J. Phys. Chem. B 2006, 110, 25371-25382
25371
Mechanism and Origin of Exciton Spin Relaxation in CdSe Nanorods† Jeongho Kim, Cathy Y. Wong, P. Sreekumari Nair, Karolina P. Fritz, Sandeep Kumar, and Gregory D. Scholes* Lash Miller Chemical Laboratories, Center for Quantum Information and Quantum Control, and Institute for Optical Sciences, UniVersity of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada ReceiVed: July 14, 2006; In Final Form: September 1, 2006
The dynamics of exciton spin relaxation in CdSe nanorods of various sizes and shapes are measured by an ultrafast transient polarization grating technique. The measurement of the third-order transient grating (3-TG) signal utilizing linear cross-polarized pump pulses enables us to monitor the history of spin relaxation among the bright exciton states with a total angular momentum of F ) (1. From the measured exciton spin relaxation dynamics, it is found that the effective mechanism of exciton spin relaxation is sensitive to the size of the nanorod. Most of the measured cross-polarized 3-TG signals show single-exponential spin relaxation dynamics, while biexponential spin relaxation dynamics are observed in the nanorod of the largest diameter. This analysis suggests that a direct exciton spin flip process between the bright exciton states with F ) (1 is the dominant spin relaxation mechanism in small nanocrystals, and an indirect spin flip via the dark states with F ) (2 contributes as the size of the nanocrystal increases. This idea is examined by simulations of 3-TG signals with a kinetic model for exciton spin relaxation considering the states in the exciton fine structure. Also, it is revealed that the rate of exciton spin relaxation has a strong correlation with the diameter, d, of the nanorod, scaled by the power law of 1/d4, rather than other shape parameters such as length, volume, or aspect ratio.
I. Introduction Colloidal semiconductor nanocrystals, or quantum dots (QDs), have been intensively investigated owing to their size-dependent optical properties1-10 and their potential for applications ranging from optical and electronic nanodevices11-13 to biological probes.14 Strong quantum confinement in three dimensions leads to discrete electronic states as in atoms; the density and energy of the electronic states can be easily tuned by adjusting the material composition, size, and shape of the nanocrystal. Advances in spintronics and quantum computation have inspired the prospect of using these well-defined electronic spin states of QDs as a means of manipulating and storing quantum information.15,16 Spin orientation can be transferred in the exciton states of suitably oriented QDs by optical excitation of exciton states with a particular total angular momentum. However, interactions of QDs with their environment result in a loss of coherence of the optically excited spin states, leading to the erasure of any carefully prepared quantum information. Although exciton spin states are not of central importance to mainstream schemes for quantum computation, it is of fundamental interest to determine the exciton spin relaxation rate in semiconductor QDs and to elucidate the mechanisms governing exciton spin relaxation. This paper is concerned with measuring exciton spin relaxation dynamics in quantum-confined semiconductor nanocrystals using an ultrafast nonlinear spectroscopic technique. From the measured spin relaxation dynamics, the effective mechanisms of exciton spin relaxation in colloidal QDs are examined, and †
Part of the special issue “Arthur J. Nozik Festschrift”. * Author to whom correspondence should be addressed. E-mail: gscholes@ chem.utoronto.ca.
the scaling of exciton spin relaxation with the size and shape of nanocrystals is elucidated. A QD consists of hundreds of unit cells in a nanometer-sized crystal. Photoexcitation creates a collective excited state, a nanoscale exciton, spanning the nanocrystal.17 That excited state is described in terms of single excitation configurations whereby an electron can be promoted from a 4-fold degenerate valence band to the doubly degenerate conduction band.4,18,19 Owing to the electron-hole exchange interaction, these configurations are mixed to produce an exciton fine structure.4 The lowest exciton fine structure, spanning only tens of meV, consists of eight states identified by their total angular momentum (F), as shown in Figure 1. Among these states, the four states with F ) +1 or F ) -1 are photoexcited according to selection rules for the absorption of left or right circularly polarized light, respectively.20,21 Exciton spin orientation is obtained by optical pumping to either F ) +1 or F ) -1 exciton states, whereby the photon angular momentum of the circularly polarized light is transferred to the QD exciton states.20,21 Exciton spin orientation relaxes via spin flips between the exciton fine structure states. This leads to equilibration among the populations of the F ) +1 and F ) -1 states, which is termed exciton spin relaxation. Exciton spin relaxation is derived from a weak interaction between the two bright exciton states, usually attributed to the nonanalytic, or long-range, part of the electron-hole exchange interaction.22-24 In comparison to the significant effort made to investigate the exchange splitting between the F ) (1 and F ) (2 states,25-28 little work has been devoted to studying the hyperfine interaction between the F ) (1 states. At low temperature, this interaction is thought to be seen as a spectral fine structure splitting between the two bright states in the
10.1021/jp0644816 CCC: $33.50 © 2006 American Chemical Society Published on Web 10/10/2006
25372 J. Phys. Chem. B, Vol. 110, No. 50, 2006
Figure 1. Absorption spectrum of CdSe quantum dots with a mean diameter of 4.3 nm. Each of the absorption features is split into a fine structure. The lowest energy exciton band, 1S3/2-1Se, consists of eight states: two states with F ) 0, four states with F ) (1, and two states with F ) (2. Bright states are shown as solid lines, while dark states are shown as dashed lines. The ordering of the fine structure states shown is that for quantum dots of spherical shape. For nanorods, the F ) 0 states may be lowered, and their splitting may be diminished.
presence of extremely high magnetic field and has been attributed to shape anisotropy of the QD.29,30 Such an assignment is questionable since no evidence for significant shape anisotropy is found in electron microscopy studies of colloidal QDs.31,32 For the samples investigated in the present work, we have clearly established the absence of oblate nanocrystals.33 Quantum beats resulting from interference between the two bright states have been observed in the time-resolved photoluminescence34,35 and pump-probe measurements of QDs.36 We suggest that the strength of this small interaction in the QD excitons can be quantified by the rate of exciton spin relaxation. This provides an alternative to direct measurement of the fine structure splitting, which is difficult as it is obscured by spectral inhomogeneity. Instead, the interaction between the F ) (1 states can be detected in the time domain via measurements of the exciton spin relaxation rate.37-39 There have been several studies investigating aspects of the spin relaxation dynamics of quantum wells and QDs.40-43 Pump-probe measurements utilizing circularly polarized light as well as cross-polarized transient grating measurements using linearly polarized light have determined the exciton spin relaxation time in InAs/GaAs quantum wells to be hundreds of picoseconds at 10 K and tens of picoseconds at room temperature.40,44 Meanwhile, from circularly polarized pump-probe measurements of CdSe QDs embedded in a glass matrix, the spin relaxation time at 10 K was determined to be as short as sub-picosecond to several picoseconds.45,46 A measurement of photoluminescence polarization anisotropy for single selfassembled InAs/GaAs QDs revealed that the longitudinal exciton spin relaxation time was short (
