All-optical control of the g-factor in self-assembled (In,Ga)As/GaAs quantum dots

Abstract

Semiconductor quantum dots have improved solid-state laser technology and introduced a new controllable zero-dimensional system to physicists. Next to laser technology, they can be applied as memory elements and (infrared) detectors as well. Quantum dots are commonly grown by epitaxial methods like Molecular Beam Epitaxy (MBE) or Metal-Organic Chemical Vapour Deposition (MOCVD), where they are embedded as a layer or multiple layers in a larger bulk-type structure. In this work, we study a MBE-grown single layer of (In,Ga)As quantum dots, which is embedded in the middle of a p-i-n junction of GaAs material. Charge carriers in quantum dots experience little disturbance from the bulk semiconductor environment, which, for example, leads to relatively long spin relaxation times. For these long spin relaxation times, in particular spin decoherence times (i.e., phaserelated relaxation), quantum dots have been mentioned as possible elements in quantum information devices. The spin of the electron can be employed for quantum information purposes, acting as the base element of these systems, the qubit. In one of the proposed device architectures, each quantum dot of the array hosts a charge carrier, which spins addressed by a radio-frequent field. To achieve addressability of each of the charge carriers in the array, one requires a locally tunable g factor. The g factor is a measure for the energy splitting between Zeeman levels of the quantum dot in a magnetic field, and is proportional to the required frequency of the radio-frequent field. This thesis considers several of these quantum information related subjects for selfassembled (In,Ga)As quantum dots. First of all, a general introduction to quantum dots and a motivation is given in Chapter 1. Chapter 2 discusses some more specific subjects of quantum dots in magnetic and electric fields, whereas chapter 3 discusses the experimental setups. Chapter 4, 5, and 6 present the main results of the thesis, pointed out in the next paragraphs. Chapter 4 presents data on the degree of circular polarization of the photoluminescence (PL) of quantum dots. This data is measured in a magnetic field, which leads to a Zeeman splitting (proportional to the g factor) between spin eigenstates of the energy levels within the quantum dot. Each of the levels emits circularly polarized photons with opposite helicity. In the case of an unbalanced occupancy of the levels, one observes a degree of circular polarization of the PL. This circular polarization contains information about the sign of the g factor, the magnitude of the g factor and the spin relaxation times between the Zeeman levels. Furthermore, we employ the built-in electric field of the p-i-n structure of the GaAs host material. By excitation of an additional continuous wave laser, the built-in electric field can be varied, which has its signature in the Stark shift in the PL spectra of the quantum dots. The first part of chapter 4 presents data in a magnetic field of 7 T, where the degree of circular polarization changes its sign in the same excitation density regime where the Stark shift (i.e., electric field) varies. We associate the sign change of the polarization with a sign change of the exciton g factor in the growth direction (where the exciton is a combined particle of the electron and hole). Since the Stark shift provides a measure for the electric field, we estimate the sign change to occur for electric fields exceeding 150 kV/cm. The sign change of the polarization is observed throughout the whole PL energy range, including the lowest energies, which excludes a sign change induced by excited states. The magnitude of the degree of circular polarization is considered in the second part of chapter 4. The magnitude of the polarization is a measure for the spin relaxation time between the exciton spin levels. We measure the magnetic field dependence of the polarization to determine the magnetic field dependence of the spin relaxation time. We observe the exciton spin relaxation time to follow a power law behavior with the magnetic field, which matches with a theoretical prediction of Tsitsishvili et al. from 2003. In high electric fields, the strong power law behavior is left and a much weaker dependence with magnetic field occurs. This confirms that quantum dots provide good spin conservation conditions for charge carriers. Chapter 5 discusses the electric field dependence of the recombination time in quantum dots. We utilize time- and spectrally-resolved PL data to combine the variation of the signal decay (related to the recombination time) and the time-dependent Stark shift. Like in chapter 4, the Stark shift at every time is a measure for the electric field. Recombination times increase from ~ 1 ns when there is no electric field up to ~ 4 nsat electric fields close to 200 kV/cm. Moreover, we observe a significant drop in the PL intensity at electric fields above 200 kV/cm. This is associated with tunneling of charge carriers out of the quantum dot. In addition to the growth direction g factors, studied in chapter 4, we consider the in-plane g factor in chapter 6. In-plane g factors are difficult to probe in experiments involving luminescence, due to optical selection rules and complex experimental geometries. A common method to measure them is by time-resolved Kerr rotation spectroscopy, where the precession of the signal in a magnetic field is proportional to the in-plane g factor, which is applied in this chapter as well. Next to the required pulsed laser to determine the temporal dependence of the signal, we employ a continuous wave He:Ne laser to control the electric field over the quantum dots. Furthermore, a relatively small in-plane magnetic field of 280 mT is applied. The oscillations in the signal indicate spin recession. Calculations of J.A.F.S. Pingenot and M.E. Flatt´e indicate that the highest frequency is likely due to the valence electron. Without electric field over the quantum dots, the in-plane valence electron g factor is found to be 0.42±0.01, whereas in electric fields exceeding 50 kV/cm, the in-plane g increases slightly (not more than 0.02). The spin decoherence time of the valence electron is found to be larger than the conduction electron for all electric fields. Both are in the order of hundreds of picoseconds. We estimate the hyperfine-interaction to induce a significant effect of decoherence of the spin of the charge carriers