Spin of Semiconductor Quantum Dots under Hydrostatic Pressure

Dec 15, 2009 - ... under hydrostatic pressure has been investigated by combining the ultrafast optical orientation method with the diamond-anvil cell ...
2 downloads 0 Views 2MB Size
Download PDF
pubs.acs.org/NanoLett

Spin of Semiconductor Quantum Dots under Hydrostatic Pressure Yun Tang,† Alexander F. Goncharov,‡ Viktor V. Struzhkin,‡ Russell J. Hemley,‡ and Min Ouyang*,† †

Department of Physics and Center for Nanophysics and Advanced Materials, University of Maryland, College Park, Maryland 20742 and ‡ Geophysical Laboratory, Carnegie Institution of Washington, D.C. 20015 ABSTRACT Spin coherence dynamics of semiconductor quantum dots under hydrostatic pressure has been investigated by combining the ultrafast optical orientation method with the diamond-anvil cell technique. Spin confined within quantum dots is observed to be robust up to several gigapascals, while electron and exciton Lande´ g factors show novel bistable characteristics prior to the first-order structural transition. This observation is attributed to the existence of a theoretically predicted metastable intermediate state at the nanoscale, for which there has been no previous experimental support. The results also reveal pressure enhanced fundamental exchange interactions for large-sized quantum dots with sizable anisotropy. These findings shed insight into underlying mechanisms of long-debated nanoscale solid-state transformations in semiconductors and are also crucial for the development of future quantum information processing and manipulation based on spin qubits of quantum dots. KEYWORDS spin, quantum dots, hydrostatic pressure, Landé g factors, solid-state transformation

S

scale solid-state transformations in semiconductors,1-3 and the results are also important for understanding structurespin correlations as well as engineering nanoscale structures to achieve desired spin property for the future development of spin-based quantum devices. CdSe QDs with diameters tunable from 2.5 to 7.0 nm were synthesized via a modified chemical method,8 and possessed a narrow size distribution of 4% and high crystallinity with the wurtzite structure under ambient conditions (Figure 1). These chemically synthesized QDs were originally capped/stabilized with a monolayer of surfactant, trioctylphosphine oxide, and were redissolved in 4-ethylpyridine as a pressure medium up to 10 GPa.2 Pressure was determined by the standard ruby fluorescence technique with a nonmagnetic Be-Cu diamond-anvil cell.9 A two-color timeresolved Faraday rotation (TRFR) technique was applied to measure spin coherence dynamics under pressure (Figure 1a) (see Supporting Information).10 Briefly, a circularly polarized laser beam with tunable energy is used to excite spin polarization of CdSe QDs at a selected energy level. At a delay time ∆t, a linearly polarized probe pulse with independent tunable photon energy measures the spin magnetization along the laser propagation direction by monitoring rotation of its linear polarization orientation (θ). When an in-plane magnetic field (H) is applied, the spins precess about the field direction, which leads to an oscillatory Faraday rotation at the sample-dependent Larmor frequency (vL). This process can be described by Ae-∆t/T2* cos(2πνL∆t + φ), where A is the amplitude, T2* is the transverse spin lifetime, and φ is the phase. A custom-made UV-visible spectrometer with fs- whitelight is used for the linear optical absorption measurements.

emiconductor quantum dots (QDs) are model systems to study various fundamental physics at the nanoscale, including solid-state phase transformation,1-3 as well as represent attractive building blocks for scalable solid-state implementations of quantum information processing by using spins of electrons and excitons as qubits.4 While recent progress has been achieved in understanding spins confined within QDs,5-7 crucial issues such as stability of spin states as well as the manipulation of spin and spin-orbit coupling require more work, mainly due to the experimental challenges involved. The application of hydrostatic pressure represents an important means by which to precisely tune and modify key material parameters, and thus offers a unique opportunity to explore various fundamental spin properties and interactions in QDs. Here we report the dependence of spin coherence dynamics in artificial lattice structures of semiconductor QDs measured by a new method that combines ultrafast optical orientation methods with diamond-anvil cell techniques. Spin confined within QDs is observed to be robust up to several gigapascals, while electron and exciton Lande´ g factors show novel bistable characteristics prior to the first-order structural transition. This observation is attributed to the existence of a theoretically predicted metastable intermediate state at the nanoscale, for which there has been no previous experimental support. The results further reveal pressure-enhanced fundamental exchange interactions for large-sized quantum dots with sizable anisotropy. Therefore, our findings shed light on the underlying mechanisms of long-debated nano-

