Spin redistribution due to Pauli blocking in quantum dots V. K. Kalevich, 1 M. Paillard, 2 K. V. Kavokin, 1 X. Marie, 2 A. R. Kovsh, 1 T. Amand, 2 A. E. Zhukov, 1 Yu. G. Musikhin, 1 V. M. Ustinov, 1 E. Vanelle, 2 and B. P. Zakharchenya 1 1 Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia 2 Laboratoire de Physique de la Matie `re Condense ´e, INSA-CNRS, 135 Av. de Rangueil, 31077 Toulouse Cedex, France Received 26 February 2001; published 21 June 2001 We have studied electron spin dynamics in self-organized InAs/GaAs quantum dots QD’s by time-resolved photoluminescence PL. The electron polarization of the QD discrete energy levels is determined from the circular polarization of the QD emission. When the GaAs barrier is optically pumped, a transient increase of the QD excited-state PL polarization is observed. This effect results from the spin dependence of electron energy relaxation as a consequence of the Pauli exclusion principle. A theoretical model qualitatively describ- ing the experimental results is developed. DOI: 10.1103/PhysRevB.64.045309 PACS numbers: 78.47.+p, 73.21.-b, 78.55.Cr, 78.66.Fd I. INTRODUCTION Physical phenomena due to spin polarization of charge carriers in semiconductors attract nowadays an increasing interest. 1,2 A new direction in applied physics, spintronics, 3 is aimed at the development of devices employing spin- polarized carriers. Quantum dot structures, where spatial mo- tion of carriers is frozen out by the quantum confinement, are often discussed as one of the possible basic components of such devices. 4 In that context, it presents a great interest to find experimental means to prepare and manipulate electron states with high spin polarization in QD’s. Recent years have been marked with optical investigations of spin-related effects in QD’s, both in continuous-wave 5–8 cw and time-resolved regime. 9–12 In particular, optical orientation and alignment of excitons with polarized light have been demonstrated, 5–9 and spin quantum beats in self- organized 10,12 or chemically synthesized 11 QD’s have been observed under magnetic 10,11 or electric 12 fields. In this paper, we report on the observation of a dynamical redistribution of the electron mean spin over the energy spec- trum in an ensemble of isolated QD’s, resulting in a drastic increase of spin polarization of the excited levels. This effect originates in the energy relaxation of electrons, which becomes spin dependent due to the Pauli exclusion principle if lower-lying states are filled with spin-polarized electrons. 7,8,10 The spin redistribution effect can be illustrated by the following simple example. Let us consider an ensemble of N D isolated QD’s with two electron levels each one ground state and one excited state. The electrons, photogenerated in the GaAs barrier by  + circularly polarized light, have a spin polarization equal to P e ( t =0) = P 0 =0.5 due to optical selection rules in bulk zinc-blende semiconductors: 13 among the total number N of photogenerated electrons, there are N ↓ =3 N /4 electrons with spin down and N ↑ =N /4 electrons with spin up. We assume in the following N N D and con- sider an infinite spin relaxation time. Under random capture of electrons into the QD’s, 9 N 2 /16N D dots on average will capture two spin-down electrons, and N 2 /16N D dots will capture two spin-up electrons. In the dots that have captured two electrons with the same spin one on each level, the electron transitions from the excited state to the ground state are blocked due to the Pauli principle. After a time delay longer than the interlevel energy relaxation time, all other dots will have no electrons on the upper level. The degree of electron polarization P 2 e on the upper level will then be equal to P 2 e =(9 N 2 -N 2 )/(9 N 2 +N 2 ) =0.8, which is greater than the photogenerated electron polarization P 0 =0.5. It is worth noting that this increase of electron polarization on upper levels does not imply the filling of the lower-lying states in all dots. The situation is different in coupled QD’s quantum dot clusters, where the electron from an upper level can relax to an empty lower-lying state in any of the QD’s in the cluster, so that energy relaxation does not depend on the electron spin until the majority of dots are filled with electrons having one spin projection. As a result, in coupled QD’s the electron polarization on upper levels should remain close to 0.5 while the pump density is not high enough to fill a considerable part of the QD ground states. Then the polarization should increase and can in principle become close to 1 when the energy relaxation for one of the spin projections is almost entirely blocked. This behavior is due to partial equilibrium within spin subbands, as a result of interdot transitions in coupled QD’s. Dyakonov and Perel’ 14 have first pointed out the possibility to observe the redistribution of electron spin over energy by detecting polarized PL under optical orienta- tion in bulk semiconductors. They considered independent formation of Fermi distributions in each of spin subbands under stationary optical orientation of electron spins by cw excitation. Provided the spin relaxation time of photoexcited electrons is much longer than their energy relaxation time and comparable to their lifetime, two quasi-Fermi-levels for electrons with different spin projections form in the electron ensemble. The mean spin of electrons between quasi-Fermi- levels is greater than the spin averaged over all the electrons. At low temperature the electron spin polarization within this energy range can approach 100%. We are not aware of any reliable experimental observation of this effect in three- or two-dimensional 3D or 2D systems, where it is hindered by overheating electrons under intense optical pumping required to create considerable phase-space filling. A structure with QD’s, being a system with extremely low density of electron PHYSICAL REVIEW B, VOLUME 64, 045309 0163-1829/2001/644/0453097/$20.00 ©2001 The American Physical Society 64 045309-1