electron or hole) plasma. It is suggested that they lead to the appearance of an infinite set of conducting current states and to the suppression of localization.

The terahertz response of a two-dimensional topological insulator in a HgTe quantum well to radiation with wavelengths of 118 and 184 μm is investigated. It is found that the photoconductivity is rather high (up to a few percent of dark conductivity) and is manifested in both the local and nonlocal responses of the system. This fact proves that the observed photoconductivity is caused by changes in the transport via edge current-carrying states. The sign and nonresonant character of the photoconductivity indicate that it is caused by the heating of electrons in the system. The analysis of experimental results makes it possible to suggest that this heating originates from the Drude absorption of terahertz radiation by metallic “droplets” appearing owing to fluctuations in the impurity potential and the gap and located in direct proximity to edge states.

The 2D semimetal in a 20 nm (100) HgTe quantum well is characterized by a comparatively low overlap between the conduction and the valence bands induced by lattice mismatch. In the present paper we report the results of transport measurements in this quantum well under hydrostatic pressure of 14.4 kbar. By applying pressure we have further reduced the band overlap, thereby creating favorable conditions for the formation of the excitonic insulator state. As a result, we observed that the metallic-like temperature dependence of the conductivity at lowering temperature sharply changes to the activated behavior, signaling the onset of an excitonic insulator regime.

The influence of e-h scattering on the conductivity and magnetotransport of 2D semimetallic HgTe is studied both theoretically and experimentally. The presence of e-h scattering leads to the friction between electron and holes resulting in a large temperature-dependent contribution to the transport coefficients. The coefficient of friction between electrons and holes is determined. The comparison of experimental data with the theory shows that the interaction between electrons and holes based on the long - range Coulomb potential strongly underestimates the e-h friction. The experimental results are in agreement with the model of strong short-range e-h interaction., Comment: 9 figures

Weak localization in a system of gapless two-dimensional Dirac fermions in HgTe quantum wells with thickness d = 6.6 nm, which corresponds to the transition from a normal to an inverted spectrum, has been investigated experimentally. A negative logarithmic correction to the conductivity of the system has been observed both at the Dirac point and in the vicinity of this point. The anomalous magnetoresistance of two-dimensional Dirac fermions is positive. This indicates that weak localization in the system of two-dimensional Dirac fermions occurs owing to localization and interaction effects in the presence of rapid spin relaxation.

A metal-insulator transition in a two-dimensional semimetal based on HgTe quantum wells is discovered. The transition is induced by a magnetic field applied parallel to the plane of the quantum well. The threshold behavior of the activation energy as a function of the magnetic-field strength and an abrupt reduction of the Hall resistance at the onset of the transition suggest that the observed effect originates from the formation of an excitonic insulator.

Cyclotron resonance of single-valley two-dimensional Dirac fermions in HgTe-based quantum wells has been experimentally investigated. The thickness of the wells is close to the critical value corresponding to the transition from the direct energy spectrum to the inverted spectrum. Under terahertz laser irradiation, transitions between the ground and first Landau levels, as well as between the first and second Landau levels, have been observed. Low magnetic fields corresponding to the cyclotron resonance, as well as the strong dependence of the position of the resonance on the electron density, indicate the Dirac character of the spectrum in these quantum wells. It has been shown that disorder plays an important role in the formation of the spectrum of two-dimensional Dirac fermions.

The first results are reported from a study of a new two-dimensional electron system, a two-dimensional semimetal, that is observed in wide quantum wells based on mercury telluride, which have an inverted band spectrum. Magnetotransport experiments confirm the existence of a semimetal state in quantum wells with (013) and (112) orientations and thicknesses of 18–21nm. These experiments show that the band overlap Δ=3–5meV. A comparison of the experimentally determined Δ with a theoretical calculation of the energy spectrum reveals the fundamental role of strain effects in the formation of the semimetal state. Scattering processes in the two-dimensional semimetal are studied and it is found that the jump in the electron mobility during electronic metal-two-dimensional semimetal transitions is caused by shielding of electron scattering on impurities by holes. The substantial, anomalous rise in the resistivity of the two-dimensional semimetal with increasing temperature is caused by electron-hole scattering. ...

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.

A two-dimensional electron-hole system consisting of light high-mobility electrons with a density of Ns = (4 - 7) × 1010 cm -2 and heavier lower-mobility holes with a density Ps = (0.7 - 1.6) × 1011 cm -2 has been discovered in a quantum well based on mercury telluride with the (013) surface orientation. The system exhibits a number of specific magnetotransport properties in both the classical magnetotransport (positive magnetoresistance and sign-variable Hall effect) and the quantum Hall effect regime. These properties are associated with the coexistence of two-dimensional electrons and holes and actually manifest the first realization of a two-dimensional semimetal.