* To whom correspondence should be addressed, [email protected]. Received for review: 11/9/2009 Published on Web: 12/15/2009 © 2010 American Chemical Society

358

DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

FIGURE 2. Spin coherence dynamics of 3.4 nm CdSe QDs under hydrostatic pressure. (a) Typical TRFR data at 1.2 GPa. Circle: experimental data with H ) 0.21 T. Red solid curve: theoretical fit with two Larmor precession frequencies. The inset shows FFT of TRFR data revealing two distinct Larmor frequencies (1.98 and 2.23 GHz). (b) Dependence of electron (lower) and exciton (upper) g factors on applied hydrostatic pressure, showing a novel g factor transition before the first-order structural phase transition occurred. Dashed lines are guides to the eye for the evolution of experimental g factors (red diamonds). Squares are theoretical calculations of pressure dependence of electron g factor by assuming continual lattice deformation of ambient wurtzite phase. In the calculation, the pressure dependence of Eg and R were determined from linear optical absorption measurement. Pressure dependence of Ep and ∆SO were obtained from theory prediction.26,27 The best fit of ambient g factor was obtained with a ) 1.7 eV·nm2, which was close to the accepted literature value.12

FIGURE 1. All optical spin resonance measurements of semiconductor QDs under pressure. (a) Experimental setup. (b) Linear optical absorption spectra of 3.4 nm CdSe QDs under selected hydrostatic pressure labeled by different number and color (1, 0.1 MPa; 2, 1.0 GPa; 3, 1.9 GPa; 4, 2.8 GPa; 5, 3.1 GPa; 6, 3.5 GPa; 7, 4.7 GPa; 8, 5.5 GPa; 9, 6.0 GPa). (Inset) Typical high-resolution transmission electron microscope image of CdSe QDs with wurtzite structure. Scale bar: 5 nm. The QDs manifest spherical symmetry with the aspect ratio of 1. (c) Size dependence of first-order structural transition pressure obtained from (b).

At low pressure linear absorption spectra of QD samples clearly exhibited discrete electronic states, which were in accord with previous calculations (Figure 1b).11,12 When the pressure was slowly increased to a critical value, absorption of CdSe QDs suddenly became featureless with the absorption changing continuously over a broad energy range. The featureless optical absorption structure at high pressure arises from the first-order solid-solid phase transition from wurtzite (with direct band gap) to rock-salt structure (with indirect band gap), a transformation first identified by X-ray diffraction (XRD) measurements.2 This critical pressure could be used as a reference to characterize structural phase transition as a function of QD size (Figure 1c). Qualitatively, this size dependence agreed well with previous experimental hystersis measurements and thermodynamics considerations of the transformation,1,2 and provided a cross check on the experiments reported here. © 2010 American Chemical Society

Importantly, our TRFR measurements clearly revealed spin coherence dynamics of electrons and excitons confined within CdSe QDs under pressure (Figure 2a). Two Larmor precession frequencies could be distinguished from fast Fourier transform (FFT) as well as beating pattern presented in raw TRFR data, which led to two different Lande´ g factors based on the relation

g)

hνL µBH

(detailed procedure for determining g factors from the TRFR data is available in the Supporting Information), where µB is 359

DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

to the lack of effective experimental characterization, the underlying mechanism of such a phase transition remains an unresolved issue. Furthermore, the wurtzite/zinc blende structure and rock-salt structure represent the most stable forms of most of the four- and six-coordinated binary compounds, respectively; hence understanding the transition mechanism of CdSe QDs is essential for manipulating the energetics of different semiconductor nanostructures to improve materials synthesis and to achieve desired materials functionalities and properties in a controlled manner. So far, two different mechanisms have been proposed (Figure 3b): the first is based on a continual deformation model, assuming high correlated atom motions during transformation;13-16 the second is a two-step process, in which a long-lived metastable intermediate phase with a hypothetic fivecoordinated structure exists before the first-order phase transition occurs.17-21 Even though a metastable intermediate state was suggested based on shock wave compression experiments with bulk semiconductors,22-24 direct experimental evidence of such metastable states at the nanoscale has been lacking. Instead, earlier reports of high-pressure XRD measurements of CdSe QDs leaned to support a continual deformation model because of no detectable changes of XRD peaks before first-order transition.1-3 As compared with experimental techniques based on structural characterization, our experiment provides a unique opportunity to directly measure electronic and excitonic effective g factors with a high degree of precision under pressure. This g factor probe plays a central role in gaining fundamental understanding of electronic band structure as well as interband optical processes. Thus our measurements offer a valuable alternative insight (from the viewpoint of electronic structure) for an underlying nanoscale solid-state transformation path. From perturbation theory the electron g factor of spherical QDs can be generalized in terms of fundamental band structure parameters, including size-dependent band gap Eg, the Kane matrix element Ep, and the spin-orbit splitting ∆SO6,25-27

