The solutions for the helical edge states for an effective continuum model for the quantum spin Hall effect in HgTe/CdTe quantum wells are presented. For a sample of a large size, the solution gives the linear dispersion for the edge states. However, in a finite strip geometry, the edge states at two sides will couple with each other, which leads to a finite energy gap in the spectra. The gap decays in an exponential law of the width of sample. The magnetic field dependence of the edge states illustrates the difference of the edge states from those of a conventional quantum Hall strip of two-dimensional electron gas.
We describe the fine structure of Dirac states in HgTe/CdHgTe quantum wells of critical and close-to-critical thickness and demonstrate the formation of an anticrossing gap between the tips of the Dirac cones driven by interface inversion asymmetry. By combining symmetry analysis, atomistic calculations, and k-p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. The zero-magnetic-field splitting of Dirac cones can be experimentally revealed in studying magnetotransport phenomena, cyclotron resonance, Raman scat…
We study indirect exchange interaction between magnetic impurities in the (001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and the case of the chemical potential placed in the energy gap of the 2D quasiparticle spectrum. We find that the indirect exchange interaction is suppressed exponentially with the distance between magnetic impurities. The presence of inversion asymmetry results in oscillations of the indirect exchange interaction with the distance and generates additional terms which are non-invariant under rotations in the (001) plane. The indirect exchange inte…
Studies of photoluminescence (PL) can provide fundamental insight into the optical properties of semiconductor nanoparticles (NPs) but the same is being limited by NP size distribution and low luminescence yield. Inorganic semiconductor core/shell structures have added advantage of durability, high luminescence quantum yield (LQY), 10-80% in the visible range and useful in biological labeling, LED and luminescence thermometry application. However, luminescence thermometry requires narrow PL line width, intense luminescence and should change with temperature linearly and reversibly which are di…
The topological insulator properties of CdTe/HgTe/CdTe quantum wells are theoretically studied. The CdTe/HgTe/CdTe quantum well behaves as a topological insulator beyond a critical well width dimension. It is shown that if the barrier(CdTe) and well-region(HgTe) are altered by replacing them with the alloy Cd$_{x}% $Hg$_{1-x}$Te of various stoichiometries, the critical width can be changed.The critical quantum well width is shown to depend on temperature, applied stress, growth directions and external electric fields. Based on these results, a novel device concept is proposed that allows to sw…
By means of a multiband effective mass Hamiltonian, a theoretical characterization of the effect of the geometrical features of the confinement profile --in particular, a longitudinal groove-- on the subbands dispersion and spin-related properties of a rectangular HgTe/CdTe nanowire is presented. Through an external electric field applied perpendicular to the wire, the interplay of the induced Rashba spin splitting and these geometrical features is investigated. It is found that by exploiting this interplay a rich complexity of the subband structure arises, permitting the generation and modula…
We study theoretically 2D HgTe/CdTe quantum well topological insulator (TI) illuminated by circularly polarized light with frequencies higher than the difference between the equilibrium Fermi level and the bottom of the conduction band (THz range). We show that electron-hole asymmetry results in spin-dependent electric dipole transitions between edge and bulk states, and we predict an occurrence of a circular photocurrent. If the edge state is tunnel-coupled to a conductor, then the photocurrent can be detected by measuring an electromotive force (EMF) in the conductor, which is proportional t…
The Andreev reflection (AR) in 2D HgTe/CdTe quantum well-superconductor hybrid systems is studied. A quantized AR with AR coefficient equal to one is predicted, which is due to the multi-Andreev reflection near the interface of the hybrid system. Importantly, this quantized AR is not only universal, i.e., independent of any system parameters and quality of the coupling of the hybrid system, it is also robust against disorder as well. As a result of this quantum Andreev effect, the conductance exhibits a quantized plateau when the external bias is less the superconductor gap.
