Te Quantum Wells Research Articles

Quantitative theory of backscattering in topological HgTe and (Hg,Mn)Te quantum wells: Acceptor states, Kondo effect, precessional dephasing, and bound magnetic polaron

We present the theory and numerical evaluations of the backscattering rate determined by acceptor holes or Mn spins in HgTe and (Hg,Mn)Te quantum wells in the quantum spin Hall regime. The role of anisotropic s-p and sp-d exchange interactions, Kondo coupling, Luttinger liquid effects, precessional dephasing, and bound magnetic polarons is quantified. The determined magnitude and temperature dependence of conductance are in accord with experimental results for HgTe and (Hg,Mn)Te quantum wells.

Effects of Charge Dopants in Quantum Spin Hall Materials.

Semiconductors' sensitivity to electrostatic gating and doping accounts for their widespread use in information communication and new energy technologies. It is demonstrated quantitatively and with no adjustable parameters that the presence of paramagnetic acceptor dopants elucidates a variety of hitherto puzzling properties of two-dimensional topological semiconductors at the topological phase transition and in the regime of the quantum spin Hall effect. The concepts of resonant states, charge correlation, Coulomb gap, exchange interaction between conducting electrons and holes localized on acceptors, strong coupling limit of the Kondo effect, and bound magnetic polaron explain a short topological protection length, high hole mobilities compared with electron mobilities, and different temperature dependence of the spin Hall resistance in HgTe and (Hg,Mn)Te quantum wells.

Energy and spin relaxation of excitons in CdMnTe/CdMgTe quantum wells

The energy and spin relaxation of excitons and trions is studied in the (Cd, Mn)Te/(Cd,Mg)Te quantum wells containing hole magnetic polarons by means of polarized photoluminescence technique. It was found that under circularly polarized photoexcitation with an energy higher than the ground state energy of the exciton, photoluminescence is also polarized. This fact points to the presence of the spin memory of the excitons in these systems. It is suggested that the long spin memory is due to the magnetic polaron formation stabilizing the spin of the exciton. Under quasiresonant excitation of the trion states an inverted sign of circular polarization degree is observed in the radiation spectrum. Such inversion of the polarization degree requires the special mechanism of the spin relaxation, associated with the spin flip of an electron in the trion magnetic polaron state. Application of the external magnetic field in the Voigt geometry leads to the depolarization of the excitonic radiation. The cause of this depolarization is the destabilization of the magnetic polaron and the shortening of the spin relaxation time of the exciton.

Magnetic ion relaxation time distribution within a quantum well

Time-resolved optically detected magnetic resonance (ODMR) is a valuable technique to study the local deformation of the crystal lattice around magnetic ion as well as the ion spin relaxation time. Here we utilize selective Mn-doping to additionally enhance the inherent locality of the ODMR technique. We present the time-resolved ODMR studies of single {(Cd,Mg)Te/(Cd,Mn)Te} quantum wells (QWs) with manganese ions located at different positions along the growth axis -- in the center or on the sides of the quantum well. We observe that spin-lattice relaxation of Mn$^{2+}$ significantly depends on the ion-carrier wavefunction overlap at low-magnetic fields. Interestingly, the effect is clearly observed in spite of very low carrier density, which suggests the potential for control of the Mn$^{2+}$ ion relaxation rate by means of the electric field in future experiments.

Simulation of far-infrared HgTe/HgCdTe quantum-well vertical-cavity surface-emitting laser

We propose an original design for a far-infrared vertical-cavity surface-emitting laser based on a heterostructure with ten 4.7-nm HgTe / Hg0.3Cd0.7Te quantum wells grown on a [013] GaAs substrate. Its characteristics were calculated, and it was shown that the quality factor of the proposed resonator design can reach 248 at a wavelength of 23.25 μm, which is sufficient for the occurrence of laser generation at this wavelength at a temperature of 20 K and a concentration of nonequilibrium carriers of 1.4 × 1010 cm − 2. The estimate of the threshold pump intensity using CO2 laser radiation at a wavelength of 10.6 μm is 1 W / cm2, which makes it possible to expect continuous wave mode lasing. Such a low-threshold pump intensity should also lead to lasing at substantially higher temperatures.

