arXiv subjects

A. V. Germanenko

Publications and source records attributed to A. V. Germanenko.

At least 19 recordsLinked to original sources

arXiv2024

The manifestation of Fermi level oscillations in the magnetoresistance of HgTe quantum wells with a split spectrum

Shubnikov-de Haas (SdH) oscillations and magneto-intersubband oscillations of magnetoresistance of structures with single HgTe quantum wells with a width of (10-18) nm have been experimentally studied. The spectrum of the conduction band in these structures is split by the spin-orbit interaction. This leads to beats of the SdH oscillations and the appearance of low-frequency magneto-intersubband oscillations. The mutual position of the antinodes of the SdH oscillations and the maxima of the magneto-interband oscillations is unusual -- in low magnetic fields it is directly opposite to the predictions of the theory. Measurements in high magnetic fields, in which the relative amplitude of the SdH oscillations becomes greater than 0.2-0.3, show a change in the relative position of the antinodes of the SdH oscillations and the maxima of low-frequency oscillations. Numerical calculations and additional measurements at different temperatures show that the observed effects are due to oscillations of the Fermi level in the magnetic field.

cond-mat.mes-hall↗

arXiv2023

The guide to the guiding center aka pseudo-momentum operator construction

The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations, describing the wave functions of highly degenerate Landau levels in the classical non-relativistic case, are formulated. The proposed gauge-invariant approach was used also for the construction of the equations describing the quasi-relativistic carriers behavior in the homogeneous/inhomogeneous magnetic field in the single layer graphene.

cond-mat.mes-hall↗

arXiv2022

Quantum oscillations of transport coefficients and capacitance: an unexpected manifestation of the spin-Hall effect

The results of systematic experimental studies of quantum oscillations of resistivity, Hall coefficient and capacitance in GaAs and In$_x$Ga$_{1-x}$As quantum wells (QWs) with a simple electron spectrum and HgTe QWs with a complicated non-parabolic spectrum and strong spin-orbit interaction are reported. A striking result is the ratio of the amplitudes of the resistance and Hall coefficient oscillations. In GaAs QW with a simple spectrum characterized by negligibly small Zeeman and spin-orbit splitting, the ratio of amplitudes is close to that predicted theoretically. In HgTe QWs, this ratio is very different and behaves differently in QWs with normal and inverted electron spectra. In HgTe WQs with a normal spectrum, it tends to a theoretical value with an increase of the filling factor ($N$), while for HgTe QWs with an inverted spectrum, it differs significantly from the theoretical one for all available $N$. It is assumed that such a difference in the ratio of amplitudes in GaAs and HgTe QWs is due not to the peculiarities of the energy spectrum of HgTe, but to the peculiarities of electron scattering due to spin-orbit interaction with the potential of the scatterers. This assumption is justified by analysis of experimental results obtained for a heterostructure with a In$_{0.2}$Ga$_{0.8}$As QW, which spectrum is very close to the GaAs QW spectrum, but characterizes by much stronger spin-orbit splitting value. It has been found that the positions of the resistance and capacitance oscillations, the difference between the phases of the resistance and Hall coefficient oscillations and its $N$ dependence are close to those observed in GaAs QW. At the same time the ratio of the amplitude of the resistance oscillations to the Hall coefficient oscillations and its $N$ dependence differs very strongly and they are close to that observed in HgTe quantum wells.

cond-mat.mes-hall↗

arXiv2021

Transformation of an energy spectrum and wave functions in the crossover from two- to three-dimensional topological insulator in HgTe quantum wells: long and thorny way

A magnetotransport and quantum capacitance of the two-dimensional electron gas in HgTe/Cd$_x$Hg$_{1-x}$Te quantum wells of a width ($20.2-46.0$)~nm are experimentally investigated. It is shown that the first energy subband of spatial quantization is split due to the spin-orbit interaction and the split branches are single-spin, therewith the splitting strength increases with the increase of the quantum well width. The electron effective masses in the branches are close to each other within the actual density range. Magneto-intersubband oscillations (MISO) observed in the structures under study exhibit the growing amplitude with the increasing electron density that contradicts to the expected decrease of wave function overlap for the rectangular quantum well. To interpret the data obtained, we have used a self-consistent approach to calculate the electron energy spectrum and the wave function within framework of the \emph{kP}-model. It has been in particular shown that the MISO amplitude increase results from the increasing overlap of the wave functions due to their shift from the gate electrode with the gate voltage increase known as phenomenon of the negative electron polarizability. The results obtained from the transport experiments are supported by quantum capacitance measurements.