FIGURE 3. Lande´ g factor transition at intermediate pressure. (a) QD size dependence of g factor transition pressure. (b) Schematics of two different underlying transformation mechanisms of firstorder phase transition. A five-coordinated structure (P63 mmc space group) is used to represent metastable intermediate structure in path 2.

Bohr magnet and h is Planck’s constant. Following the previous report under ambient conditions6 as well as our experimental result of size dependence of both g factors (see Figure S1 in the Supporting Information), we can assign unambiguously observed two g factors at low pressure to the electron (lower) and the exciton (higher), respectively. We further characterized in detail both the electron and exciton g factors as a function of pressure (Figure 2b). Surprisingly, a novel bistable characteristic of the g factors was clearly observed: Both the electron and exciton g factors remained stable over a specific pressure range above ambient conditions and then increased with pressure and stabilized at different values up to the onset of the rock-salt phase. This observed g factor transition was further ascertained by assigning transition pressure to the midpoint of the two bistable g factors (Figure 2b and 3a). The monotonic increase in the g factor transition pressure with decreasing QD size suggests that the transition is an intrinsic pressure-driven effect in the QDs. As compared with the Figure 1c, the observed g factor transition happens at a much lower pressure; thus it could not explicitly arise from the first-order structural transition, which has been confirmed by XRD measurements. In order to gain insight of pressure-induced evolution of g factors, the transformation path needs to be examined carefully. Due © 2010 American Chemical Society

ge(R) ) g0 -

2 3

(

Eg +

Ep∆SO

)(

a a + ∆SO Eg + 2 2 R R

)

where R is radius of the QDs and a is a fitting parameter in the simplest parabolic approximation. If the continual deformation model is correct, a smooth increase of ge factor is expected (Figure 2b), which is obviously in conflict with bistable g factor characteristics observed during the highpressure transformation. Therefore, our observed bistable g factor characteristics strongly suggest the existence of a long-lived metastable intermediate state during the transformation process, and the distinct g factors correspond to different electronic states induced by pressure. In particular, our measured g factor transient pressure range is qualitatively consistent with the ∼2 GPa pressure range of the onset of the theoretically predicted intermediate state.20 360

DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

FIGURE 4. Pressure-enhanced exchange interactions in 5.1 nm CdSe QDs. (a) Evolution of g factors with applied pressure. (b) (Left) Typical high-resolution transmission electron microscope image of a 5.1 nm CdSe QDs. Scale bar: 5 nm. The QDs manifest structural anisotropy with the aspect ratio of 1.04; (Right) Schematic of degeneracy lifting of the exciton fine band-edge structure (represented by HOMO-LUMO type energy levels) due to enhanced exchange interactions under pressure. Dashed lines are guides to the eye for the evolution of experimental g factors. (c) Dependence of TRFR amplitude on probe photon energy under three different pressures. Data were taken at fixed time delay ∆t ) 300 ps and normalized by the probe beam power. Green arrows highlight resonance peaks existing in all pressures, and red arrows highlight the appearance of new resonance peaks at higher pressure. For comparison, linear optical absorption spectra for different pressures are also present.

