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A valence band in narrow HgTe quantum wells contains well-conductive Dirac-like light holes at the Γ point and a poorly conductive heavy hole subband located in the local valleys. Here we propose and employ two methods to measure the density of states for these heavy holes. The first method uses a gate-recharging technique to measure thermodynamical entropy per particle. As the Fermi level is tuned with gate voltage from a light to heavy subband, the entropy increases dramatically, and the value of this increase gives an estimate for the density of states. The second method determines the density of states for heavy holes indirectly from the gate voltage dependence of the period of the Shubnikov-de Haas oscillations for light holes. The results obtained by both methods are in reasonable agreement with each other. Our approaches can be applied to measure large effective carrier masses in other two-dimensional gated systems. © 2020 American Physical Society.

The results of experimental studies of the Shubnikov-de Haas (SdH) effect in the (013)-HgTe/Hg1-xCdxTe quantum wells (QWs) of electron type of conductivity both with normal and inverted energy spectrum are reported. Comprehensive analysis of the SdH oscillations measured for the different orientations of magnetic field relative to the quantum well plane and crystallographic exes allows us to investigate the anisotropy of the Zeeman effect. For the QWs with inverted spectrum, it has been shown that the ratio of the spin splitting to the orbital one is strongly dependent not only on the orientation of the magnetic field relative to the QW plane but also on the orientation of the in-plane magnetic field component relative to crystallographic axes laying in the QW plane that implies the strong anisotropy of in-plane g-factor. In the QW with normal spectrum, this ratio strongly depends on the angle between the magnetic field and the normal to the QW plane and reveals a very slight anisotropy in the QW plane. To interpret the data, the Landau levels in the tilted magnetic field are calculated within the framework of four-band kP model. It is shown that the experimental results can be quantitatively described only with taking into account the interface inversion asymmetry. © 2020 American Physical Society.

In the present paper we study magneto-intersubband oscillations (MISO) in HgTe/Hg1-xCdxTe single quantum well with "inverted" and "normal" spectra and in In1-xGaxAs/In1-yAlyAs quantum wells with normal band ordering. For all the cases when two branches of the spectrum arise due to spin-orbit splitting, the mutual arrangement of the antinodes of the Shubnikov-de Haas oscillations and the maxima of MISO occurs opposite to that observed in double quantum wells and in wide quantum wells with two subbands occupied and does not agree with the theoretical predictions. A "toy" model is proposed that explains qualitatively this unusual result. © 2020 American Physical Society.

Spin-orbit splitting of conduction band in HgTe quantum wells was studied experimentally. In order to recognize the role of different mechanisms, we carried out detailed measurements of the Shubnikov-de Haas oscillations in gated structures with a quantum well widths from 8 to 18 nm over a wide range of electron density. With increasing electron density controlled by the gate voltage, splitting of the maximum of the oscillation Fourier spectrum f 0 into two components f 1 and f 2 and the appearance of the low-frequency component f 3 was observed. Our analysis shows that the components f 1 and f 2 are determined by the electron densities n 1 and n 2 in spin-orbit split subbands while the f 3 component results from magneto-intersubband oscillations so that it is determined by the difference between these densities Δn. This allows us to obtain all three values n 1 , n 2 and Δn independently. Comparison of the data obtained with results of self-consistent calculations carried out within the framework of four-band kP model shows that the main contribution to spin-orbit splitting comes from the Bychkov-Rashba effect. Contribution of the interface inversion asymmetry to the splitting of the conduction band turns out to be four-to-five times less than that for the valence band in the same structures. © 2019 Elsevier B.V.

The phase of quantum magneto-oscillations is often associated with the Berry phase and is widely used to argue in favor of topological nontriviality of the system (Berry phase 2πn+π). Nevertheless, the experimentally determined value may deviate from 2πn+π arbitrarily, therefore more care should be made analyzing the phase of magneto-oscillations to distinguish trivial systems from nontrivial. In this paper we suggest two simple mechanisms dramatically affecting the experimentally observed value of the phase in three-dimensional topological insulators: (i) magnetic field dependence of the chemical potential, and (ii) possible nonuniformity of the system. These mechanisms are not limited to topological insulators and can be extended to other topologically trivial and nontrivial systems. © 2018 American Physical Society.

