State Selective Pumping Reveals Spin-Relaxation Pathways in CdSe

Letter pubs.acs.org/NanoLett

State Selective Pumping Reveals Spin-Relaxation Pathways in CdSe Quantum Dots Mark J. Fernée,†,‡ Chiara Sinito,†,‡ Philippe Tamarat,†,‡ and Brahim Lounis*,†,‡ †

Université de Bordeaux, LP2N, F-33405 Talence, France Institut d’Optique & CNRS, LP2N, F-33405 Talence, France

‡

S Supporting Information *

ABSTRACT: The band-edge exciton in elongated CdSe nanocrystals is composed of an upper and lower manifold associated with heavy and light holes in which the energy separation is sensitive to the nanocrystal shape. Using resonant photoluminescence excitation, we probe the upper heavy hole exciton manifold and find rapid relaxation to the lower light hole manifold on a 5 ps time scale. State selective excitation allows the preparation of single quantum states in this system. We used this to map the hole spin relaxation pathways between the fine structure sublevels, which have energy splittings incommensurate with either optical or acoustic phonon energies. This reveals a hitherto unexpected hole spin-relaxation channel in these materials. KEYWORDS: CdSe, single nanocrystal, PL, PLE, quantum dot, spin relaxation

S

was greater than that of the electron.18 Hole relaxation pathways are particularly interesting, as the hole can be wellconfined and isolated from the surface in modern core/shell NCs and should have negligible interaction with the nucleus,19 factors which should strongly inhibit hole spin relaxation. This warrants further study of the hole spin relaxation process in CdSe NCs. State-selective excitation is a powerful technique that has been utilized for deterministic quantum state preparation and advanced single photon sources in self-assembled quantum dots.20,21 Under pulsed excitation, state-selective excitation can isolate both the electron and hole relaxation processes in nanocrystals.10,22,23 These techniques have been used to look for inhibited exciton relaxation24,25 due to phenomenon referred to as an “optical phonon bottleneck” and have subsequently provided significant insight into energy relaxation processes between different quantum-size levels.6,9,10,23,26,27 In particular, state selective excitation has been crucial for isolating individual electron and hole relaxation processes23 and consequently identifying the role of the surface ligands in hole relaxation.9,10 In general, these techniques give no insight into spin relaxation of the respective charge carriers as there is insufficient resolution of the fine structure at an ensemble level and the pulse bandwidth is too broad to select individual fine structure levels. Nevertheless, the concept of state selective excitation can also be potentially relevant to relaxation within

pin is a fundamental quantum mechanical property that holds great promise for the storage of quantum information.1,2 Hence, spin relaxation is of considerable interest in solid-state systems as it provides the ultimate limitation for spin coherence. Quantum dots based on colloidal nanocrystals (NCs) can potentially allow facile placement of spin systems into optical2,3 and plasmonic4,5 cavities, enabling efficient photon delivery and collection. In order to consider NCs as possible spin systems, we need to understand their relaxation pathways. Energy relaxation in semiconductor nanocrystals (NCs) has been widely studied in order to gain insight into the relaxation mechanisms and dissipative processes6−10 with a view to ultimately controlling such processes.11 Such relaxation studies have only focused on relaxation between the different quantum confined energy levels defined by the carrier envelope functions. In addition, each excitonic state has an angular momentum fine structure that is determined by the crystal structure of the material. Relaxation between different fine structure states can involve angular momentum changing transitions, which can further constrain the possible relaxation pathways. Thus, studies that resolve the excitonic fine structure can potentially provide new insight into energy relaxation mechanisms. So far, spin relaxation has been studied in CdSe NCs using Faraday rotation,12,13 photon echo techniques,14 and single NC spectroscopy.15−18 At cryogenic temperatures, spin relaxation has been inferred in individual charged NCs18 and in neutral NC spectroscopy.15−17 In both cases, spin relaxation near the band-edge has been found to be slow, such that the bright state radiative rate can exceed the spin relaxation rate. For charged NCs, it was found that the hole spin relaxation rate © 2014 American Chemical Society