While the g-factor transition was observed for all the QDs we investigated (as summarized in Figure 3a), there existed subtle differences between small- and large-sized CdSe QDs: For all large-sized QDs (g5 nm in diameter) we consistently observed three g factors at higher pressure (Figure 4a; also see Figure S2 in the Supporting Information), which suggested that this observation should be an intrinsic sizerelated effect. In order to reveal such fine effect, we further investigated correlation between energy level scheme and g factors by carrying out additional spectroscopic measurements. In general, optical study of the quantum size levels is very challenging because of inhomogeneous broadening and cannot be achieved simply by linear absorption measurements (Figure 1b). In contrast, TRFR has been demonstrated to be not only a unique and sensitive experimental probe for spin coherence dynamics but also a precise spectroscopic technique for directly identifying individual exciton transitions that reveal the fine electronic energy level scheme (Figure 4b).28-30 For example, related TRFR spectroscopic study of a colloidal CdS@CdSe quantum dotquantum well system has revealed its fine energy levels, which showed consistency with kp perturbation calculations.28 Similarly, we carried out measurement of dependence of TRFR oscillation amplitude on probe energy under different pressures. In these experiments, a wavelength tunable probe with ∼5 meV energy resolution was achieved by passing the light through a monochromator after transmission through the DAC. Under ambient conditions, TRFR spectra exhibited pronounced resonances close to the ab© 2010 American Chemical Society

sorption edges that could not be seen in linear absorption spectra and could be further assigned to fine energy level transition evaluated with kp calculations (Figure 4c).28 While all the resonance peaks that appeared under ambient conditions remained as the pressure was increased, two more new resonance peaks could be immediately identified with small amplitude and became more pronounced at higher pressure, which agreed well with the increased number of g factors within the same pressure range. In contrast, we carried out the same measurements for small-sized QDs and such a control experiment showed no new resonance peaks during the entire transformation path. Therefore, we attributed our observed increased number of g factors to the pressure-enhanced fundamental exchange interactions in large-sized QDs,31 based on following facts: (i) For chemically synthesized QDs it has been shown that while smaller size QDs possessed very symmetrical spherical shape, larger size QDs started manifesting anisotropy.8 This can also be clearly seen by comparing high-resolution TEM images in the Figures 1b and 4b and in Figure S2 in Supporting Information, which shows the increase of aspect ratio of QDs with the size. Under hydrostatic pressure, the aspect ratio can be significantly enhanced due to different compression ratios along different crystal axis. (ii) The evolution of initially 8-fold degenerate ground state in a wurtzite spherical QD could be obtained from theoretical analysis of fine band-edge exciton structure when electronhole exchange interactions, crystal field. and anisotropy effects were considered (Figure 4b).6,32 As a result, crystal 361

DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

(3)

field splitting and electron-hole exchange interactions would be significantly augmented in the more anisotropic QDs due to stronger confinement,11 thus leading to energy level degeneracy lifting and the g factors splitting. (iii) The correlation between energy level splitting and the increased number of g factors of large sized quantum dots at high pressure was indeed clearly observed in the Figure 4c. In summary, investigations of quantum confined spin coherence dynamics of semiconductor QDs under pressure reveal that the spin of semicnoductor QDs is very robust up to ∼2 GPa. This observation is important for understanding the stability of spin qubits of QDs in the future quantum information processing devices. In contrast to former studies of nanoscale solid-state transformation by XRD and linear optical absorption, our new combinatory technique by using TRFR and diamond-anvil cell high-pressure technique together provides a unique insight into the transformation process from the viewpoint of electronic state property changes. A surprising pressure-driven g-factor transition was observed along the transformation path that could be attributed to the theoretically predicted metastable intermediate state not been explicitly observed yet at the nanoscale. This finding marks an important step toward deep understanding of the underlying mechanism of related long debated nanoscale solid-state transformation. Furthermore, the current study reveals pressure-enhanced fundamental fine exchange interactions that should provide deepened understanding necessary for future manipulation of spin states by interfacial/surface strain layer fabrication.33,34

(4)

(5) (6) (7) (8) (9)

(10)

(11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25)

Acknowledgment. We gratefully acknowledge funding from an NSF CAREER award (DMR-0547194), ONR YIP award (N000140710787), Beckman YIP grant (0609259093), NSF MRSEC seed fund, NSF/EAR (EAR-0711358), DOE/BES (DE-FG02-02ER45955) for supporting the high pressure measurements, NSF/DMR (DMR 0805056), CDAC (DE-FC5208NA28554), and the Balzan Foundation.

(26) (27) (28)

Supporting Information Available. Experimental methods and supporting figures (Figures S1 and S2). This material is available free of charge via the Internet at http://pubs. acs.org.

(29) (30) (31)

REFERENCES AND NOTES

(33)

(1) (2)

(34)

(32)

Tolbert, S. H.; Alivisatos, A. P. Science 1994, 265, 373–376. Tolbert, S. H.; Alivisatos, A. P. J. Chem. Phys. 1994, 102, 4642– 4656.