The energy spectrum of the valence band in HgTe/CdxHg1-xTe quantum wells of a width (8-20) nm has been studied experimentally by magnetotransport effects and theoretically in the framework of a four-band kP method. Comparison of the Hall density with the density found from a period of the Shubnikov-de Haas (SdH) oscillations clearly shows that the degeneracy of states of the top of the valence band is equal to 2 at the hole density p<5.5×1011cm-2. Such degeneracy does not agree with the calculations of the spectrum performed within the framework of the four-band kP method for symmetric quantum wells. These calculations show that the top of the valence band consists of four spin-degenerate extremes located at k≠0 (valleys) which gives the total degeneracy K=8. It is shown that taking into account the "mixing of states" at the interfaces leads to the removal of the spin degeneracy that reduces the degeneracy to K=4. Accounting for any additional asymmetry, for example, due to the difference in the mixing parameters at the interfaces, the different broadening of the boundaries of the well, etc., leads to reduction of the valleys degeneracy, making K=2. It is noteworthy that for our case twofold degeneracy occurs due to degeneracy of two single-spin valleys. The hole effective mass (mh) determined from analysis of the temperature dependence of the amplitude of the SdH oscillations shows that mh is equal to (0.25±0.02)m0 and weakly increases with the hole density. Such a value of mh and its dependence on the hole density are in a good agreement with the calculated effective mass. © 2017 American Physical Society.

The Zeeman splitting of the conduction band in the HgTe quantum wells both with normal and inverted spectrum has been studied experimentally in a wide electron density range. The simultaneous analysis of the Shubnikov-de Haas (SdH) oscillations in low magnetic fields at different tilt angles and of the shape of the oscillations in moderate magnetic fields gives a possibility to find the ratio of the Zeeman splitting to the orbital one and anisotropy of g-factor. It is shown that the ratios of the Zeeman splitting to the orbital one are close to each other for both types of structures, with a normal and inverted spectrum and they are close enough to the values calculated within kP method. In contrast, the values of g-factor anisotropy in the structures with normal and inverted spectra are strongly different and for both cases differ significantly from the calculated ones. We assume that such disagreement with calculations is a result of the interface inversion asymmetry in the HgTe quantum well, which is not taken into account in the kP calculations. © 2017 Elsevier B.V.

Energy spectra both of the conduction and valence bands of the HgTe quantum wells with a width close to the Dirac point were studied experimentally. Simultaneous analysis of the Shubnikov-de Haas oscillations and the Hall effect over a wide range of electron and hole densities yields surprising results: the top of the valence band is strongly split by spin-orbit interaction while the splitting of the conduction band is absent, within experimental accuracy. This holds true for the structures with normal and inverted band ordering. The results obtained are inconsistent with the results of kP calculations, in which the smooth electric field across the quantum well is only reckoned in. It is shown that taking into account the asymmetry of the quantum-well interfaces within a tight-binding method gives reasonable agreement with the experimental data. © 2016 American Physical Society.

The results of experimental study of quantum interference effects in small magnetic fields in narrow HgTe quantum wells of hole-type conductivity with a normal energy spectrum are presented. Interpretation of the data is performed with taking into account the strong spin-orbit splitting of the energy spectrum of the two-dimensional hole subband. It is shown that the phase relaxation time found from the analysis of the shape of magnetoconductivity curves in the case when the Fermi level lies in the monotonic part of the energy spectrum of the valence band behaves itself analogously to that observed in narrow HgTe quantum wells of electron-type conductivity. It increases in magnitude with the increasing conductivity and decreasing temperature following the 1/T law. Such a behavior corresponds to the inelasticity of electron-electron interaction as the main mechanism of the phase relaxation and agrees well with the theoretical predictions. For the higher conductivity, despite the fact that the dephasing time remains inversely proportional to the temperature, it strongly decreases with the increasing conductivity. It is presumed that the reason for such a peculiarity could be nonmonotonic character of the hole energy spectrum. An additional channel of inelastic interaction occurs when the Fermi level approaches the secondary maxima in the depth of the valence band. © 2015 American Physical Society.