Received: April 18, 2014 Revised: July 16, 2014 Published: July 21, 2014 4480

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the band-edge exciton using steady-state techniques, which have sufficient resolution to probe individual fine structure states. Indeed, depending on the NC crystal structure and morphology, the band-edge manifold of (1Se, 1S3/2) states may be grouped into heavy-hole (hh, spin projection on the crystal c-axis of 3/2) and light-hole (lh, spin projection of 1/2) bands, which can be separated by tens of millielectron volts.28−30 Thus, relaxation between the hh and lh states could potentially give access to hole spin relaxation and in addition may provide a useful probe of energy relaxation just a few tens of millielectron volts above the lowest energy band-edge states, where one may expect a phonon bottleneck. In this report we use high-resolution resonant photoluminescence excitation spectroscopy (RPLE) to reveal both the upper heavy-hole and the lower light-hole manifold of states in single elongated CdSe NCs. Direct excitation of the upper heavy-hole states as well as the optical phonon sideband of a lh state is used to probe state-resolved energy relaxation. The results are analyzed using a rate equation model in order to identify specific branching ratios and ultimately shed light on the charge carrier relaxation mechanism in the NC. Our experimental setup has been described elsewhere.15,17,30 Briefly, we use commercial NCs emitting at 655 nm that consist of a CdSe core with both CdS and ZnS shell layers and have a wurtzite crystal structure (see Supporting Information). Here we make use of the sample’s inhomogeneous growth along the wurtzite crystal c-axis to select rod-shaped NCs where the light hole determines the observed band-edge spectroscopic properties.30 In fact, the spectroscopic determination of the NC morphology provides a convenient means to compare the photophysics across a wide variety of aspect ratios with NCs exhibiting the same excellent spectral stability required for such investigations. The NCs are embedded in a poly(vinyl alcohol) matrix deposited on to clean glass coverslips. The sample is mounted in a liquid helium bath magneto-optical cryostat where the low pressure helium exchange gas medium can maintain a temperature of 2 K. The experiment uses an epifluorescence microscope geometry with a high numerical aperture microscope objective contained inside the cryostat and operated in a scanning confocal mode so that individual NCs can be isolated and studied. The RPLE scans are conducted using circularly polarized excitation from a tunable cw dye laser with a ∼10 GHz mode envelope width, which sets the resolution of the technique. The laser output is stabilized by an amplitude noise eater, which maintains a uniform excitation power across the entire scan range. A sharp low-pass filter (Semrock RazorEdge, ∼10 meV transition region) is used to suppress the laser while detecting a Stokes shifted signal from the NC. In Figure 1a we show a series of photoluminescence (PL) spectra obtained from a single NC at 2 K for different applied magnetic fields. The spectra display multiple sharp zerophonon-lines associated with emission from different band-edge fine structure sublevels.30 The emergence of a low energy line with increasing applied field indicates the presence of a lowest energy dark state. These spectra have previously been assigned to rod-shaped NCs where the lowest energy band-edge fine structure originates from the light-hole valence band.30 This three-state manifold has the angular momentum assignment: 0L, 1L, and 0U with increasing energy, with the 1L state being doubly degenerate. In Figure 1b we use RPLE scans of the band-edge states (detecting the optical phonon replica, which is Stokes shifted by ∼26.8 meV) at both zero field and 6 T and

Figure 1. Identification of the band-edge fine structure. (a) A series of PL spectra obtained at 2 K revealing a lowest energy “dark” state in the presence of a magnetic field. (b) RPLE scans of the band-edge exciton taken at 2 K both with and without an applied magnetic field revealing the “dark” state at 6 T as well as Zeeman splitting of the 1L state. (Note: asterisks mark the ac1 acoustic phonon replica.)