© 2010 American Chemical Society

362

Wickham, J. N.; Herhold, A. B.; Alivisatos, A. P. Phys. Rev. Lett. 2000, 84, 923–926. Burkard, G.; Loss, D. In Semiconductor Spintronics and Quantum Computation; Awschalom, D. D., Samarth, N., Loss, D., Eds.; Springer-Verlag: Berlin, Germany, 2002; pp 229-276. Wong, C. Y.; Kim, J.; Sreekumari Nair, P.; Nagy, M. C.; Scholes, G. D. J.Phys.Chem.C 2009, 113, 795–811. Gupta, J. A.; Awschalom, D. D.; Efros, Al. L.; Rodina, A. V. Phys. Rev. B. 2002, 66, 125307. Ouyang, M.; Awschalom, D. D. Science 2003, 301, 1074–1078. Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706–8715. Hemley, R. J.; Mao, H. K. In High-Pressure Phenomena, Proceedings of the International School of Physics, “Enrico Fermi” Course CXLVII, (eds Hemley, R. J., Chlarottl, G. L., Bernasconi, M., Ulivi, L., Eds.; IOS Press: Amsterdam, 2002; pp 3-40. Awschalom, D. D.; Samarth, N. In Semiconductor Spintronics and Quantum Computation; Awschalom, D. D., Samarth, N., Loss, D., Eds.; Springer-Verlag: Berlin, Germany, 2002; pp 147-194. Efros, Al. L.; Rosen, M. Annu. Rev. Mater. Sci. 2000, 30, 475–521. Efros, Al. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. Phys. Rev. B 1996, 54, 4843–4856. Limpijumnong, S.; Jungthawan, S. Phys. Rev. B 2004, 70, No. 054104. Sowa, H. Acta Crystallogr., Sect. A 2005, 61, 325–330. Zahn, D.; Grin, Y.; Leoni, S. Phys. Rev. B 2005, 72, No. 064110. Wilson, M.; Hutchinson, F.; Madden, P. A. Phys. Rev. B 2002, 65, No. 094109. Catti, M. Phys. Rev. B 2002, 65, 224115. Grunwald, M.; Rabani, E.; Dellago, C. Phys. Rev. Lett. 2006, 96, 255701. Limpijumnong, S.; Lambrecht, W. R. L. Phys. Rev. B 2001, 63, 104103. Miao, M. S.; Lambrecht, W. R. L. Phys. Rev. Lett. 2005, 94, 225501. Shimojo, F.; Kodiyalam, S.; Ebbsjo, I.; Kalla, R. K.; Nakano, A.; Vashishta, P. Phys. Rev. B 2004, 70, 184111. Knudson, M. D.; Gupta, Y. M. J. Appl. Phys. 2002, 91, 9561–9571. Sharma, S. M.; Gupta, Y. M. Phys. Rev. B 1998, 58, 5964–5971. Tang, Z. P.; Gupta, Y. M. J. Appl. Phys. 1997, 81, 7203–7212. Kiselev, A. A.; Ivchenko, E. L.; Rossler, U. Phys. Rev. B 1998, 58, 16353–16359. Kapustina, A. B.; Petrov, B. V.; Rodina, A. V.; Seisyan, R. P. Phys. Solid State 2000, 42, 1242–1252. Li, J. B.; Li, G.-H.; Xia, J.-B.; Zhang, J.-B.; Lin, Y.; Xiao, X.-R. J. Phys.: Condens. Matter 2001, 13, 2033–2043. Berezovsky, J.; Ouyang, M.; Meier, F.; Awschalom, D. D.; Battaglla, D.; Peng, X. Phys. Rev. B 2005, 71, 081309(R). Schrier, J.; Whaley, K. B. Phys. Rev. B 2003, 67, 235301. Meier, F.; Awschalom, D. D. Phys. Rev. B 2005, 71, 205315. Nahalkova, P.; Sprinzl, D.; Maly, P.; Nemec, P.; Gladilin, V. N.; Devreese, J. T. Phys. Rev. B 2007, 75, 113306. Fu, H. X.; Wang, L. W.; Zunger, A. Phys. Rev. B 1999, 59, 5568– 5574. Kato, Y.; Myers, R. C.; Gossard, A. C.; Awschalom, D. D. Nature 2004, 427, 50–53. Smith, A. M.; Mohs, A. M.; Nie, S. Nat. Nanotechnol. 2009, 4, 56– 63.

DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362