Light-hole States Research Articles

Modeling of planar germanium hole qubits in electric and magnetic fields

Hole-based spin qubits in strained planar germanium quantum wells have received considerable attention due to their favorable properties and remarkable experimental progress. The sizeable spin-orbit interaction in this structure allows for efficient qubit operations with electric fields. However, it also couples the qubit to electrical noise. In this work, we perform simulations of a heterostructure hosting these hole spin qubits. We solve the effective mass equations for a realistic heterostructure, provide a set of analytical basis wavefunctions, and compute the effective g-factor of the heavy-hole ground state. Our investigations reveal a strong impact of highly excited light-hole states located outside the quantum well on the g-factor. We find that sweet spots, points of operations that are least susceptible to charge noise, for out-of-plane magnetic fields are shifted to impractically large electric fields. However, for magnetic fields close to in-plane alignment, partial sweet spots at low electric fields are recovered. Furthermore, sweet spots with respect to multiple fluctuating charge traps can be found under certain circumstances for different magnetic field alignments. This work will be helpful in understanding and improving the coherence of germanium hole spin qubits.

Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level.

The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.

Effects of strain and hydrostatic pressure on exciton properties in asymmetric zinc-blende (In,Ga)N/GaN coupled double quantum wells

Within the effective mass approximation, we studied the light-hole and heavy-hole exciton states and their optical properties, such as oscillator strength and radiative decay time, in asymmetric zinc-blende GaN/InxGa1−xN/GaN/InyGa1−yN/GaN coupled double quantum wells. The variational method was performed under strain and hydrostatic pressure. The light-hole and heavy-hole exciton binding energies as a function of the left-well width and/or right-well width, middle-barrier thickness, and indium concentration x(y) of (In,Ga)N material are analyzed in detail. The light-hole and heavy-hole exciton binding energies show an increasing trend with increase of hydrostatic pressure. The hydrostatic pressure not only results in an increase in exciton binding energy, interband transition energy, and oscillator strength but also a decrease in the emission wavelength and radiative decay time. In addition, the biaxial strain dependence of the emission wavelength, radiative decay time, and interband transition energy of the exciton is very remarkable.

(Invited) Optoelectronic Quantum Information Processing: An All-Group IV Integrated Platform

Achieving coherent optical photon-to-spin conversion is a long-sought-after strategy for surmounting current fundamental limits in optical schemes that hinder the long-distance distribution of entanglement. Moreover, photon-to-spin interfaces are also essential for a direct mapping of the quantum information encoded in photon flying qubits to stationary spin processors. However, the lack of scalable materials offering an efficient interaction with optical photons along with optimal spin properties remains a formidable obstacle hindering the development of these quantum technological components. With this perspective, this presentation will discuss strategies to address these challenges by leveraging the degrees of freedom offered by group IV (Si)GeSn semiconductors, namely strain and composition, to tailor the electronic structure and eventually fulfill these prerequisites. These innovative systems do not only have the potential to enable coherent photon-to-spin interfaces, but because of their compatibility with the semiconductor industry they will also offer scalability, manufacturability, and cost-effectiveness.We will show that this family of semiconductors provide an additional flexibility to control the charge carrier states and achieve a selective confinement of holes. The latter benefit from a quiet quantum environment that has been at the core of increasingly reliable quantum processors and memories. However, most if not all available experimental studies of two-dimensional gas systems have been thus far focused on heavy-hole (HH) states. This is attributed to the nature of the heterostructures currently available (e.g, Ge/SiGe, InGaAs/GaAs), where compressive strain lifts the valence band degeneracy and leaves HH states energetically well above the light-hole (LH) states. We will demonstrate that tensile strained Ge/GeSn quantum wells alleviate these limitations and allow to selectively confine LH provided the strain is higher than 1%. This requires strain relaxed, high Sn content GeSn buffer layers to be used to grow Ge quantum wells with LH ground state, high g-factor anisotropy, and a tunable splitting of the hole subbands. The optical and electronic properties of these low-dimensional systems will be described and discussed. Spin injection and coherent control will also be addressed. Additionally, qubit designs exploiting the ability to engineer LH states and the Ge large spin-orbit coupling allowing fast all-electrical spin-manipulation schemes will also be presented and discussed.