We study the spin-dependent transmission through interfaces between a HgTe/CdTe quantum well (QW) and a metal - both for the normal metal and the superconducting case. Interestingly, we discover a new type of spin Hall effect at these interfaces that happens to exist even in the absence of structure and bulk inversion asymmetry within each subsystem (i.e. the QW and the metal). Thus, this is a pure boundary spin Hall effect which can be directly related to the existence of exponentially localized edge states at the interface. We demonstrate how this effect can be measured and functionalized fo…
We analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Green's function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signature of the gap of the edge states due to their finite overlap from opposite sample boundaries -- both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst sig…
We study the disorder effect on the transport properties in the HgTe/CdTe semiconductor quantum wells. We confirm that at a moderate disorder strength, the initially un-quantized two terminal conductance becomes quantized, and the system makes a transition to the novel topological Anderson insulator (TAI). Conductances calculated for the stripe and cylinder samples reveal the topological feature of TAI and supports the idea that the helical edge states may cause the anomalous quantized plateaus. The influence of disorder is studied by calculating the distributions of local currents. Base on th…
We compute the phase diagram of the HgTe/CdTe quantum wells in the 3 dimensional (3D) parameter space of Dirac mass, Fermi level and disorder strength. The phase diagram reveals the Quantum spin-Hall, the metallic and the normal insulating phases. The phase boundary of the Quantum spin-Hall state is shown to be strongly deformed by the disorder. Taking specific cuts into this 3D phase diagram, we recover the so called topological Anderson insulator (TAI) phase, but now we can demonstrate explicitly that TAI is not a distinct phase and instead it is part of the Quantum spin-Hall phase. The calc…
We propose a minimal effective two-dimensional Hamiltonian for HgTe/CdHgTe quantum wells (QWs) describing the side maxima of the first valence subband. By using the Hamiltonian, we explore the picture of helical edge states in tensile and compressively strained HgTe QWs. We show that both dispersion and probability density of the edge states can differ significantly from those predicted by the Bernevig-Hughes-Zhang (BHZ) model. Our results pave the way towards further theoretical investigations of HgTe-based quantum spin Hall insulators with direct and indirect band gaps beyond the BHZ model.
In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field $B_\mathrm{c}$, above which only quantum Hall (QH) states can be found. Using linear-response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to non-equidistan…
HgTe quantum wells possess remarkable physical properties as for instance the quantum spin Hall state and the 'single-valley' analog of graphene, depending on their layer thicknesses and barrier composition. However, double HgTe quantum wells yet contain more fascinating and still unrevealed features. Here we report on the study of the quantum phase transitions in tunnel-coupled HgTe layers separated by CdTe barrier. We demonstrate that this system has a 3/2 pseudo spin degree of freedom, which features a number of particular properties associated with the spin-dependent coupling between HgTe …
The quantum spin Hall (QSH) states discovered in an inverted band of InAs/GaSb and HgTe/CdTe quantum wells categorize them among the very superior candidates for topological insulators. In the presence of a magnetic field, these QSH states persist up to a magnetic field equal to the critical field, beyond which the edge states would consist of normal quantum Hall (QH) states. We provide the expression of this critical field which is found consistent with some previous literature. The critical field partitioned the spectrum into two types of quantum states, \textit{viz}. , the Quantum spin Hall…
We study the evolutions of the nonmagnetic disorder-induced edge states with the disorder strength in the HgTe/CdTe quantum wells. From the supercell band structures and wave-functions, it is clearly shown that the conducting helical edge states, which are responsible for the reported quantized conductance plateau, appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with the increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple with each other through the locali…
We report transport studies on a three dimensional, 70 nm thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semi-metallic HgTe, which thus becomes a three dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.
We theoretically study the thermoelectric transport properties of strained HgTe in the topological insulator phase. We developed a model for the system using a Dirac Hamiltonian including the effect of strain induced by the interface between HgTe and the CdTe substrate. The conductivity tensor was explored assuming the electrons are scattered by charge impurities, while the thermopower tensor was addressed using the Mott relation. Seebeck and Nernst responses exhibit remarkable enhancements in comparison with other two-dimensional Dirac materials, such as graphene, germanane, prosphorene and s…
We investigate the interplay of superconductivity and the topological order in the topological insulator (TI) formed in HgTe-CdTe quantum wells coupled to the s-wave isotropic superconductor (SC) placed on top of CdTe layer. Proximity effect induces superconducting correlations in TI effecting classification of the TI electronic states. Depending on the strength of the coupling and the initial chemical potentials in SC and TI, the edge states either (i) become gapped, or (ii) hybridize into localized Andreev states, or else (iii) merge with the bulk states turning the TI into an anisotropic na…
The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time-reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge. Recently, it has been shown that HgTe quantum wells realize this novel effect. In this work, we start from realistic tight-binding models and demonstrate the existence of the helical edge states in HgTe quantum wells and calculate their physical properties. We also show that 3d HgTe is a topological insulator under uniaxial strain, and show that the surface states are described by single-component mass…
We investigate the Andreev reflection process in high-mobility HgTe/CdTe quantum wells. We find that Andreev conductance probes the dynamics of massive 2+1 Dirac fermions, and that both specular Andreev reflection and retroreflection can be realized even in presence of a large mismatch between the Fermi wavelengths at the two sides of the normal/superconducting junction.