The results of an experimental study of the energy spectrum of a valence band in a HgTe quantum well of width d<6.3 nm with normal spectrum in the presence of a strong spin-orbit splitting are reported. The analysis of the temperature, magnetic field, and gate voltage dependences of the Shubnikov-de Haas oscillations allows us to restore the energy spectrum of the two valence-band branches, which are split by the spin-orbit interaction. Comparison with a theoretical calculation shows that a six-band kP theory well describes all the experimental data in the vicinity of the top of the valence band. © 2014 American Physical Society.

The results of experimental study of interference induced magnetoconductivity in narrow quantum well HgTe with a normal energy spectrum are presented. Analysis is performed by taking into account the conductivity anisotropy. It is shown that the fitting parameter τφ corresponding to the phase relaxation time increases in magnitude with the increasing conductivity (σ) and decreasing temperature following the 1/T law. Such a behavior is analogous to that observed in the usual two-dimensional systems with a simple energy spectrum and corresponds to the inelasticity of electron-electron interaction as the main mechanism of the phase relaxation. However, it drastically differs from that observed in the wide HgTe quantum wells with the inverted spectrum, in which τφ, being obtained by the same way, is practically independent of σ. It is presumed that a different structure of the electron multicomponent wave function for the inverted and normal quantum wells could be the reason for such a discrepancy. © 2013 American Physical Society.

The results of an experimental study of the magnetoresistivity and the Hall and Shubnikov-de Haas effects for a heterostructure with a HgTe quantum well of 20.2 nm width are reported. The measurements were performed on gated samples over a wide range of electron and hole densities including the vicinity of a charge neutrality point. Analyzing the data, we conclude that the electron and hole energy spectra are in qualitative agreement with those calculated within the framework of kP model. The electron and hole subbands are overlapped due to the nonmonotonic dispersion of the hole subband resulting in a semimetallic state. The main result of the paper, however, is the drastic quantitative difference in the experimental and calculated spectra of the hole subband. So, the hole effective mass found from the analysis of the Shubnikov-de Haas oscillations is positive and equal to approximately 0.2m0 and practically independent of the quasimomentum (k) starting from k2в‰0.7Ч1012 cm-2, while the theory predicts negative (electronlike) effective mass up to k2в‰6Ч1012 cm-2. The experimental effective mass near k=0, where the hole energy spectrum is electronlike, is close to -0.005m0, whereas the theoretical value is about -0.1m0. © 2013 American Physical Society.

The magnetoresistivity and the Hall and Shubnikov-de Haas effects in heterostructures with a single 20.2-nm-wide quantum well made from the gapless semiconductor HgTe are studied experimentally. The measurements are performed on gated samples over a wide range of electron and hole densities. The data obtained are used to reconstruct the energy spectrum of electrons and holes in the vicinity of the extrema of the quantum-confinement subbands. It is shown that the charge-carrier dispersion relation in the investigated systems differs from that calculated within the framework of the conventional kp model. © 2013 Pleiades Publishing, Ltd.

