Hyperfine interaction mediated exciton spin relaxation in (In,Ga)As quantum dots

H. Kurtze, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer

Phys. Rev. B 85, 195303 – Published 4 May 2012

Abstract

The population dynamics of dark and bright excitons in (In,Ga)As/GaAs quantum dots is studied by two-color pump-probe spectroscopy in an external magnetic field. With the field applied in Faraday geometry and at $T < 20$ K, the dark excitons decay on a ten nanoseconds time scale unless the magnetic field induces a resonance with a bright exciton state. At these crossings their effective lifetime is drastically shortened due to spin flips of either electron or hole by which the dark excitons are converted into bright ones. Due to the quasielastic character we attribute the origin of these flips to the hyperfine interaction with the lattice nuclei. We compare the exciton spin relaxation times in the two resonances and find that the spin flip involving an electron is approximately 25 times faster than the one of the hole. A temperature increase leads to a considerable, nonmonotonic decrease of the dark exciton lifetime. Here phonon-mediated spin flips due to the spin-orbit interaction gradually become more important.

Received 6 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.195303

Authors & Affiliations

H. Kurtze¹, D. R. Yakovlev¹, D. Reuter², A. D. Wieck², and M. Bayer¹

¹Experimentelle Physik 2, Technische Universität Dortmund, D-44221 Dortmund, Germany
²Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

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Vol. 85, Iss. 19 — 15 May 2012

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Images

Figure 1
(a) Level diagram of bright (angular momentum $M = \pm 1$ ) and dark ( $M = \pm 2$ ) excitons for the QDs under study, subject to an external magnetic field $B_{z}$ along the QD growth direction. $δ_{0}$ denotes the (isotropic) exchange interaction energy; $τ_{rad}$ is the radiative decay time. (b) Sketch of the experimental configuration as described in the text. (c) Time-resolved DT trace, observed for a pump (probe) excitation density of $I_{0} = 10$ W/cm $^{2}$ (1 W/cm $^{2}$ ) at $T = 10$ K. Note the log $_{10}$ scale for the vertical axis. The inset gives a cross-sectional transmission electron micrograph image of an unannealed self-assembled InGaAs/GaAs QD, nominally identical to the as-grown QDs in this work.Reuse & Permissions
Figure 2
Contour plot of DT traces (along the vertical axis) vs applied magnetic field in Voigt configuration (B $⊥$ z, along the horizontal axis). $T = 10$ K, $I_{0}$ pump power.Reuse & Permissions
Figure 3
(a) Fine structure of bright and dark exciton states in the studied QDs subject to a longitudinal magnetic field. The arrows represent the exciton spin configurations where the electron spins $S_{e, z} = + 1 / 2$ and $- 1 / 2$ are symbolized by thin arrows pointing up and down, respectively. The thick arrows give the corresponding orientations of the hole spin $J_{h, z} = \pm 3 / 2$ . (b) Contour plot of DT traces vs Faraday magnetic field strength. $T = 10$ K, pump power $I_{0}$ . (c) Dots: DT values from (b), averaged over a delay time interval of 150 ps before pump arrival vs magnetic field. The dots in the main panel (inset) show DT values with (without) a baseline subtraction. The solid line is a fit to the DT data by two Gaussians, both of 1.56 T width for each resonance, with each Gaussian shown by the dashed lines.Reuse & Permissions
Figure 4
(a) Contour plot of normalized DT traces for varying temperatures from 5 K to 180 K; $B = 0$ , excitation power $I_{0}$ . (b) The data points give relaxation times $τ_{1 \leftrightarrow 2}^{fit}$ obtained from a fit to the DT data set from panel (a). Solid lines show calculated single-phonon relaxation times from $M = \pm 1$ to $M = \pm 2$ excitons (and vice versa) as described in the text (log $_{10}$ scale).Reuse & Permissions
Figure 5
DT averaged over a negative delay time interval of 150 ps before pump arrival vs magnetic field for various temperatures as indicated. The data are baseline subtracted as in Fig. 3c.Reuse & Permissions
Figure 6
(a) Normalized DT values vs delay time at field amplitudes of $B = 0$ , 3 T, and 4.7 T in Faraday configuration (scattered dots). The traces were set to zero at $Δ t = 0$ . (b) Total exciton population as modeled by a set of rate equations; see text. The numbers give the different values of the parameter $τ^{fit}$ mapping the spin flip of the involved $M = - 2$ dark excitons into $\pm$ 1 bright ones and vice versa. (Both panels log $_{10}$ scale.)Reuse & Permissions

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