find that the magnetic field has lifted the degeneracy of the 1L state, which has split into two states separated by ∼260 μeV. This splitting is compatible with g-factors that were previously determined for the bright state found in the heavy-hole band.17 The RPLE result also highlights the increase in spectral resolution obtained with this technique, which is approximately a factor of 3 greater than that which is possible with our PL measurements. In order to increase the signal-to-noise ratios of the states with low oscillator strength, high excitation intensities (∼30 W cm−2) were needed, which consequently saturated the strong 0U transition and enhanced the acoustic phonon replicas. The sharp acoustic phonon line labeled ac1 can also be seen at high energy side of the 1L and 0L transitions of the RPLE scans as well as at the low energy side of the PL spectra in Figure 4. This mode is approximately 300 μeV and is assigned to the axial extension mode observed in nanorods.31,32 Its energy is less than half that of the lowest energy acoustic phonon mode found in similarly sized (∼10 nm diameter) spherical NCs,18 consistent with a NC with an aspect ratio of ∼2. The lines ac2− 4 are attributed to higher energy acoustic phonon modes33 of the elongated nanocrystal. The advantage of RPLE is that it is an absorption technique that can detect higher lying energy states34,35 that are not visible in PL measurements due to rapid nonradiative relaxation. However, RPLE also includes a detection efficiency factor that can be state-dependent. This is especially true when detecting the LO phonon signal, as it has been shown that band-edge states with different oscillator strengths can exhibit different couplings to the LO phonon replica15 (see also Supporting Information). In addition the apparent peak heights can be strongly affected by spectral diffusion and so only serves as a qualitative indication of the transition oscillator strength. The detection of higher energy states is demonstrated in Figure 2a, where we combine two RPLE spectra, one recorded when 4481

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Figure 2. Light-hole and heavy-hole manifolds. (a) PLE scans of both the lower lh state manifold and the upper hh state manifold as well as the optical phonon replica region (labeled P) obtained at 2 K. (b) The evolution of the fine structure as a function of NC aspect ratio calculated for a 2.5 nm transverse radius NC of wurtzite structure. The yellow shaded region matches the observed hh/lh band separation.

scanning the laser over the band edge states while recording emission at the LO phonon band, and the second recorded by scanning the laser over the higher energy region while detecting the emission from the low lying band edge states. The RPLE signal recorded from the higher energy region is therefore enhanced by an order of magnitude and reveals a higher energy manifold of states as well as a broad complex absorption structure nominally associated with the optical phonon sideband (simultaneous creation of an exciton with an optical phonon in the NC). We associate the peak labeled P to the excitation of the 0U exciton state along with the simultaneous creation of a 26.8 meV LO phonon. The nature of the optical phonon sideband is consistent with resonances involving different optical phonons observed in recent Raman studies on CdSe NCs36,37 (see the Supporting Information). Situated approximately 20 meV from the band-edge states are two sharp resonances. The energy separation between these two resonances is ∼1.2 meV, which is close to the 1.4 meV separation of the 1L and 0U states. To understand the upper states we looked to the theoretical model of the band-edge fine structure treating elliptical perturbations.28,30 It estimates a NC with an aspect ratio of ∼2.5 (see Figure 2b), which is within the range of aspect ratios found from TEM analysis of the NCs (see Supporting Information) and consistent with the low energy acoustic phonon mode we observe in this NC. The model shows clearly two branches to the band edge exciton at high aspect ratios. Given the attribution of the lower states in Figure 1, the upper states are assigned to the heavy-hole manifold with exciton angular momenta of 1 and 2. Note that the fine structure spacings result from the electron−hole exchange interaction and are expected to be similar for the fine structure splitting in both the hh and lh manifolds28 in agreement with our observation. While the state with angular momentum 2 should be dark, we note that in colloidal NCs this state is universally observed in emission in the absence of external magnetic fields with a wide range of radiative lifetimes,38 indicative of some extrinsic coupling. We find that the upper heavy-hole manifold states are much broader than those of the light-hole manifold at the band edge. In fact the lines are fit by Lorentzian functions as shown in Figure 3. A comparison with the narrow line widths of the lower band-edge states (i.e., line widths of order 1−10 GHz15,39) suggests that the upper state line shape is lifetime limited. A full-width at half-maximum of 130 μeV corresponds to a ∼5 ps lifetime. In general, we have studied tens of single

Figure 3. Energy relaxation between the lh and the hh band edge states. (a) The states of the upper hh band with Lorentzian fits of 130 μeV full width at half-maximum (fwhm). (b) The fwhm plotted as a function of the lh−hh energy splitting for 10 individual NCs.