Angle-resolved optically detected magnetic resonance as a tool for strain determination in nanostructures

In this paper, we apply the angle-resolved optically detected magnetic resonance (ODMR) technique to study a series of strained (Cd, Mn)Te/(Cd, Mg)Te quantum wells (QWs) produced by molecular beam epitaxy. By analyzing characteristic features of ODMR angular scans, we determine the strain-induced axial-symmetry spin Hamiltonian parameter $D$ with neV precision. Furthermore, we use low-temperature optical reflectivity measurements and x-ray diffraction scans to evaluate the local strain present in the QW material. In our analysis, we take into account different thermal expansion coefficients of the GaAs substrate and CdTe buffer. The additional deformation due to the thermal expansion effects has the same magnitude as the deformation that originates from the different compositions of the samples. Based on the evaluated deformations and values of the strain-induced axial-symmetry spin Hamiltonian parameter $D$, we find the strain spin-lattice coefficient ${G}_{11}=(72.2\ifmmode\pm\else\textpm\fi{}1.9)$ neV for ${\mathrm{Mn}}^{2+}$ in CdTe and shear deformation potential $b=(\ensuremath{-}0.94\ifmmode\pm\else\textpm\fi{}0.11)$ eV for CdTe.

Optical manifestation of magnetic polarons bound to excitons and resident holes in a (Cd,Mn)Te quantum well

Photoluminescence and multiple ${\mathrm{Mn}}^{2+}$ spin-flip Raman scattering (SFRS) are studied in the (Cd,Mn)Te/(Cd,Mg)Te quantum well with excess resident hole concentration under resonance continuous-wave photoexcitation in the localized states of excitons and trions at $T=1.5$ K. A magnetic polaron shift of both exciton and trion photoluminescence is observed to be increasing with an increase in the magnetic field up to 6 T applied perpendicularly to the sample growth axis (Voigt geometry). Exciton magnetic polaron shift in magnetic field is attributed to the adiabatic energy transfer from the exchange reservoir to the Zeeman reservoir during the precession of the ${\mathrm{Mn}}^{2+}$ ions in the summary field of external magnetic and exchange hole fields. A mechanism of the magnetic polaron shift of trion photoluminescence is suggested. It is related to direct photoexcitation of the triplet trion state, which is stable in the conditions which are provided by the resident hole magnetic polarons. In these conditions, the ${\mathrm{Mn}}^{2+}$ magnetic moment experiences additional magnetization in the double exchange field provided by two holes in the triplet trion state. It is observed that the maximum efficiency of multiple ${\mathrm{Mn}}^{2+}$ spin-flip Raman scattering falls into the energy range corresponding to the states of localized excitons where the exciton magnetic polaron shift is observed. From this we conclude that the magnetic polaron state could be an intermediate state of the multiple ${\mathrm{Mn}}^{2+}$ SFRS process.

Magnetic field dependence of the in-plane hole g factor in ZnSe- and CdTe-based quantum wells

The effective $g$ factor of holes is measured in modulation-doped ZnSe/(Zn,Mg)(S,Se) quantum wells and from surface-state $p$-doped CdTe/(Cd,Mg)Te quantum wells by time-resolved pump-probe Kerr rotation. The measurements are performed at a temperature of 1.7 K and in magnetic fields up to 5 T applied in the Voigt geometry with orientation perpendicular to the quantum-well growth axis. The absolute value of the in-plane hole $g$ factor increases with growing magnetic field in both studied heterostructures. A theoretical model is developed that considers the influence of magnetic field and interface mixing of heavy-hole and light-hole states on the $g$ factor. The model results are in good agreement with the experimental data.

Temperature and chemical potential dependence of the parity anomaly in quantum anomalous Hall insulators

The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a momentum-dependent mass term. Each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. In this work, we analyze the finite temperature Hall conductivity of a single Chern insulator in 2+1 space-time dimensions under the influence of a chemical potential and an out-of-plane magnetic field. At zero magnetic field, this non-dissipative transport coefficient originates from the parity anomaly of planar quantum electrodynamics. We show that the parity anomaly itself is not renormalized by finite temperature effects. However, it induces two terms of different physical origin in the effective action of a Chern insulator, which is proportional to the Hall conductivity. The first term is temperature and chemical potential independent, and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction and valence band states. In particular, we show that the relativistic mass of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic mass enhances these corrections. Moreover, we extend our analysis to finite magnetic fields and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in orbital fields.