The results of an experimental study of the magnetoconductivity of two-dimensional (2D) electron gas caused by suppression of the interference quantum correction in a HgTe single quantum well heterostructure with an inverted energy spectrum are presented. It is shown that only the antilocalization magnetoconductivity is observed at relatively high conductivity, σ(20 - 30)G 0, where G 0=e2/2π2. The antilocalization correction demonstrates a crossover from 0. 5ln(τ φ/τ) to 1.0ln(τ φ/τ) behavior with increasing conductivity (here τ φ and τ are the phase relaxation and transport relaxation times, respectively). It is interpreted as a result of crossover to the regime when the two chiral branches of the electron energy spectrum independently contribute to the weak antilocalization. At lower conductivity, σ<(20 - 30)G 0, the magnetoconductivity behaves similarly to that in usual 2D systems with fast spin relaxation: It is negative in low magnetic fields and positive in higher ones. We have found that the temperature dependences of the fitting parameter τ φ corresponding to the phase relaxation time demonstrate reasonable behavior, close to 1/T, over the whole conductivity range from 5G 0 up to 130G 0. However, the τ φ value remains practically independent of conductivity, in contrast to conventional 2D systems with simple energy spectra, in which τ φ is enhanced with conductivity. © 2012 American Physical Society.

The electron-electron interaction quantum correction to the conductivity of the gated single quantum well InP/In 0.53Ga 0.47As heterostructures is investigated experimentally. The analysis of the temperature and magnetic field dependences of the conductivity tensor allows us to obtain the diffusion part of the interaction correction for different values of spin-relaxation rate, 1/τ s. The surprising result is that the spin-relaxation processes do not suppress the interaction correction in the triplet channel and thus do not enhance the correction in magnitude contrary to theoretical expectations even in the case of relatively fast spin relaxation, 1/Tτ s (20-25) 1. © 2012 American Physical Society.

We present the results of experimental investigations of the interference quantum correction to the conductivity of the gated double quantum well Al xGa 1-xAs/GaAs/Al xGa 1-xAs heterostructures. Analyzing the positive magnetoconductiv-ity we obtain the interwell transition rate and the phase relaxation rate under the conditions when one and two quantum wells are occupied. It has been found that the interwell transition rate resonantly depends on the difference between the electron densities in the wells in accordance with the theoretical estimate. The central point, however, is that the dephasing rate in the lower quantum well is independent of whether the upper quantum well contributes to the conductivity or not. The results obtained are interpreted within framework of the recent theory for the dephasing and electron-electron interaction in the double well structures [Burmistrov I S, Gornyi I V and Tikhonov K S 2011 Phys. Rev. B 84 075338].

The electron-electron interaction quantum correction to the conductivity of the gated double well AlxGa1-xAs/GaAs structures is investigated experimentally. The analysis of the temperature and magnetic field dependences of the conductivity tensor allows us to obtain reliably the diffusion part of the interaction correction for the regimes when the structure is balanced (i.e., for equal electron concentrations in the wells) and when only one quantum well is occupied. The surprising result is that the interaction correction does not reveal resonant behavior: it is practically the same for both regimes. © 2011 American Physical Society.

The nonlinear behavior of the Hall resistivity at low magnetic fields in single quantum well GaAs/ Inx Ga1-xAs/GaAs heterostructures with degenerated electron gas is studied. It has been found that this anomaly is accompanied by the weaker temperature dependence of the conductivity as compared with that predicted by the first-order theory of the quantum corrections to the conductivity. We show that both effects in strongly disordered systems stem from the second order quantum correction caused by the effect of weak localization on the interaction correction and vice versa. This correction contributes mainly to the diagonal component of the conductivity tensor, it depends on the magnetic field such as the weak localization correction and on the temperature like the interaction contribution. © 2010 The American Physical Society.

The temperature and magnetic-field dependences of the conductivity of the heterostructures with asymmetric Inx Ga1-x As quantum well are studied. It is shown that the metalliclike temperature dependence of the conductivity observed in the structures investigated is quantitatively understandable within the whole temperature range, T=0.4-20 K. It is caused by the interference quantum correction at fast spin relaxation for 0.4 K4-6 K, the metalliclike behavior is determined by the phonon scattering. © 2007 The American Physical Society.

