26 research outputs found
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
-model. So, the hole effective mass is equal to approximately and
practically independent of the quasimomentum () up to cm, while the theory predicts negative (electron-like)
effective mass up to cm. The experimental
effective mass near k=0, where the hole energy spectrum is electron-like, is
close to , whereas the theoretical value is about
The valence band energy spectrum of HgTe quantum wells with inverted band structures
The energy spectrum of the valence band in HgTe/CdHgTe quantum
wells with a width ~nm has been studied experimentally by
magnetotransport effects and theoretically in framework -bands -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 ~cm. Such degeneracy does not agree with the
calculations of the spectrum performed within the framework of the -bands
-method for symmetric quantum wells. These calculations show that the top
of the valence band consists of four spin-degenerate extremes located at (valleys) which gives the total degeneracy . 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 . 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 . It is
noteworthy that for our case two-fold degeneracy occurs due to degeneracy of
two single-spin valleys. The hole effective mass () determined from
analysis of the temperature dependence of the amplitude of the SdH oscillations
show that is equal to and weakly increases with the
hole density. Such a value of and its dependence on the hole density are
in a good agreement with the calculated effective mass.Comment: 8 pages, 11 figure
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.Comment: 10 pages, 16 figure
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 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.Comment: 9 pages including 3 pages of Supplemental Material, 9 figure
Energy spectrum of valence band in HgTe quantum wells on the way from a two to the three dimensional topological insulator
The magnetic field, temperature dependence and the Hall effect have been
measured in order to determine the energy spectrum of the valence band in HgTe
quantum wells with the width (20-200)nm. The comparison of hole densities
determined from the period Shubnikov-de Haas oscillations and the Hall effect
shows that states at the top of valence band are double degenerate in teh entry
quantum wells width the width range. The cyclotron mass determined from
temperature dependence of SdH oscillations increases monotonically from
(0.2-0.3) mass of the free electron, with increasing hole density from 2e11 to
6e11 cm^-2. The determined dependence has been compared to theoretical one
calculate within the four band kp model. The experimental dependence was found
to be strongly inconsistent with this predictions. It has been shown that the
inclusion of additional factors (electric field, strain) does not remove the
contradiction between experiment and theory. Consequently it is doubtful that
the mentioned kp calculations adequately describe the valence band for any
width of quantum well.Comment: 7 pages 8 figure
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.Comment: 7 pages, 7 figure
Nonlocal resistance and its fluctuations in microstructures of band-inverted HgTe/(Hg,Cd)Te quantum wells
We investigate experimentally transport in gated microsctructures containing
a band-inverted HgTe/Hg_{0.3}Cd_{0.7}Te quantum well. Measurements of nonlocal
resistances using many contacts prove that in the depletion regime the current
is carried by the edge channels, as expected for a two-dimensional topological
insulator. However, high and non-quantized values of channel resistances show
that the topological protection length (i.e. the distance on which the carriers
in helical edge channels propagate without backscattering) is much shorter than
the channel length, which is ~100 micrometers. The weak temperature dependence
of the resistance and the presence of temperature dependent reproducible
quasi-periodic resistance fluctuations can be qualitatively explained by the
presence of charge puddles in the well, to which the electrons from the edge
channels are tunnel-coupled.Comment: 8 pages, 4 figures, published versio
Anisotropic conductivity and weak localization in HgTe quantum wells with a normal energy spectrum
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
Renormalization of the conduction band spectrum in HgTe quantum wells by electron-electron interaction
The energy spectrum of the conduction band in HgTe/CdHgTe quantum
wells of a width 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 , where nm is a critical width of
quantum well corresponding to the Dirac-like energy spectrum, is close to the
calculated values over the whole electron density range; with increasing width,
at 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 nm, where the ratio
between the calculated and experimental masses reaches the value of two and
begins to decrease with a further increase. We assume that observed
behavior of the electron effective mass results from the spectrum
renormalization due to electron-electron interaction.Comment: 8 pages, 10 figure
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 to 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 into two
components and and the appearance of the low-frequency component
was observed. Analysis of these results shows that the components
and give the electron densities and in spin-orbit split
subbands while the component results from magneto-intersubband
oscillations so that . 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.Comment: 6 pages, 6 figure