NCs that exhibit higher energy spectral lines in the region ∼10−20 meV above the band edge as shown in Figure 3b, and all lines are broadened similar to the data presented here (see Supporting Information), indicating this is a general phenomenon. Such broadening indicates rapid nonradiative relaxation to the lower light-hole states, which is interesting as it occurs in the phonon bottleneck regime, where the optical phonon energies40 are too large to facilitate relaxation between the hh and the lh bands. On the other hand, the 20 meV energy gap is approximately an order of magnitude greater than the low order acoustic phonon energies (only the low frequency acoustic phonon modes are strongly coupled to the exciton transitions, as indicated in Figure 1b), which makes relaxation via the emission of multiple acoustic phonons very inefficient. In addition, the fact that we observe two PL peaks separated by 1.4 meV, which is within the available acoustic phonon energies, indicates that acoustic phonon mediated relaxation is inefficient.18 Thus, the hh to lh band relaxation must be mediated by an extrinsic relaxation channel.10,11,41 This is unexpected as our NCs are extremely well passivated by multiple semiconductor layers. The quality of the surface passivation can be inferred from the stable emission intensity with fluctuations determined purely by shot noise15 and the long-term stability of the single NC spectra. Therefore, we expect surface hole traps play no role in the relaxation. However, it has been reported that the hole relaxation predominately occurs via a nonadiabatic surface relaxation9 and the presence of a semiconductor shell merely serves as a barrier to slow this relaxation.10 Here we find that hole relaxation is more than an order of magnitude slower than 4482

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Figure 4. Photoluminescence spectra obtained with state-selective pumping of PL at 2 K. Insets represent the population pathways to the luminescent states after laser excitation. The laser excites (a) the LO phonon sideband of the 0U level, (b) the 2 state, and (c) the 1U state. (d) The PL signal obtained at 2 K while pumping far above the band-edge with a 532 nm laser. (e) Illustration of the rate equation model used to determine the pumping rates. The four-level system can be effectively replaced by a two-level system (see the Supporting Information).

spectra at 2 K displaying multiple zero-phonon-lines with energy spacing greater than kBT, as seen in Figure 1. If we now consider the case of direct pumping of the |mF| = 2 hh hole state in Figure 4b, we see that the relaxation pathway does not end at the 0U state. This result alone indicates that the energy relaxation is state selective. We can understand this result based on our previous angular momentum assignments. The two state comprises an exciton with a heavy hole (spin projection of ±3/2). A hole spin flip of ±1 from this state leads to the lh exciton state ±1L with total angular momentum of ±1. Therefore, our observation is consistent with the relaxation of the hole only, leaving the electron spin unchanged. When pumping the 1U state we see in Figure 4c that the upper and lower energy emission lines have different weights compared to the LO phonon sideband pumping case of Figure 4a. The spectra indicate a dominant relaxation to the 0U state with minor relaxation to the lower 1L and 0L states. As we have established that the relaxation occurs via a hh to lh spin flip, we can exclude 1U → 1L relaxation path (which requires flipping of both electron and hole spins) and thus readily calculate the branching ratio, as 85% probability of relaxing to the 0U state and 15% probability of relaxing to the 0L state. The use of state-selective pumping provides a means for establishing the relaxation pathways between the upper hh and lower lh states. We now use this insight into analyze the offresonant pumping spectrum in Figure 4d. The relative spectral weights of the lines observed in the PL should satisfy a twolevel rate equation model16 as depicted in Figure 4e, where the A level represents the 0U state and the B level represents ±1L,

found in ligand passivated CdSe NCs. This is consistent with an increased separation between the hole (which should be well confined in the core in these NCs) and the surface. The nature of the upper states and the relaxation channel is probed further by recording the PL spectra at different laser frequencies that selectively excite the LO phonon sideband P, the 1U, and 2 states. In Figure 4 we show three PL spectra obtained at 2 K by selectively pumping the LO phonon sideband (Figure 4a) and the upper hh manifold states (Figure 4b,c). We immediately see significant modification of the spectral weights of the band edge zero-phonon-lines depending on the excitation. State-selective pumping allows us to probe individual relaxation rates. In Figure 4a we pump directly the LO phonon sideband labeled, P. In this case the excitation is exactly 1 LO phonon energy blue-shifted from the 0U level and so should exclusively excite the 0U level along with the creation of an LO phonon. In addition, the observed sharp cutoff of this LO phonon replica ensures that the excitation energy will not excite the lower states (note this technique has been used for state-selective pumping in self-assembled quantum dots20,21). It is then straightforward to derive the ratio of the radiative decay rate from the 0U state, ΓU, to the nonradiative relaxation rate to the lower states, γ0, as, ΓU/γ0 = 2.8. For these elongated nanocrystals, γ0 should provide an upper limit of both the electron and lh spin flip rate, which is notably small at this ∼meV energy splitting (ΓU−1 is of the order of 10 ns,15 which leads to a γ0−1 of the order of 30 ns). It is this slow spin relaxation at the band-edge that allows the acquisition of PL 4483