Results of numerical simulation of the weak localization in two-dimensional systems in wide range of magnetic filed are presented. Three cases are analyzed: (i) the isotropic scattering and randomly distributed scatterers; (ii) the anisotropic scattering and randomly distributed scatterers; (iii) the isotropic scattering and the correlated distribution of the scatterers. It is shown that the behavior of the conductivity beyond the diffusion regime strongly depends on the scattering anisotropy and correlation in the scatterer distribution. © 2006 The American Physical Society.

Anomalous low-field magnetoresistance in p -type strained quantum wells is studied. It is experimentally shown that the Bychkov-Rashba mechanism leads to the cubic in quasimomentum spin-orbit splitting of the hole energy spectrum and the antilocalization behavior of low-field magnetoresistance is well described by the Hikami-Larkin-Nagaoka expression. © 2005 The American Physical Society.

The interference induced transverse negative magnetoresistance of GaAs/InxGa1-xAs/GaAs quantum well heterostructures has been studied in the presence of strong in-plane magnetic field. It is shown that the effect of in-plane magnetic field is determined by the interface roughness and strongly depends on the relationship between mean free path, phase breaking length, and roughness correlation length. Analysis of the experimental results allows us to estimate parameters of short- and long-range correlated roughness which have been found in a good agreement with atomic force microscopy data obtained for just the same samples.

Weak antilocalization is studied in an InxGa1-xAs quantum well. Anomalous magnetoresistance is measured and described theoretically in fields perpendicular, tilted, and parallel to the quantum well plane. Spin and phase-relaxation times are found as functions of temperature and parallel field. It is demonstrated that spin dephasing is due to the Dresselhaus spin-orbit interaction. The values of electron spin-splittings and spin-relaxation times are found in the wide range of two-dimensional density. Application of in-plane field is shown to destroy weak antilocalization due to competition of Zeeman and microroughness effects. Their relative contributions are separated, and the values of the in-plane electron g factor and characteristic size of interface imperfections are found.

We show that the study of nonlinearity conductivity gives a possibility to determine the condition when the diffusion conductivity changes to the hopping one with increasing disorder. It is experimentally shown that the conductivity of single quantum well GaAs/InGaAs/GaAs heterostructures behaves like diffusive one down to the value approaching (2-3) × 10-2e2/h. © 2004 Elsevier B.V. All rights reserved.

The contribution of the electron-electron interaction to conductivity is analyzed step by step starting from the high conductivity in gated GaAs/InxGa1−xAs/GaAs heterostructures with different starting disorders. We demonstrate that the diffusion theory works down to kFl≃1.5−2, where kF is the Fermi quasimomentum and l is the mean free path. It is shown that the e–e interaction gives smaller contribution to the conductivity than the interference independent of the starting disorder, and its role rapidly decreases with decreasing kFl. © 2003 The American Physical Society.

A weak localization effect has been studied in macroscopically inhomogeneous 2D system. It is shown that although the real phase breaking length tends to infinity when the temperature tends to zero such a system can reveal a saturated behavior of the temperature dependence of that parameter which is obtained from the standard analysis of the negative magnetoresistance and usually identified by experimenters with the phase braking length., This article is from ADA408025 Nanostructures: Physics and Technology International Symposium (9th), St. Petersburg, Russia, June 18-22, 2001 Proceedings

The temperature and gate voltage dependencies of the phase breaking time is studied experimentally in the structures with quantum well based on GaAs/InGaAs. There is shown that arising of the states at the Fermi energy in the doped layers (Sn & layer in our case) leads to significant decreasing of the phase breaking time and to weakness its temperature dependence., This article is from ADA408025 Nanostructures: Physics and Technology International Symposium (9th), St. Petersburg, Russia, June 18-22, 2001 Proceedings

A weak-localization effect has been studied in macroscopically inhomogeneous two-dimensional system. It is shown that there is a regime where fits of the low-field negative magnetoresistance with the standard weak localization theory for a uniform system give a dephasing time which saturates as one goes to lower temperatures, even though the true dephasing time diverges as the temperature goes to zero. © 2001 The American Physical Society.

