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Register a new userThe valence band energy spectrum of HgTe quantum wells with inverted band structures
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Alexander Germanenko
Publication date
2017
fields
Physics
and research's language is
English
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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 $p< 5.5times 10^{11}$~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 $k eq 0$ (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 $(0.25pm0.02),m_0$ 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.
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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 $d<d_c$, where $d_csimeq6.3$ 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 $d>(7-8)$ 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.
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 $0.1<F<0.3$. Given the fact that our devices are shorter than the most pessimistic estimate of the ballistic dephasing length, these observations exclude the possibility of one-dimensional helical edge transport. Instead, we suggest that a disordered multi-mode conduction is responsible for the edge transport in our experiment.
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.
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.
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.
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