A Light-Hole Germanium Quantum Well on Silicon.

The quiet quantum environment of holes in solid-state devices is at the core of increasingly reliable architectures for quantum processors and memories. However, due to the lack of scalable materials to properly tailor the valence band character and its energy offsets, the precise engineering of light-hole (LH) states remains a serious obstacle toward coherent optical photon-spin interfaces needed for a direct mapping of the quantum information encoded in photon flying qubits to stationary spin processors. Herein, to alleviate this long-standing limitation, an all-group-IV low-dimensional system is demonstrated, consisting of a highly tensile strained germanium quantum well grown on silicon allowing new degrees of freedom to control and manipulate the hole states. Wafer-level, high bi-isotropic in-plane tensile strain (<1%) is achieved using strain-engineered, metastable germanium-tin alloyed buffer layers yielding quantum wells with LH ground state, high g-factor anisotropy, and a tunable splitting of the hole sub-bands. The epitaxial heterostructures display sharp interfaces with sub-nanometer broadening and show room-temperature excitonic transitions that are modulated and extended to the mid-wave infrared by controlling strain and thickness. This ability to engineer quantum structures with LH selective confinement and controllable optical response enables manufacturable silicon-compatible platforms relevant to integrated quantum communication and sensing technologies.

Broadband and photovoltaic THz/IR response in the GaAs-based ratchet photodetector.

High-performance broadband infrared (IR)/terahertz (THz) detection is crucial in many optoelectronic applications. However, the spectral response range of semiconductor-based photodetectors is limited by the bandgaps. This paper proposes a ratchet structure based on the GaAs/AlxGa1−xAs heterojunction, where the quasi-stationary hot hole distribution and intravalence band absorption from light or heavy hole states to the split-off band overcome the bandgap limit, ensuring an ultrabroadband photoresponse from near-IR to THz region (4 to 300 THz). The peak responsivity of the proposed structure can reach 7.3 A/W, which is five orders of magnitude higher than that of the existing broadband photon-type detector. Because of the ratchet effect, the proposed photodetector has a bias-tunable photoresponse characteristic and can operate in the photovoltaic mode with a broad photocurrent spectrum (18 to 300 THz). This work not only demonstrates a broadband photon-type THz/IR photodetector but also provides a method to study the light-responsive ratchet.

Quantum beats of light-hole and heavy-hole excitons in reflection spectra of GaAs/AlGaAs quantum well

In this work we experimentally study dynamics of the heavy-hole and light-hole exciton states in a quantum well under coherent excitation of both excitonic resonances using co- and cross-linear and circular polarizations of pump and probe beams. Oscillations of basic parameters of excitonic resonances are observed. Their dependence on the polarization of the pump and probe beams is used to determine the structure of states of the heavy-hole and light-hole excitons by means of theoretical modelling of experimental data. Keywords: quantum well, excitons, quantum beats, light-hole exciton, heavy-hole exciton.

Investigating the physics of higher-order optical transitions in InAs/GaSb superlattices

We present an optical spectroscopy analysis of the molecular beam epitaxy-grown InAs/GaSb quantum systems to study the higher-order optical transitions in InAs/GaSb superlattices (SLs). We have investigated two type-II SL structures with different layer widths: $\mathrm{In}{\mathrm{As}}_{8\mathrm{ML}}/\mathrm{Ga}{\mathrm{Sb}}_{8\mathrm{ML}}$ and $\mathrm{In}{\mathrm{As}}_{10\mathrm{ML}}/\mathrm{Ga}{\mathrm{Sb}}_{10\mathrm{ML}}$. To experimentally determine the spectral distribution of the higher-order transitions, the Fourier-transformed photoluminescence and Fourier-transformed photomodulated reflectance measurements were used. These measurements were undertaken vs temperature and incident polarization of the probing beam. Complementary theoretical calculations based on the eight $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ formalism were also performed to identify the electron and heavy and light hole energy band ladder. Polarization-dependent measurements indicated the interchanging nature of the light and heavy hole states for the second and third valence band vs the SL wave vector $({k}_{z})$ along the growth direction. The results were compared with other calculations based on different models and existing experimental results, then summarized and reviewed for possible numerical parameters application ranges in the interface modeling.