Quantum corrections to the conductivity have been studied in the two types of low-mobility two-dimensional heterostructures: those with doped quantum well, and doped barriers. The consistent analysis shows that for the structures where electrons occupy the states only in the quantum well, all the temperature and magnetic field dependences of the components of resistivity tensor are well described by the theories of the quantum corrections. Contribution of the electron-electron interaction to the conductivity has been reliably determined for the structures with different electron density. A possible reason of large scatter in experimental data relating to the contribution of electron-electron interaction, obtained in previous papers, is analyzed. The role of the carriers occupying the states of the doped layers is discussed.

The temperature and gate voltage dependences of the phase breaking time are studied experimentally in GaAs/InGaAs heterostructures with a single quantum well. It is shown that appearance of states at the Fermi energy in the doped layers leads to a significant decrease of the phase breaking time of the carriers in the quantum well and to saturation of the phase breaking time at low temperature.

The weak localization correction to the conductivity in coupled double layer structures was studied both experimentally and theoretically. The statistics of the closed paths was determined from analysis of the magnetic field and temperature dependencies of the negative magnetoresistance for magnetic field perpendicular and parallel to the structure plane. The comparison of the results with the results of computer simulation of carrier motion at scattering shows that inter-layer tunneling plays decisive role in the weak localization., TPres: 8th Int Symp Nanostructures: Physics and Technology, St Petersburg, Russia, 19-23 Jun 2000, p66-69. This article is from ADA407315 Nanostructures: Physics and Technology International Symposium (8th) Held in St. Petersburg, Russia on June 19-23, 2000 Proceedings

The results of computer simulation of particle motion over the plane with randomly distributed scatters are presented. They are used to analyse the influence of scattering anisotropy on the negative magnetoresistance due to weak localisation. It is shown that the magnetic field dependence of magnetoresistance in this case can be described by the well known expression. obtained in the diffusion limit for isotropic scattering. but with the prefactor less than unity and breaking-phase length which differs from the true value., Pres: 7th Int Symp Nanostructures: Physics and Technology, St Petersburg, Russia. 14-18 Jun 1999. p190-193. This article is from ADA407055 Nanostructures: Physics and Technology. 7th International Symposium. St. Petersburg, Russia, June 14-18, 1999 Proceedings

The results of experimental and theoretical studies of zero-bias anomaly (ZBA) in the Pb-oxide-(Formula presented)-InAs tunnel structures in magnetic field up to 6 T are presented. A specific feature of the structures is a coexistence of the two-dimensional (2D) and 3D states at the Fermi energy near the semiconductor surface. The dependence of the measured ZBA amplitude on the strength and orientation of the applied magnetic field is in agreement with the proposed theoretical model. According to this model, electrons tunnel into 2D states, and move diffusively in the 2D layer, whereas the main contribution to the screening comes from 3D electrons. © 1999 The American Physical Society.

The magnetoresistance in weak localization regime was thoroughly investigated both for the classical and quantum two-dimensional (2D) electron systems., Pres: 6th Int Symp Nanostructures: Physics and Technology, St Petersburg, Russia. 22-26 Jun 1998. p135. This article is from ADA406591 Nanostructures: Physics and Technology International Symposium (6th) held in St. Petersburg, Russia on June 22-26, 1998 Proceedings

We present results of tunnelling studies of p-Hg1-xCdxTe-oxide-Al structures with 0.165 < x < 0.2 in a magnetic field up to 6 T. The tunnelling conductivity oscillations resulting from the Landau quantization of the energy spectrum in the semiconductor volume are investigated. under an in-plane magnetic field the amplitudes of tunnelling conductivity maxima connected with the tunnelling into a and b spin sublevels are found to differ substantially from one another, and the amplitude ratio varies from structure to structure. To understand the cause of this behaviour, the tunnelling conductivity for this magnetic field orientation is calculated taking into consideration the multi-band energy spectrum. It is shown that the contributions of the different spin sublevels to the tunnelling conductivity are dissimilar and the relationship between them depends strongly on the value of surface potential.