All-electrically tunable networks of Majorana bound states

Second-order topological superconductors (SOTSs) host localized Majorana fermions and provide a new platform for topological quantum computation. We propose a remarkable and feasible way to realize networks based on SOTSs which allow to nucleate and braid Majorana bound states (MBSs) in an all-electrical manner without fine-tuning. The proposed setups are scalable in a straightforward way and can accommodate any even number of MBSs. Moreover, the MBSs in the networks allow defining qubits whose states can be initialized and read out by measuring Josephson currents flowing between SOTS islands. Our proposal can be implemented in monolayers of $\text{FeTe}{}_{1-x}\text{Se}_{x}$, monolayers of 1T'-WTe$_2$, and inverted Hg(Cd)Te quantum wells in proximity to conventional superconductors.

Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator.

The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.

Charged Exciton Dissociation Energy in (Cd,Mn)Te Quantum Wells with Variable Disorder and Carrier Density

We report on the magneto-photoluminescence of (Cd,Mn)Te/(Cd,Mg)Te quantum wells excited by photons with varied energy. We observe that laser illumination modifies the carrier density and Coulomb disorder in the quantum wells. Three different regimes are analyzed, corresponding to low hole density with low disorder, low hole density with significant disorder, and high hole density. By using the diluted magnetic semiconductor as a quantum well material, we can induce the spin singlet–triplet transition of charged excitons in a magnetic field. This transition is then used as a tool to determine the charged exciton dissociation energy. With this approach, we find the same value for the dissociation energy in all the regimes of hole density and disorder. Our result is compared with the dissociation energy obtained from the PL splitting between the X and X^{!! +} lines at zero field, which exhibits significantly greater variation.

Anisotropy of the 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.

Quantum beats in the polarization of the spin-dependent photon echo from donor-bound excitons in CdTe/(Cd,Mg)Te quantum wells

We study the quantum beats in the polarization of the photon echo from donor-bound exciton ensembles in semiconductor quantum wells. To induce these quantum beats, a sequence composed of a circularly polarized and a linearly polarized picosecond laser pulse in combination with an external transverse magnetic field is used. This results in an oscillatory behavior of the photon echo amplitude, detected in the $\sigma^+$ and $\sigma^-$ circular polarizations, occurring with opposite phases relative to each other. The beating frequency is the sum of the Larmor frequencies of the resident electron and the heavy hole when the second pulse is polarized along the magnetic field. The beating frequency is, on the other hand, the difference of these Larmor frequencies when the second pulse is polarized orthogonal to the magnetic field. The measurement of both beating frequencies serves as a method to determine precisely the in-plane hole $g$ factor, including its sign. We apply this technique to observe the quantum beats in the polarization of the photon echo from the donor-bound excitons in a 20-nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te quantum well. From these quantum beats we obtain the in-plane heavy hole $g$ factor $g_h=-0.143\pm0.005$.

Photoluminescence of CdTe quantum wells doped with cobalt and iron

Cobalt and iron dopants in semiconductors are killers of excitonic photoluminescence. In particular, photoluminescence of quantum wells doped with Co and Fe poses a challenge and has not been reported so far. Here, we show molecular beam epitaxy growth and photoluminescence studies of (Cd,Co)Te and (Cd,Fe)Te quantum wells in (Cd,Mg)Te. We compare the results to well-known structures: CdTe and (Cd,Mn)Te quantum wells, and we conclude that 0.2% of Fe reduces photoluminescence intensity by 3 orders of magnitude, and similar concentration of Co reduces PL intensity by about 5 orders of magnitude. We also present the influence of the dopant's concentration on emission efficiency in external magnetic field. Structures with low doping levels require weaker fields to reduce the quenching effect.