cond-mat.mes-hall↗

arXiv2020

Magneto-intersubband oscillations in two dimensional systems with energy spectrum split due to spin-orbit interaction

In the present paper we study magneto-intersubband oscillations (MISO) in HgTe/Hg$_{1-x}$Cd$_x$Te single quantum well with "inverted" and "normal" spectra and in conventional In$_{1-x}$Ga$_x$As/In$_{1-y}$Al$_y$As 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 supposed that explain qualitatively this unusual result.

cond-mat.mtrl-sci↗

arXiv2019

Aniotropy of in-plane g-factor of electrons in HgTe quantum wells

The results of experimental studies of the Shubnikov-de Haas (SdH) efect in the (013)-HgTe/Hg$_{1-x}$Cd$_x$Te 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 \emph{kP} model. It is shown that the experimental results can be quantitatively described only with taking into account the interface inversion asymmetry.

cond-mat.mes-hall↗

arXiv2019

Negative polarizability of 2D electrons in HgTe quantum well

The polarizability of electrons occupying the lowest subband of spatial quantization in CdTe/Cd$_x$Hg$_{1-x}$Te/CdTe quantum wells is calculated. It is shown that polarizability in the quantum well without cadmium is negative, i.e., the displacement of an electron in an electric field applied perpendicularly to the quantum well plane is opposite to the force acting on it. The negative polarizability of 2D electrons can reduce the dielectric constant of quantum wells by up to $(10-15)$ percent.

cond-mat.mes-hall↗

arXiv2018

Spin-orbit splitting of the conduction band in HgTe quantum wells: role of different mechanisms

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 Fourier spectrum $f_0$ into two components $f_1$ and $f_2$ and the appearance of the low-frequency component $f_3$ was observed. Analysis of these results shows that the components $f_1$ and $f_2$ give 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 $f_3=f_1 - f_2$. Comparison of these data with results of self-consistent calculations carried out within the framework of four-band \emph{kP}-model shows that a 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.

cond-mat.mtrl-sci↗

arXiv2018

Renormalization of the conduction band spectrum in HgTe quantum wells by electron-electron interaction

The energy spectrum of the conduction band in HgTe/Cd$_x$Hg$_{1-x}$Te quantum wells of a width $d=(4.6-20.2)$ nm has been experimentally studied in a wide range of electron density. For this purpose, the electron density dependence of the effective mass was measured by two methods: by analyzing the temperature dependence of the Shubnikov-de Haas oscillations and by means of the quantum capacitance measurements. There was shown that the effective mass obtained for the structures with $d (7-8)$ nm, the experimental effective mass becomes noticeably less than the calculated ones. This difference increases with the electron density decrease, i.e., with lowering the Fermi energy; the maximal difference between the theory and experiment is achieved at $d = (15-18)$ nm, where the ratio between the calculated and experimental masses reaches the value of two and begins to decrease with a further $d$ increase. We assume that observed behavior of the electron effective mass results from the spectrum renormalization due to electron-electron interaction.

cond-mat.mtrl-sci↗

arXiv2017

The valence band energy spectrum of HgTe quantum wells with inverted band structures

The energy spectrum of the valence band in HgTe/Cd$_x$Hg$_{1-x}$Te quantum wells with a width $(8-20)$~nm has been studied experimentally by magnetotransport effects and theoretically in framework $4$-bands $kP$-method. Comparison of the Hall density with the density found from 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 $p< 5.5\times 10^{11}$~cm$^{-2}$. Such degeneracy does not agree with the calculations of the spectrum performed within the framework of the $4$-bands $kP$-method for symmetric quantum wells. These calculations show that the top of the valence band consists of four spin-degenerate extremes located at $k\neq 0$ (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 two-fold degeneracy occurs due to degeneracy of two single-spin valleys. The hole effective mass ($m_h$) determined from analysis of the temperature dependence of the amplitude of the SdH oscillations show that $m_h$ is equal to $(0.25\pm0.02)\,m_0$ and weakly increases with the hole density. Such a value of $m_h$ and its dependence on the hole density are in a good agreement with the calculated effective mass.

