Heavy-hole Mixing Research Articles

Hyperfine coupling of hole and nuclear spins in symmetric (111)-grown GaAs quantum dots

In self assembled III-V semiconductor quantum dots, valence holes have longer spin coherence times than the conduction electrons, due to their weaker coupling to nuclear spin bath fluctuations. Prolonging hole spin stability relies on a better understanding of the hole to nuclear spin hyperfine coupling which we address both in experiment and theory in the symmetric (111) GaAs/AlGaAs droplet dots. In magnetic fields applied along the growth axis, we create a strong nuclear spin polarization detected through the positively charged trion X$^+$ Zeeman and Overhauser splittings. The observation of four clearly resolved photoluminescence lines - a unique property of the (111) nanosystems - allows us to measure separately the electron and hole contribution to the Overhauser shift. The hyperfine interaction for holes is found to be about five times weaker than that for electrons. Our theory shows that this ratio depends not only on intrinsic material properties but also on the dot shape and carrier confinement through the heavy-hole mixing, an opportunity for engineering the hole-nuclear spin interaction by tuning dot size and shape.

Magnetospectroscopy of excited states in charge-tunable GaAs/AlGaAs [111] quantum dots

We present a combined experimental and theoretical study of highly charged and excited electron-hole complexes in strain-free (111) GaAs/AlGaAs quantum dots grown by droplet epitaxy. We address the complexes with one of the charge carriers residing in the excited state, namely, the ``hot'' trions X$^{-*}$ and X$^{+*}$, and the doubly negatively charged exciton X$^{2-}$. Our magneto-photoluminescence experiments performed on single quantum dots in the Faraday geometry uncover characteristic emission patterns for each excited electron-hole complex, which are very different from the photoluminescence spectra observed in (001)-grown quantum dots. We present a detailed theory of the fine structure and magneto-photoluminescence spectra of X$^{-*}$, X$^{+*}$ and X$^{2-}$ complexes, governed by the interplay between the electron-hole Coulomb exchange interaction and the heavy-hole mixing, characteristic for these quantum dots with a trigonal symmetry. Comparison between experiment and theory of the magneto-photoluminescence allows for precise charge state identification, as well as extraction of electron-hole exchange interaction constants and $g$-factors for the charge carriers occupying excited states.

Effect of uniaxial stress on electroluminescence, valence band modification, optical gain, and polarization modes in tensile strained p-AlGaAs/GaAsP/n-AlGaAs laser diode structures: Numerical calculations and experimental results

The effects of uniaxial compression in [110] direction on energy-band structures, heavy and light hole mixing, optical matrix elements, and gain in laser diodes with “light hole up” configuration of valence band levels in GaAsP quantum wells with different widths and phosphorus contents are numerically calculated. The development of light and heavy hole mixing caused by symmetry lowering and converging behavior of light and heavy hole levels in such quantum wells under uniaxial compression is displayed. The light or heavy hole nature of each level is established for all considered values of uniaxial stress. The results of optical gain calculations for TM and TE polarization modes show that uniaxial compression leads to a significant increase of the TE mode and a minor decrease of the TM mode. Electroluminescence experiments were performed under uniaxial compression up to 5 kbar at 77 K on a model laser diode structure (p-AlxGa1−xAs/GaAs1−yPy/n-AlxGa1−xAs) with y = 0.16 and a quantum well width of 14 nm. They reveal a maximum blue shift of 27 meV of the electroluminescence spectra that is well described by the calculated change of the optical gap and the increase of the intensity being referred to a TE mode enhancement. Numerical calculations and electroluminescence data indicate that uniaxial compression may be used for a moderate wavelength and TM/TE intensity ratio tuning.

Dark-Bright Mixing of Interband Transitions in Symmetric Semiconductor Quantum Dots

In photoluminescence spectra of symmetric [111] grown GaAs/AlGaAs quantum dots in longitudinal magnetic fields applied along the growth axis, we observe in addition to the expected bright states also nominally dark transitions for both charged and neutral excitons. We uncover a strongly nonmonotonic, sign-changing field dependence of the bright neutral exciton splitting resulting from the interplay between exchange and Zeeman effects. Our theory shows quantitatively that these surprising experimental results are due to magnetic-field-induced ±3/2 heavy-hole mixing, an inherent property of systems with C(3v) point-group symmetry.

Strain-induced darkening of trapped excitons in coupled quantum wells at low temperature

In GaAs/AlGaAs coupled quantum wells, strain-induced traps may be used to confine excitons in in-plane, harmonic traps. Using these traps, we have pursued Bose-Einstein condensation (BEC) of long-lived, spatially indirect excitons. Here, we report a remarkable transition of the indirect exciton luminescence pattern with increasing strain, increasing exciton density, and decreasing temperature, to a spatial pattern exhibiting a large dark spot at the trap center, where we expect the exciton density to be maximum. The mechanism of particle loss is ruled out as an explanation for this dark spot. While the onset criteria are approximately consistent with the conditions for BEC of a weakly interacting gas, the conspicuous proximity in energy of the indirect light-hole states suggests that an explanation employing the single-particle physics of light-hole--heavy-hole mixing may explain the phenomenon. The effect of the strain is modeled, and the resulting landscape of indirect exciton spin states is discussed. The relative oscillator strengths of these states are predicted by an exact numerical solution of the two-particle Schr\"odinger equation for electrons and holes in coupled quantum wells and an electric field. The contrast in oscillator strengths is sufficient to produce this luminescence pattern, but this analysis suggests a strongly diminished lifetime as stress is increased. The opposite lifetime dependence is observed experimentally. Additionally, the temperature dependence eludes explanation by this mechanism.

Exciton states in spherical parabolic GaAs quantum dots

The lowest (s, S) and (p, P) exciton states of a GaAs quantum dot with an isotropic parabolic potential are calculated. Hole states are calculated from the Luttinger - Kohn scheme in the spherical approximation, thus taking light-hole and heavy-hole mixing into account. Exciton states are obtained from an expansion of the wavefunction in a basis formed by products of electron and hole states, and the size dependence of the exciton levels is investigated. By comparison to a one-band model it is found that the effect of valence band mixing is very important and that the one-band model overestimates the exciton energy by more than 20% in the case of strong confinement.

Hole states in GaAs/AlAs heterostructures and the limitations of the Luttinger model

We present microscopic results for hole scattering at a [001] GaAs-AlAs single interface, with k ‖ = 0 , which show strong bulk light hole — heavy hole mixing. The hole scattering process is found to be due to the differences in the cell periodic wavefunctions of the materials of the interface, invalidating the fundamental assumption of the effective mass theory of hole states in heterostructures. We show that the mixing of light- and heavy-hole states is much larger than that obtained from a phenomenological model based on the Luttinger Hamiltonian. The time reversal symmetry aspects of bulk Bloch spinor states, in the presence of the spin-orbit interaction, are found to play an important role in determining the magnitude of the scattering amplitudes of the various bulk states. In the light of these calculations, we question the validity of the effective mass theory/Luttinger Hamiltonian approach, usually employed to describe heterostructure hole states.