Short range proximity effect induced by exchange interaction in tunnel-coupled CdTe and (Cd,Mn)Te quantum wells

The coherent spin dynamics of electrons in tunnel-coupled CdTe and (Cd,Mn)Te quantum wells (QWs) is studied by time-resolved pump-probe Kerr rotation. The coupled QWs have different thicknesses; the narrow one is doped by ${\mathrm{Mn}}^{2+}$ magnetic ions. A short range proximity effect between them is observed: the Zeeman splitting of electrons in the wide QW is given in addition to the intrinsic electron $g$ factor by the exchange interaction with the ${\mathrm{Mn}}^{2+}$ ions mediated by electron tunneling into the narrow QW. The exchange interaction strength scales with the ${\mathrm{Cd}}_{0.88}{\mathrm{Mg}}_{0.12}\mathrm{Te}$ barrier thickness separating the QWs. The Kerr rotation signal measured on the wide QW shows two close frequencies of electron spin Larmor precession in a transverse magnetic field. These components have very different spin dephasing times, 50 ps and 1 ns. The two frequencies originate from electrons in the wide QW being either part of an exciton or being resident. The proximity effect of the exciton electron is smaller due to the binding by Coulomb interaction, which decreases the tunneling to the narrow well. The experimental data are in good agreement with model calculations.

Electron mass in a HgTe quantum well: Experiment versus theory

Abstract The energy spectrum of the conduction band in HgTe/Cd x Hg 1 − x Te quantum wells with 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 c ≃ 6 . 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 many-body effects.

Study of the Auger Recombination Energy Threshold in a Series of Waveguide Heterostructures with HgTe/Cd0.7Hg0.3Te QWs Near 14 μm

Stimulated emission from a heterostructure with Hg0.903Cd0.097Te/Cd0.7Hg0.3Te quantum wells, placed in a waveguide layer of wide-gap CdHgTe, is obtained at wavelengths of 14–11 μm and a temperatures of 18–80 K. The threshold Auger recombination energy is calculated for a set of heterostructures with quantum wells of pure HgTe with a band gap of 90 meV (wavelength 14 μm). The possibility of fabricating lasers operating at 14 μm and working temperatures higher than that of liquid nitrogen is demonstrated.

Nuclear spin dynamics influenced and detected by electron spin polarization in CdTe/(Cd,Mg)Te quantum wells

Nuclear spin coherence and relaxation dynamics of all constituent isotopes of an n-doped CdTe/(Cd,Mg)Te quantum well structure are studied employing optically detected nuclear magnetic resonance. Using time-resolved pump-probe Faraday ellipticity, we generate and detect the coherent spin dynamics of the resident electrons. The photogenerated electron spin polarization is transferred into the nuclear spin system, which becomes polarized and acts back on the electron spins as the Overhauser field. Under the influence of resonant radio frequency pulses, we trace the coherent spin dynamics of the nuclear isotopes $^{111}$Cd, $^{113}$Cd, and $^{125}$Te. We measure nuclear Rabi oscillations, the inhomogeneous dephasing time $T_2^*$, the spin coherence time $T_2$, and the longitudinal relaxation time $T_1$. Furthermore, we investigate the influence of the laser excitation and the corresponding electron spin polarization on the nuclear spin relaxation time and find a weak extension of this time induced by interaction with the electron spins.

Single-beam optical measurement of spin dynamics in CdTe/(Cd,Mg)Te quantum wells

We study optical pumping of resident electron spins under resonant excitation of trions in n-type CdTe/(Cd,Mg)Te quantum wells subject to a transverse magnetic field. In contrast to the comprehensively used time-resolved pump-probe techniques with polarimetric detection, we exploit here a single beam configuration in which the time-integrated intensity of the excitation laser light transmitted through the quantum wells is detected. The transmitted intensity reflects the bleaching of light absorption due to optical pumping of the resident electron spins and can be used to evaluate the Larmor precession frequency of the optically oriented carriers and their spin relaxation time. Application of the magnetic field leads to depolarization of the electron spin ensemble so that the Hanle effect is observed. Excitation with a periodic sequence of laser pulses leads to optical pumping in the rotating frame if the Larmor precession frequency is synchronized with the pulse repetition rate. This is manifested by the appearance of Hanle curves every 3.36 or 44.2 mT for pulse repetition rates of 75.8 or 999 MHz, respectively. From the experimental data we evaluate the g factor of |g|=1.61 and the spin relaxation time of 14 ns for the optically pumped resident electrons, in agreement with previous time-resolved pump-probe studies.