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0 L state manifold (see Supporting Information). The population rates of the levels are W and gW for levels A and B, respectively, and the radiative rates are ΓA = ΓU, ΓB = ΓL. In the low temperature/weak pump limit, we can derive the relationship γ0 = ΓA(ρ − g)/(g + 1), where ρ ∼ 2 is the ratio of the integrated signal of the lower PL spectral line to the upper one. The LO phonon sideband pumping data, which gives ΓA/ γ0 = 2.8, lead to g = 1.2. This result strongly deviates from the naive relaxation model of equal population rates, W, to all states in the lh manifold (due to randomization of charge carrier spins and phases;16,38 see also Supporting Information), which requires g = 3 because of the B-level 3-fold degeneracy. To understand this result, we consider a slight modification of the spin randomization model, where we suppose that, after absorption of a photon, the 1U and 2 hh states are initially equally populated and subsequently relax to the lower lh levels (0U, ±1L, and 0L). In this cascade model the relaxation pathways obtained previously using state-selective excitation (Figure 4b,c) lead to g ∼ 1.3, which is consistent with our data. We now consider the effect of a cascade in the lh → hh case where the spin randomization hypothesis has been previously applied.16,38 This is the case of sphere like NCs, where the upper lh states comprise 0L, 0U, and 1U and the lower hh states comprise 1L and 2 (see left side of Figure 2b). In this case, hole relaxation following ΔJ= ± 1 will relax the 0L and 0U states to the 1L state, while the 1U state will relax to the 2 state. If we use the spin randomization model for the initial population of the lh states, then state selective relaxation will result in equal population rates of the hh states as also expected from random spin population hypothesis (see Supporting Information). Thus, the spin-dependent cascade relaxation model for the (1Se,1S3/2) band-edge exciton is consistent with the data in this report as well as previous studies of the hh band, while direct random population of the lower lh states is incompatible with the data in Figure 4d. In summary, we have mapped both the heavy-hole and lighthole band-edge manifold of states in single CdSe NCs using single NC RPLE at cryogenic temperatures. We find the upper heavy-hole states are significantly broadened indicating efficient relaxation to the lower light-hole states with a 5 ps lifetime. Selectively exciting the upper heavy-hole states and monitoring the band-edge PL probes the nature of this relaxation. We find significant excitation dependence in the PL indicative of stateselective relaxation pathways, where the hh → lh relaxation process involves a hole angular momentum change of ±1. The energy relaxation comprises a regime where intrinsic phononmediated energy relaxation should be strongly inhibited. Thus, this hh → lh relaxation must be mediated by an extrinsic relaxation pathway, such as surface states and ligand-related pathways. Overall this work reveals a hole relaxation mechanism via coupling to an external spin. Such an external spin coupling provides a plausible mechanism for the universal observation of PL from the nominally dark 2 state. From a potential applications perspective, we have demonstrated selective pumping of different individual states within the band-edge. Nonresonant direct pumping should have applications for precise delivery of quanta to strongly coupled systems, such as cavity coupled NC states for efficient extraction of single photons.

Letter

ASSOCIATED CONTENT

S Supporting Information *

Description and electron microscopy characterization of the NCs used in this work. A description of how the RPLE technique was implemented. Additional RPLE data showing the upper states with a line width analysis. Additional PL and RPLE data of the optical phonon replica from different NCs. Detailed derivation of the rate equation model used in this work. Additional data consistent with the cascade model proposed in this work. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel./Fax: + 33 5 5701 7202. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Agence Nationale de la Recherche, Région Aquitaine, the European Research Council, and the Institut Universitaire de France. We thank Serguei Goupalov for fruitful discussions.

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