Technion – Israel Institute of Technology Physics Department and Solid State Institute Eilon Poem, Stanislav Khatsevich, Yael Benny, Illia Marderfeld and David Gershoni The Physics Department and The Solid State Institute, Technion, Haifa 32000, Israel Antonio Badolato and Pierre M. Petroff Materials Department, University of California Santa Barbara, Santa Barbara, California 93106, USA Supported by the US-Israeli Binational Science Foundation (BSF) and by the Russell Berrie Nanotechnology Institue (RBNI) Negative polarization memory of charged excitons in a single Quantum Dot

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Outline Background and Motivation Quantum Dots Experiment – Polarization sensitive PL-Excitation Results – Negative and positive circular polarization memory Theoretical model Comparison with the experiment Conclusions

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Achievements of semiconductor technology, using Quantum Dots Accurate charge control, up to the single electron level L.P. Kowenhoven et al, Rep. Prog. Phys. 64, 701 (2001)

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Achievements of semiconductor technology, using Quantum Dots Single photon emitters Z. Yuan et al, Science 295, 102 (2002)

Technion – Israel Institute of Technology, Physics Department and Solid State Institute The final frontier: spin control Two main directions:  Spintronics: Electrical injection of spin-polarized currents using ferromagnetic electrodes  Opto-Spintronics: Optical generation of carriers with a well-defined spin state using polarized light and selection-rules

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Dots Quantum Dots What is a QD? A nanometeric droplet of a semiconductor of one kind (InAs) embedded within a semiconductor of another kind (GaAs). A a 3D trap for charge carriers Discrete energy levels. V ~10nm

Technion – Israel Institute of Technology, Physics Department and Solid State Institute h Discrete Emission Optical excitation Electron Hole Continuum Discrete energy levels Diffusion into the QD I h QD QD - Photoluminescence

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Few Carrier states of a QD PL energy (eV) Intensity (counts/sec) Coulomb interactionsCoulomb interactions give each configuration a different energy More than one transition near the single electron- hole pair recombination energy.

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Experiment 2. Incident polarized light creates an electron-hole pair with a known spin state in a high-lying energy level of the QD. 3. The electron and hole quickly decay to the lowest possible energy level. Their spin state may change during this decay. 4. A recombination a an electron-hole pair takes place, and a photon is emitted. The relation between the polarization of the emitted photon to that of the absorbed photon - the ‘Polarization Memory’ - may add information regarding the spin dynamics during the decay process. 1. Initially there may be a few charge-carriers inside the QD, occupying their ground sate.

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Our Sample Self-assembled Quantum-Dots embedded within a microcavity p-i-n junction Enables controlled charging of the QDs

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Voltage dependent PL X -3 XX -1 X -1 XX -2 Excitation Energy: 1.369eV Temperature: 20K Positive charging Negative charging Line identification: E. Poem et al, PRB 76, (2007) Degree of circular polarization memory X -2 X0X0 X +1

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Polarization memory PL Intensity (cts./10sec./pix.) Degree of Polarization Memory PL Energy (eV) Excitation Energy: 1.369eV Temperature: 20K Voltage: +5.9V

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Theoretical approach Solves the few-particles Schrödinger equation Finds energy levels and spin-configurations Calculates polarized optical transition probabilities Used to identify spectral lines by their polarized fine structure Full Configuration-Interaction, including the electron-hole exchange interaction

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Theoretical approach Calculates the expected emission spectrum in any polarization, under excitation in any polarization. For this, additional assumptions regarding the relaxation process are needed: During the decay process, the electron preserves its spin, while the hole has a 50% probability of flipping its spin. [V. K. Kalevich et al, PRB 72, (2005)]

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Theoretical approach The main observations are reproduced using the above assumption and the inclusion of the electron-hole exchange splitting: states in which the spins of the electron and hole are parallel have different energies than states with anti-parallel spins. No electron-hole exchange: 4-fold degeneracy Electron-hole exchange for cylindrical symmetry Additional splitting for reduced symmetry

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Example: X -3 (S=3/2, S z =1/2)(S=3/2, S z =-1/2)(S=3/2, S z =-3/2)

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Comparison of calculation and experiment Transition probability (arb. units) PL Intensity (cts./sec./pix.) PL Energy (eV)

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Comparison of calculation and experiment Degree of Polarization Memory PL Energy (eV)

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Conclusions QDs may be used to optically control the spin of a single particle. We investigate the reaction of a QD to polarized optical excitation. Under certain quasi-resonant optical excitation, negatively charged excitonic transitions can have either positive, negative or no circular-polarization memory. We explain all our experimental observations using our full configuration interaction model including e-h exchange interaction, and one crucial assumption: Photoexcited electrons maintain their spin polarization, while holes do not.

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Dots Quantum Dots Confine a few, or even a single electron (or hole) Absorb and emit single photons Carrier spin and photon polarization are related Control of a single electron spin may be achievable through polarized light

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Experimental setup

Technion – Israel Institute of Technology, Physics Department and Solid State Institute Method of calculation Given the numbers Ne, Nh, of electrons and holes in the QD, the many-carrier states are calculated using the Single Band Envelope Function - Full Configuration Interaction approach. The electron-hole exchange interaction is included [E. Poem et al, PRB 76, (2007)]. The lowest energy states are taken as the QD initial states prior to excitation. To simulate quasi-resonant excitation, an e-h pair in a chosen polarization is added to the initial sates, into the highest single carrier levels. The branching ratios for (non-radiative) decay from the resulting excited states to the lowest energy states of Ne+1 electrons and Nh+1 holes are calculated, allowing for 50% probability of hole spin-flip. The probabilities of radiative transitions starting from the lowest Ne+1, Nh+1 states are calculated for a chosen polarization. The results of the 2 previous stages are multiplied.