Light hole states in a strained quantum dot: Numerical calculation and phenomenological models

Starting from the numerical solution of the 6-band \textbf{k.p} description of a lattice-mismatched ellipsoidal quantum dot situated inside a nanowire, including a spin Zeeman effect with values appropriate to a dilute magnetic semiconductor, we propose and test phenomenological models of the effect of the built-in strain on the heavy hole, light hole and exciton states. We test the validity and the limits of a description restricted to a ($\Gamma_8$) quadruplet of ground states and we demonstrate the role of the interactions of the light-hole state with light-hole excited states. We show that the built-in axial strain not only defines the character, heavy-hole or light-hole, of the ground state, but also mixes significantly the light-hole state with the split-off band's states: Even for a spin-orbit energy as large as 1 eV, that mixing induces first-order modifications of properties such as the spin value and anisotropy, the oscillator strength, and the electron-hole exchange, for which we extend the description to the light-hole exciton. CdTe/ZnTe quantum dots are mainly used as a test case but the concepts we discuss apply to many heterostructures, from mismatched II-VI and III-V quantum dots and nanowires, to III-V nanostructures submitted to an applied stress and to silicon nanodevices with even smaller residual strains.

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.

Activated and Metallic Conduction in p -Type Modulation-Doped Ge - Sn Devices

$G{e}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ quantum wells can be incorporated into $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Ge}$--based structures with low-carrier effective masses, high mobilities, and the possibility of direct band-gap devices with x \ensuremath{\sim} 0.1. However, the electrical properties of p-type $G{e}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ devices are dominated by a thermally activated mobility and metallic behavior. At 30 mK the transport measurements indicate localization with a mobility of $380\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{2}$/Vs, which is thermally activated with a temperature-independent carrier density of 4 \ifmmode\times\else\texttimes\fi{} ${10}^{11}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. This weakly disordered system with conductivity, \ensuremath{\sigma} \ensuremath{\sim} ${e}^{2}$/h, where e is the fundamental charge and h is Planck's constant, is a result of negatively charged ``Sn-vacancy'' complex states in the barrier layers that act as hole traps. A measured hole effective mass of 0.090 \ifmmode\pm\else\textpm\fi{} $0.005{m}_{e}$ from the Shubnikov-de Haas effect, where ${m}_{e}$ is the free electron mass shows that the valence band is heavy hole dominated and is similar to p-type $\mathrm{Ge}$ with the compressive strain playing the role of quenching the spin-orbit coupling and shifting the unoccupied light-hole states to higher hole energies. The $G{e}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ devices have a high quantum mobility of approximately 36 000 ${\mathrm{cm}}^{2}$/Vs that is not thermally activated. The ratio of transport-to-quantum mobility of approximately 0.01 in $G{e}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ devices is unusual and points to several competing scattering mechanisms in the different experimental regimes.

Pseudospin-electric coupling for holes beyond the envelope-function approximation

In the envelope-function approximation, interband transitions produced by electric fields are neglected. However, electric fields may lead to a spatially local $(k\text{\ensuremath{-}}\mathrm{independent})$ coupling of band (internal, pseudospin) degrees of freedom. Such a coupling exists between heavy-hole and light-hole (pseudo)spin states in III-V semiconductors, such as GaAs, or in group IV semiconductors (germanium, silicon,...) with broken inversion symmetry. Here, we calculate the electric-dipole (pseudospin-electric) coupling for holes in GaAs from first principles. We find a transition dipole of 0.5 debye, a significant fraction of that for the hydrogen-atom $1s\ensuremath{\rightarrow}2p$ transition. In addition, we derive the Dresselhaus spin-orbit coupling that is generated by this transition dipole for heavy holes in an asymmetric quantum well. A quantitative microscopic description of this pseudospin-electric coupling may be important for understanding the origin of spin splitting in quantum wells, spin coherence/relaxation $({T}_{2}^{*}/{T}_{1})$ times, spin-electric coupling for cavity-QED, electric-dipole spin resonance, and spin nonconserving tunneling in double quantum dot systems.

