Wave-vector filtering effect of the electric-magnetic barrier in HgTe quantum wells

Because of the helicity of electrons in HgTe quantum wells(QWs) with inverted band structures,the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in the HgTe QWs.This behavior is similar to Dirac electrons in graphene.In this paper,we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier.We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers.The confining effect will have a potential application in nanodevices based on HgTe QWs.     

Wave-vector filtering effect of electric–magnetic barrier in HgTe quantum wells

Because of helicity of electrons in HgTe quantum wells (QWs) with inverted band structure, the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in HgTe QWs. This behavior is similar to Dirac electrons in graphene. In this paper, we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier. We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers. The confining effect will have potential application in nanodevices based on HgTe QWs.     

Mobility of Dirac electrons in HgTe quantum wells

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.     

Weak localization of Dirac fermions in HgTe quantum wells

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.     

Effects of the Electron—Electron Interaction in the Magneto-Absorption Spectra of HgTe/CdHgTe Quantum Wells with an Inverted Band Structure

JETP Letters - Magneto-absorption in HgTe/CdHgTe quantum wells with an inverted band structure in magnetic fields up to 30 T has been studied. It has been shown that the positions of...     

Weak antilocalization in HgTe quantum wells near a topological transition

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.     

Zero-energy states bound to a magnetic π-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a π-flux is a generic feature of the topologically non-trivial phase of the M–B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.     

The robustness of the quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

The quantum spin Hall effect(QSHE) was first realized in HgTe quantum wells(QWs),which remain the only known two-dimensional topological insulator so far.In this paper,we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE.We start with the case of constant mass with random distributions,and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small.When the number is infinite and corresponds to the real fluctuation,we find that the QSHE is not only robust,but also can be generated by relatively strong fluctuation.Our results imply that the thickness fluctuation does not cause backscattering,and the QSHE is robust to it.     

Magnetospectroscopy of double HgTe/CdHgTe QWs with inverted band structure in high magnetic fields up to 30 T

Magnetoabsorption in far and mid IR ranges in double HgTe/CdHgTe quantum wells with inverted band structure has been studied in high magnetic fields up to 30 T. Numerous intraband and interband transitions have been revealed in the spectra and interpreted within axial 8 × 8 k·p model. Splitting of dominant magnetoabsorption lines resulting from optical transitions from hole-like zero-mode Landau level has been discovered and discussed in terms of a built-in electric field and collective phenomena.     

Cyclotron resonance in a two-dimensional semimetal based on a HgTe quantum well

Microwave cyclotron resonance of electrons and holes at the metal-to-semimetal transition in HgTe quantum wells with an inversed band structure has been investigated. The resonance has been studied by measuring microwave photoresistance in the frequency range of 35–170 GHz. The effective cyclotron masses of electrons and holes have been determined. A shift of the cyclotron resonance of the two-dimensional electrons at the metal-to-semimetal transition possibly caused by plasma effects in the two-dimensional semimetal has been discovered.     

Quantum spin Hall effect in inverted type-II semiconductors

The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells and in this Letter we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. The quantum well exhibits an "inverted" phase similar to HgTe/CdTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to the asymmetric structure of this quantum well, the effects of inversion symmetry breaking are essential. Remarkably, the topological quantum phase transition between the conventional insulating state and the quantum spin Hall state can be continuously tuned by the gate voltage, enabling quantitative investigation of this novel phase transition.     

Manifestation of a semimetallic state in cyclotron resonance in low-symmetry HgTe-based quantum wells

Cyclotron-resonance measurements in 21-nm-thick HgTe/CdHgTe quantum wells of different crystallographic orientations have been performed. It has been found that, in contrast to the structures with the (001) orientation of the quantum-well plane, (013)-oriented quantum wells are semimetallic and their absorption spectra exhibit both electron and hole cyclotron-resonance lines. The simultaneous presence of the two types of charge carriers originates from an overlap between the upper heavy-hole quantum-confinement subbands hh1 and hh2. This overlap is caused by the strong interaction of these subbands with the Dyakonov-Khaetskii interface state. Calculations carried out using the eight-band kp-Hamiltonian indicate that, for known values of the band-structure parameters, the overlap between hh2 and hh1 subbands does not occur; this result is in agreement with the cyclotron-resonance data for (001)-oriented structures. The enhanced interaction between heavy-hole and interface states owing to the existence of steps at low-symmetry heterointerfaces may be the mechanism responsible for the appearance of an overlap between subbands in HgTe quantum wells with orientation different from (001).     