We experimentally investigate spin-polarized electron transport between a permalloy ferromagnet and the edge of a two-dimensional electron system with band inversion, realized in a narrow, 8~nm wide HgTe quantum well. In zero magnetic field, we observe strong asymmetry of the edge potential distribution with respect to the ferromagnetic ground lead. This result indicates, that the helical edge channel, specific for the structures with band inversion even at the conductive bulk, is strongly coupled to the ferromagnetic side contact, possibly due to the effects of proximity magnetization. It all…
We investigate theoretically the electron states in HgTe quantum dots (QDs) with inverted band structures. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of HgTe quantum dot with an inverted band structure are fully spin-polarized, and show ring-like density distributions near the boundary of the QD and spin-angular momentum locking. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such QD structure and oscillate with increasing magnetic fields. This feature offers us a practical way to detect t…
This work presents theoretical demonstration of a carrier trap unit formed by dual topological insulator constrictions (TIC) on the HgTe/CdTe quantum well (QW) with inverted band structures. The sample of HgTe/CdTe QW is patterned into a Hall bar device and a topological quantum dot is created by adding split gate electrodes closely on the QW. In sharp contrast to conventional semiconductor quantum dots, the presence or absence of topological edge states in the proposed quantum hall bar system leads to distinct propagating/insulating state of the TICs with large on/off ratio. This topological …
We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band kp-model, which takes into account the absence of a spatial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective g-factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions are simultaneously satisfied -- electron-hole asymmetry and the absence of an inversio…
The quantum spin Hall insulator (QSHI) state has been demonstrated in two semiconductor systems - HgTe/CdTe quantum wells (QWs) and InAs/GaSb QW bilayers. Unlike the HgTe/CdTe QWs, the inverted band gap in InAs/GaSb QW bilayers does not open at the $Γ$ point of the Brillouin zone, preventing the realization of massless Dirac fermions. Here, we propose a new class of semiconductor systems based on InAs/Ga(In)Sb multilayers, hosting a QSHI state, a graphene-like phase and a bilayer graphene analogue, depending on their layer thicknesses and geometry. The QSHI gap in the novel structures can reac…
We calculate the dispersion of the plasmon-LO modes taking into account the spatial dispersion of the electronic polarizability. It is shown that stimulated emission of the plasmon-LO mode is possible in the frequency range corresponding to the Reststrahlen band of GaAs both in a 6 nm wide HgTe/CdTe QW and in a 5 nm wide HgTe/Cd0.7Hg0.3Te QW grown on the (013) plane. Due to the anisotropy of the dispersion law for the plasmon-LO mode, the [03-1] direction appears to be optimal for generation.
We study the hyperfine interaction between the nuclear spins and the electrons in a HgTe quantum well, which is the prime experimentally realized example of a two-dimensional topological insulator. The hyperfine interaction is a naturally present, internal source of broken time-reversal symmetry from the point of view of the electrons. The HgTe quantum well is described by the so-called Bernevig-Hughes-Zhang (BHZ) model. The basis states of the BHZ model are combinations of both S- and P-like symmetry states, which means that three kinds of hyperfine interactions play a role: (i) The Fermi con…
We study nonlocal resistance in an H-shaped two-dimensional HgTe/CdTe quantum well consist of injector and detector, both of which can be tuned in the quantum spin Hall or metallic spin Hall regime. Because of strong spin-orbit interaction, there always exist spin Hall effect and the nonlocal resistance in HgTe/CdTe quantum well. We find that when both detector and injector are in the quantum spin Hall regime, the nonlocal resistance is quantized at $0.25\frac{h}{e^2}$, which is robust against weak disorder scattering and small magnetic field. While beyond this regime, the nonlocal resistance …
We report on the observation of a circular photogalvanic current excited by terahertz (THz) laser radiation in helical edge channels of HgTe-based 2D topological insulators (TIs). The direction of the photocurrent reverses by switching the radiation polarization from right-handed to left-handed one and, for fixed photon helicity, is opposite for the opposite edges. The photocurrent is detected in a wide range of gate voltages. With decreasing the Fermi level below the conduction band bottom, the current emerges, reaches a maximum, decreases, changes its sign close to the charge neutrality poin…
Using $\vec{k}$$\cdot$$\vec{p}$ theory, we derive an effective four band model describing the physics of the typical two-dimensional topological insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in z-direction inversion breaking and in-plane confining potentials. We find that up to third order in perturbation theory, only the inversion breaking potential generates new elements to the four band Hamiltonian that are off-diagonal in spin space. When this new effective Hamiltonian is folded into an effective two band model for the conduction (electron) or valence (heavy hole) band…
The experiments in quantum spin Hall insulator candidate materials, such as HgTe/CdTe and InAs/GaSb heterostructures, indicate that in addition to the topologically protected helical edge modes these multilayer heterostructures may also support additional edge states, which can contribute to the scattering and the transport. We use first-principles calculations to derive an effective tight-binding model for HgTe/CdTe, HgS/CdTe and InAs/GaSb heterostructures, and we show that all these materials support additional edge states which are sensitive to the edge termination. We trace the microscopic…
We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an "inverted" type at a critical thickness $d_c$. We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.