Acceptor-related infrared optical absorption in GaAs/AlGaAs quantum wells

Abstract The results of the theoretical and experimental investigations of optical response of the acceptor centers in narrow GaAs/AlGaAs quantum wells in the infrared spectral range are presented. In the theoretical part, we focused on the probabilities of the photoionization of acceptor centers taking into account the complicated valence band structure and intermixing the light and heavy hole states. We used the finite-difference method to quantize the Luttinger-Kohn Hamiltonian and the decomposition of the impurity potential over the eigenstates of this Hamiltonian with the quantum well profile to obtain the acceptor state energies and wavefunctions in momentum space. The momentum-dependent decomposition coefficients were used to calculate the optical matrix elements of the hole transitions from localized acceptor states to 2D continuum states in dipole approximation. Calculated spectral and polarization dependencies of the infrared optical absorption due to photoionization of acceptors are discussed. Equilibrium absorption spectra of the polarized infrared radiation were measured in a wide temperature range. Spectral positions of the observed absorption peaks are in satisfactory agreement with theoretical calculations.

Electronic states and interband tunneling conditions in type-II quantum well heterostructures

Type-II quantum well (QW) heterostructures based on the InAs/GaSb/AlSb material system have important applications in interband tunneling and midinfrared optoelectronic devices. From the perspective of interband tunneling conditions in widely used type-II QWs such as N-QW, W-QW, and M-QW structures, this work studies how energy levels for electronic and light-hole states are varied with various combinations of semiconductor material layers. Using a two-band model, analytical expressions are derived for the transition well widths that correspond to the critical layer thicknesses for bound- or quasibound states to appear in the interband tunneling region in type-II heterostructures, which provide meaningful connections to semiconductor material parameters. Calculations of transition well widths are carried out for several InAs/GaSb/AlSb-based type-II QW structures. The results and understanding gained from the study may be helpful in designing and developing midinfrared optoelectronic devices such as interband cascade lasers, photodetectors, and thermophotovoltaic cells.

Effect of Lateral Electric Field on the Transition Energies of Heavy Hole State and Light Hole State in a Semiconductor Quantum Dot

Using effective mass approximation, this study theoretically investigated how the ground state of the valence band in an inverse parabolic quantum dot (IPQD) reaches the light hole state by strengthening the confinement in the QD plane through the application of a lateral electric field on IPQDs. We calculated the exact analytical solution in the form of the Heun function associated with a complex eigenvalue for the degenerate and excited energy states of the electron, light hole (LH), and heavy hole (HH), in the IPQD context. Our results showed that, for a large QD size, the inverse parabolic quantum confinement (IPQC) potential removed the electron and hole degeneracy, while in the strong confinement region (small QD size), crossing occurred. In addition, the results offered another way of switching the ground state energy of the valence band inside QDs from the HH to LH state when applying a lateral electric field on a QD with an IPQC potential. Consequently, different optical transitions were established, and from the lateral electric field, we obtained a larger quantum Stark shift in IPQD compared with the parabolic QD (PQD), and the excited state energies showed a linear Stark shift in both the QDs.

Probing the light hole/heavy hole switching with correlated magneto-optical spectroscopy and chemical analysis on a single quantum dot

A whole series of complementary studies have been performed on the same single nanowire containing a quantum dot: cathodoluminescence spectroscopy and imaging, micro-photoluminescence spectroscopy under magnetic field and as a function of temperature, and energy-dispersive x-ray spectrometry and imaging. The ZnTe nanowire was deposited on a Si3N4 membrane with Ti/Al patterns. The complete set of data shows that the CdTe quantum dot features the heavy-hole state as a ground state, although the compressive mismatch strain promotes a light-hole ground state as soon as the aspect ratio is larger than unity (elongated dot). A numerical calculation of the whole structure shows that the transition from the heavy-hole to the light-hole configuration is pushed toward values of the aspect ratio much larger than unity by the presence of a (Zn, Mg)Te shell, and that the effect is further enhanced by a small valence band offset between the semiconductors in the dot and around it.