Photoexcitation in two-dimensional topological insulators

One of the most fascinating challenges in Physics is the realization of an electron-based counterpart of quantum optics, which requires the capability to generate and control single electron wave packets. The edge states of quantum spin Hall (QSH) systems, i.e., two-dimensional (2D) topological insulators realized in HgTe/CdTe and InAs/GaSb quantum wells, may turn the tide in the field, as they do not require the magnetic field that limits the implementations based on quantum Hall effect. However, the band structure of these topological states, described by a massless Dirac fermion Hamiltonian, prevents electron photoexcitation via the customary vertical electric dipole transitions of conventional optoelectronics. So far, proposals to overcome this problem are based on magnetic dipole transitions induced via Zeeman coupling by circularly polarised radiation, and are limited by the g-factor. Alternatively, optical transitions can be induced from the edge states to the bulk states, which are not topologically protected though.Here we show that an electric pulse, localized in space and/or time and applied at a QSH edge, can photoexcite electron wavepackets by intra-branch electrical transitions, without invoking the bulk states or the Zeeman coupling. Such wavepackets are spin-polarised and propagate in opposite directions, with a density profile that is independent of the initial equilibrium temperature and that does not exhibit dispersion, as a result of the linearity of the spectrum and of the chiral anomaly characterising massless Dirac electrons. We also investigate the photoexcited energy distribution and show how, under appropriate circumstances, minimal excitations (Levitons) are generated. Furthermore, we show that the presence of a Rashba spin–orbit coupling can be exploited to tailor the shape of photoexcited wavepackets. Possible experimental realizations are also discussed.     

Generation of Fabry–Pérot oscillations and Dirac state in two-dimensional topological insulators by gate voltage

We investigate electron transport through Hg Te ribbons embedded by strip-shape gate voltage through using a nonequilibrium Green function technique. The numerical calculations show that as the gate voltage is increased, an edgerelated state in the valence band structure of the system shifts upwards, then hangs inside the band gap and merges into the conduction band finally. It is interesting that as the gate voltage is increased continuously, another edge-related state in the valence band also shifts upwards in the small-k region and contacts the previous one to form a Dirac cone in the band structure. Meanwhile in this process, the conductance spectrum displays as multiple resonance peaks characterized by some strong antiresonance valleys in the band gap, then behaves as Fabry–P′erot oscillations and finally develops into a nearly perfect quantum plateau with a value of 2e~2/h. These results give a physical picture to understand the formation process of the Dirac state driven by the gate voltage and provide a route to achieving particular quantum oscillations of the electronic transport in nanodevices.     

Features of Magneto-Intersubband Oscillations in HgTe Quantum Wells

JETP Letters - Magneto-intersubband oscillations (MISOs) in single quantum wells of the gapless semiconductor HgTe have been studied experimentally. It has been shown that, in contrast to MISOs in...     

Electronic structure of rectangular HgTe quantum dots

We theoretically investigate the single- and few-electron ground-states properties of HgTe topological insulator quantum dots with rectangular hard-wall confining potential using configuration interaction method. For the case of single electron, the edge states is robust against the deformation from a square quantum dot to a rectangular ones, in contrast to the bulk states, the energy gap of the QDs increased due to the coupling of the opposite edge states; for the case of few electrons, the electrons first fill the edge states in the bulk band gap and the addition energy exhibit universal even-odd oscillation due to the shape-independent two-fold degeneracy of the edge states. The size of this edge shell can be controlled by tuning the dot size, shape or the bulk band gap via lateral or vertical electric gating respectively of the HgTe quantum dot.     

Growth and studies of Hg1−xCdxTe based low dimensional structures

The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8×8 k·p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained.Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV.By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg_1−xMn_xTe QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current.Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.     

Numerical study of localization in quantum spin hall state of HgTe/CdTe system

HgTe/CdTe quantum well has served as a new material in realizing the quantum spin Hall state. We investigate the localization and scaling behavior of electronic states in HgTe/CdTe quantum wells through the scaling analysis. A phase diagram where the boundary separating the localized and extended states is plotted in the parameter space which is spanned with disorder strength and Fermi energy. We also discuss the implications of these results on the behavior of topological insulator.     

Cyclotron resonance of Dirac ferions in HgTe quantum wells

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.     

Features of Photoluminescence of Double Acceptors in HgTe/CdHgTe Heterostructures with Quantum Wells in a Terahertz Range

JETP Letters - The terahertz photoluminescence spectra of HgTe/CdHgTe heterostructure with quantum wells under interband optical excitation with a power of 3 to 300 mW have been studied in the...