We investigate the behavior of spin polarized currents in two-dimensional topological insulators (TI). Stationary solutions inside a HgTe/CdTe quantum well (QW) were obtained by Bernevig-Hughes-Zhang (BHZ) model modified by a electric and magnetic barrier inside a non-completely insulating bulk. An attenuated quantum spin Hall (QSH) effect occurs in the gaped region with an apparent Klein-like paradox. Even more interesting, for strong potential regime, the interaction between the quasiparticles and the barriers allows spin inversion of this electronic states in a distinct channel conduction. …
We experimentally investigate electron transport through the interface between a superconductor and the edge of a two-dimensional electron system with band inversion. The interface is realized as a tunnel NbN side contact to a narrow 8~nm HgTe quantum well. It demonstrates a typical Andreev behavior with finite conductance within the superconducting gap. Surprisingly, the conductance is modulated by a number of equally-spaced oscillations. The oscillations are present only within the superconducting gap and at lowest, below 1~K, temperatures. The oscillations disappear completely in magnetic f…
Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent topological conductance phenomena, such as spin-momentum locked quantum transport or topological superconductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence lengths are enhanced up to 5 $μ$m when tuning the wires…
Varying the quantum-well width in an HgTe/CdTe heterostructure allows to realize normal and inverted semiconducting band structures, making it a prototypical system to study two-dimensional (2D) topological-insulator behavior. We have calculated the zero-temperature thermodynamic density of states $D_\mathrm{T}$ for the electron-doped situation in both regimes, treating interactions within the Hartree-Fock approximation. A distinctively different behavior for the density dependence of $D_\mathrm{T}$ is revealed in the inverted and normal cases, making it possible to detect the system's topolog…
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional two-fold rotation symmetry is mediated by an emergent stable two-dimensional Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry…
We investigate lateral p-n junctions, electrostatically defined in 14 nm-wide HgTe-based quantum wells (QWs) with inverted band structure. The p-n junctions resistances are close to $h/2e^2$, consistent with some previous experiments on 8-10 nm QWs, and the current-voltage characteristics are highly linear, indicating the transport via ballistic helical edge states. Shot noise measurements are performed in order to further verify the underlying transport mechanism. We discuss the role of unknown inelastic relaxation rates in the leads and in the edge channels for the correct interpretation of …
We demonstrate theoretically that electric field can drive a quantum phase transition between band insulator to topological insulator in CdTe/HgCdTe/CdTe quantum wells. The numerical results suggest that the electric field could be used as a switch to turn on or off the topological insulator phase, and temperature can affect significantly the phase diagram for different gate voltage and compositions. Our theoretical results provide us an efficient way to manipulate the quantum phase of HgTe quantum wells.