Energy reversal of light- and heavy-hole excitons bound to isoelectronic centers

Isoelectronic centers in semiconductor hosts offer convenient optical access to both heavy- and light-hole states, thus providing powerful resources for the ultrafast control of electron or hole spins. From a detailed analysis of the fine structure of excitons bound to isoelectronic defects of ${C}_{s}$ symmetry formed by two nitrogen impurities in GaAs, we demonstrate that the lowest energy states, normally exhibiting a strongly dominant heavy-hole character, can be reversed to a dominant light-hole character by the strain found in the vicinity of the emitter. This reversal suggests that strain could be used to engineer the orbital composition and ordering of excitonic states, allowing enhanced optical control over spin states.

Chloride-Induced Thickness Control in CdSe Nanoplatelets.

Current colloidal synthesis methods for CdSe nanoplatelets (NPLs) routinely yield samples that emit, in discrete steps, from 460 to 550 nm. A significant challenge lies with obtaining thicker NPLs, to further widen the emission range. This is at present typically achieved via colloidal atomic layer deposition onto CdSe cores, or by synthesizing NPL core/shell structures. Here, we demonstrate a novel reaction scheme, where we start from 4.5 monolayer (ML) NPLs and increase the thickness in a two-step reaction that switches from 2D to 3D growth. The key feature is the enhancement of the growth rate of basal facets by the addition of CdCl2, resulting in a series of nearly monodisperse CdSe NPLs with thicknesses between 5.5 and 8.5 ML. Optical characterization yielded emission peaks from 554 nm up to 625 nm with a line width (fwhm) of 9–13 nm, making them one of the narrowest colloidal nanocrystal emitters currently available in this spectral range. The NPLs maintained a short emission lifetime of 5–11 ns. Finally, due to the increased red shift of the NPL band edge photoluminescence excitation spectra revealed several high-energy peaks. Calculation of the NPL band structure allowed us to identify these excited-state transitions, and spectral shifts are consistent with a significant mixing of light and split-off hole states. Clearly, chloride ions can add a new degree of freedom to the growth of 2D colloidal nanocrystals, yielding new insights into both the NPL synthesis as well as their optoelectronic properties.

Magnetospatial dispersion of semiconductor quantum wells

Polarization conversion of light reflected from quantum wells governed by both magnetic field and light propagation direction is observed. We demonstrate that the polarization conversion is caused by the magnetospatial dispersion in quantum wells which manifests itself in the reflection coefficient contribution bilinear in the in-plane components of the magnetic field and the light wave vector. The magnetospatial dispersion is shown to arise due to structure inversion asymmetry of the quantum wells. The effect is resonantly enhanced in the vicinity of the heavy-hole exciton. We show that microscopically the magnetospatial dispersion is caused by the mixing of heavy- and light-hole states in the quantum well due to both orbital effect of the magnetic field and the in-plane hole motion. The degree of the structure inversion asymmetry is determined for GaAs/AlGaAs and CdTe quantum wells.

Substrate dependence of TM-polarized light emission characteristics of BAlGaN/AlN quantum wells

To study the substrate dependence of light emission characteristics of transverse-magnetic (TM)-polarized light emitted from BAlGaN/AlN quantum wells (QWs) grown on GaN and AlN substrates were investigated theoretically. It is found that the topmost valence subband for QW structures grown on AlN substrate, is heavy hole state (HH1) while that for QW structures grown on GaN substrate is crystal-field split off light hole state (CL1), irrespective of the boron content. Since TM-polarized light emission is associated with the light hole state, the TM-polarized emission peak of BAlGaN/AlN QW structures grown on GaN substrate is expected to be much larger than that of the QW structure grown on AlN substrate. Also, both QW structures show that the spontaneous emission peak of BAlGaN/AlN QW structures would be improved with the inclusion of the boron. However, it rapidly begins to decrease when the boron content exceeds a critical value.