The scattering mechanisms in a two-dimensional semimetal based on a HgTe quantum well, where the electron and hole densities are controlled over a wide range by applying the gate voltage, have been studied. It is shown that impurity scattering prevails in this system at low temperatures. Interparticle scattering (in this case, electrons and holes) has been observed to directly affect the resistance of the metal.

A two-dimensional electron-hole system consisting of light high-mobility electrons with a density of Ns = (4–7) × 1010 cm−2 and a mobility of μn = (4–6) × 105 cm2/V s and heavier low-mobility holes with a density of Ps = (0.7–1.6) × 1011 cm−2 and a mobility of μp = (3–7) × 104 cm2/V s has been discovered in a quantum well based on mercury telluride with the (013) surface orientation. The system exhibits a number of specific magnetotransport properties in both the classical magnetotransport (positive magnetoresistance and alternating Hall effect) and the quantum Hall effect regime. These properties are associated with the coexistence of two-dimensional electrons and holes.

The results of a study of the magnetic-field-induced quantum Hall liquid-insulator transition and the plateau-to-plateau transition in a high mobility two-dimensional electron gas in an HgTe quantum well are reported. The applicability of the universal scaling models (such as the universal critical exponent description and the semicircle model) for the description of these transitions is analyzed. It is shown that neither of these descriptions is completely adequate for the system under study.

We investigate electron transport through the interface between a niobium superconductor and the edge of a two-dimensional semimetal, realized in a 20~nm wide HgTe quantum well. Experimentally, we observe that typical behavior of a single Andreev contact is complicated by both a pronounced zero-bias resistance anomaly and shallow subgap resistance oscillations with $1/n$ periodicity. These results are demonstrated to be independent of the superconducting material and should be regarded as specific to a 2D semimetal in a proximity with a superconductor. We interpret these effects to originate from the Andreev-like correlated process at the edge of a two-dimensional semimetal., 5 pages

Our experimental studies of electron transport in wide (14 nm) HgTe quantum wells confirm persistence of a two-dimensional topological insulator state reported previously for narrower wells, where it was justified theoretically. Comparison of local and nonlocal resistance measurements indicate edge state transport in the samples of about 1 mm size at temperatures below 1 K. Temperature dependence of the resistances suggests an insulating gap of the order of a few meV. In samples with sizes smaller than 10 $\mu$m a quasiballistic transport via the edge states is observed., Comment: article with 3 figures plus supplementary material with 2 figures

We investigate the current noise in HgTe-based quantum wells with an inverted band structure in the regime of disordered edge transport. Consistent with previous experiments, the edge resistance strongly exceeds $h/e^2$ and weakly depends on the temperature. The shot noise is well below the Poissonian value and characterized by the Fano factor with gate voltage and sample to sample variations in the range $0.1, Comment: added Ref, minor corrections, as published

We present magnetotransport measurements in HgTe quantum well with inverted band structure, which expected to be a two-dimensional topological insulator having the bulk gap with helical gapless states at the edge. The negative magnetoresistance is observed in the local and nonlocal resistance configuration followed by the periodic oscillations damping with magnetic field. We attribute such behaviour to Aharonov-Bohm effect due to magnetic flux through the charge carrier puddles coupled to the helical edge states. The characteristic size of these puddles is about 100 nm., Comment: 6 pages, 6 figures

We report magnetotransport properties of electrons in a new kind of two-dimensional electron system (2DES)-a narrow single quantum well with electron density so large that the electrons splash out of the well. We show that the system is a two-component 2D electron gas consisting of very low mobility (μ = × 10 3 cm 2 V - 1 s - 1 ) main part of the electrons and very small fraction (about 1% of all) of the electrons with much higher (10 times) mobility. The anomalous behavior of the magnetoresistance ρ x x and Hall resistance ρ x y of this system was observed. The sharp change of the transport properties at the moment of overfilling of the quantum well gives the possibility to determine the value of the band offset ΔE c on the interface Al 0 . 3 Ga 0 . 7 As/GaAs using the results of the self-consistent calculation of the energy diagram of the studied structure. As the result we have obtained ΔE c = (0.18-0.20)eV. This value is significantly less than the well-known ΔE c = 0.24 eV found in optical experiments.

A 2D semimetal has been observed in 20 nm HgTe quantum wells with (100) surface orientation. At the charge neutrality point the hole and electron density were determined as N s = P s ≈ 1.2 × 10 10 cm − 2 and the band overlap was estimated at 1–1.5 meV. This observation confirms that a semimetallic state is a universal property of wide HgTe-based quantum wells with an inverted energy band structure independently of surface orientation. Energy band structure calculation shows that the strain caused by the lattice mismatch of HgTe and CdTe plays a crucial role in the formation of the conduction and valence band overlap. We show that in the investigated semimetal the ratio of the hole density to the electron density P s / N s may change from 1 up to about 102.