Interplay between strain and size quantization in a class of topological insulators based on inverted-band semiconductors
Air Force Research Laboratory（空军研究实验室）；KBR（KBR公司）；Department of Physics and Astronomy, Ohio University（俄亥俄大学物理与天文系）；Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU（材料物理中心（CFM-MPC），CSIC-UPV/EHU联合中心）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Química, University of the Basque Country UPV/EHU（巴斯克大学化学学院先进聚合物与材料系：物理、化学与技术）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基，巴斯克科学基金会）
In order to study heterostructures composed both of materials with strongly different parameters and of materials with narrow band gaps, we have developed an approach, which combines the spherical 8-band effective-mass Hamiltonian and the Burt's envelope function representation. Using this method, electron and hole states are calculated in CdS/HgS/CdS/H_2O and CdTe/HgTe/CdTe/H_2O quantum-dot quantum-well heterostructures. Radial components of the wave functions of the lowest S and P electron and hole states in typical quantum-dot quantum wells (QDQWs) are presented as a function of radius. The…
Inverted HgTe/CdTe quantum wells have been used as a platform for the realization of 2D topological insulators, bulk insulator materials with spin-helical metallic edges states protected by time-reversal symmetry. This work investigates the spectrum and the charge transport in HgTe/CdTe quantum well junctions both in the topological regime and in the absence of time-reversal symmetry. We model the system using the BHZ effective Hamiltonian and compute the transport properties using recursive Green's functions with a finite differences' method. Specifically, we have studied the material's spati…
The quantum spin Hall (QSH) state is a topologically non-trivial 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. In this work we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. Because of a rare band alignment the quantum well band structure exhibits an "inverted" phase similar to CdTe/HgTe quantum wells, which is a QSH state when the Fermi level lies inside the…
We present a theory of the electron structure and the Zeeman effect for the helical edge states emerging in two-dimensional topological insulators based on HgTe/HgCdTe quantum wells with strong natural interface inversion asymmetry. The interface inversion asymmetry, reflecting the real atomistic structure of the quantum well, drastically modifies both bulk and edge states. For the in-plane magnetic field, this asymmetry leads to a strong anisotropy of the edge-state effective $g$-factor which becomes dependent on the edge orientation. The interface inversion asymmetry also couples the counter…
HgTe-based quantum wells (QWs) recently attracted a lot of attention for the realization of a two-dimensional topological insulator with protected helical edge states. Another class of topological systems are topological superconductors (TSCs) with Majorana edge states. In this paper, we show how proximity induced s-wave superconductivity in the bulk of HgTe-QWs and in the presence of a Zeeman field can exhibit a TSC with chiral Majorana edge states. We calculate the topological invariants and the corresponding Majorana edge states explicitly within a four-band model accounting for inversion s…
Topological insulators represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D topological insulator or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe qua…
We investigate a bilayer system of critical HgTe quantum wells each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic inter-layer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological $\mathbb Z_2$ invariant of the resulting mean field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, …
Using analytical formulas as well as a finite-difference scheme, we investigate the magnetic field dependence of the energy spectra and magnetic edge states of HgTe/CdTe-based quantum wells in the presence of perpendicular magnetic fields and hard walls, for the band-structure parameters corresponding to the normal and inverted regimes. Whereas one cannot find counterpropagating, spin-polarized states in the normal regime, below the crossover point between the uppermost (electron-like) valence and lowest (hole-like) conduction Landau levels, one can still observe such states at finite magnetic…
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 he…
We study transport properties of HgTe quantum wells with critical well thickness, where the band gap is closed, and the low energy spectrum is described by a single Dirac cone. In this work, we examined both macroscopic and micron-sized (mesocopic) samples. In micron-sized samples, we observe a magnetic field induced, quantized resistance ($\sim h/2e^{2}$) at Landau filling factor $ν=0$, corresponding to the formation of helical edge states centered at the charge neutrality point (CNP). In macroscopic samples, the resistance near zero Landau level (LL) reveals strong oscillations, which we att…
We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single is…
We report on a strong nonlinear behavior of the photogalvanics and photoconductivity under excitation of HgTe quantum wells (QWs) by intense terahertz (THz) radiation. The increasing radiation intensity causes an inversion of the sign of the photocurrent and transition to its superlinear dependence on the intensity. The photoconductivity also shows a superlinear raise with the intensity. We show that the observed photoresponse nonlinearities are caused by the band-to-band \emph{light} impact ionization under conditions of a photon energy less than the forbidden gap. The signature of this kind …
We show that burying of the Dirac point in semiconductor-based quantum-spin-Hall systems can generate unexpected robustness of edge states to magnetic fields. A detailed ${\bf k\cdot p}$ band-structure analysis reveals that InAs/GaSb and HgTe/CdTe quantum wells exhibit such buried Dirac points. By simulating transport in a disordered system described within an effective model, we further demonstrate that buried Dirac points yield nearly quantized edge conduction out to large magnetic fields, consistent with recent experiments.
We experimentally investigate spin-polarized electron transport between two ferromagnetic contacts, placed at the edge of a two-dimensional electron system with band inversion. The system is realized in a narrow (8~nm) HgTe quantum well, the ferromagnetic side contacts are formed from a pre-magnetized permalloy film. In zero magnetic field, we find a significant edge current contribution to the transport between two ferromagnetic contacts. We experimentally demonstrate that this transport is sensitive to the mutual orientation of the magnetization directions of two 200~$μ$m-spaced ferromagneti…
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. T…