cond-mat.mtrl-sci↗

arXiv2015

Spin-orbit splitting of valence and conduction bands in HgTe quantum wells near the Dirac point

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 Hall effect over a wide range of electron and hole densities gives surprising result: 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. Astonishingly, but such a ratio of the splitting values is observed as for structures with normal spectrum so for structures with inverted one. These results do not consistent with the results of kP calculations, in which the smooth electric filed 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.

cond-mat.mtrl-sci↗

arXiv2014

Weak antilocalization of holes in HgTe quantum wells with a normal energy spectrum

The results of experimental study of interference induced magnetoconductivity 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 for the relatively low conductivity 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 a nonmonotonic character of the hole energy spectrum could be the reason for such a peculiarity. An additional channel of the inelastic interaction between the carriers in the main and secondary maxima occurs when the Fermi level arrives the secondary maxima in the depth of the valence.

cond-mat.mes-hall↗

arXiv2014

Hole transport and valence band dispersion law in a HgTe quantum well with normal energy spectrum

The results of an experimental study of the energy spectrum of the 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. The comparison with the 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.

cond-mat.mtrl-sci↗

arXiv2013

Anisotropic conductivity and weak localization in HgTe quantum well with normal energy spectrum

The results of experimental study of interference induced magnetoconductivity in narrow quantum well HgTe with the normal energy spectrum are presented. Analysis is performed with taking into account the conductivity anisotropy. It is shown that the fitting parameter τ_ϕcorresponding 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 usual two-dimensional systems with 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 τ_ϕbeing 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 reason for such a discrepancy.

cond-mat.mes-hall↗

arXiv2012

Two-dimensional semimetal in a wide HgTe quantum well: magnetotransport and energy spectrum

The results of experimental study of the magnetoresistivity, the Hall and Shubnikov-de Haas effects for the heterostructure with HgTe quantum well of 20.2 nm width are reported. The measurements were performed on the gated samples over the wide range of electron and hole densities including vicinity of a charge neutrality point. Analyzing the data we conclude that the energy spectrum is drastically different from that calculated in framework of $kP$-model. So, the hole effective mass is equal to approximately $0.2 m_0$ and practically independent of the quasimomentum ($k$) up to $k^2\gtrsim 0.7\times 10^{12}$ cm$^{-2}$, while the theory predicts negative (electron-like) effective mass up to $k^2=6\times 10^{12}$ cm$^{-2}$. The experimental effective mass near k=0, where the hole energy spectrum is electron-like, is close to $-0.005 m_0$, whereas the theoretical value is about $-0.1 m_0$.

cond-mat.mes-hall↗

arXiv2012

Weak antilocalization in HgTe quantum well with inverted energy spectrum

The results of experimental study of the magnetoconductivity of 2D electron gas caused by suppression of the interference quantum correction in HgTe single quantum well heterostructure with the inverted energy spectrum are presented. It is shown that only the antilocalization magnetoconductivity is observed at the relatively high conductivity $σ>(20-30)G_0$, where $G_0= e^2/2π^2\hbar$. The antilocalization correction demonstrates a crossover from $0.5\ln{(τ_ϕ/τ)}$ to $1.0\ln{(τ_ϕ/τ)}$ behavior with the increasing conductivity or decreasing temperature (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 contribute to the weak antilocalization independently. At lower conductivity $σ<(20-30)G_0$, the magnetoconductivity behaves itself analogously to that in usual 2D systems with the fast spin relaxation: being negative in low magnetic field it becomes positive in higher one. 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 the conductivity in distinction to the conventional 2D systems with the simple energy spectrum, in which $τ_ϕ$ is enhanced with the conductivity.

cond-mat.dis-nn↗

arXiv2011

Interaction correction to the conductivity of two-dimensional electron gas in In$_x$Ga$_{1-x}$As/InP quantum well structure with strong spin-orbit coupling

The electron-electron interaction quantum correction to the conductivity of the gated single quantum well InP/In$_{0.53}$Ga$_{0.47}$As heterostructures 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 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, $1/Tτ_s\simeq (20-25)\gg 1$.

cond-mat.str-el↗

arXiv2011

Interaction correction to conductivity of Al$_x$Ga$_{1-x}$As/GaAs double quantum well heterostructures near the balance

The electron-electron interaction quantum correction to the conductivity of the gated double well Al$_x$Ga$_{1-x}$As/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 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.

cond-mat.mes-hall↗