Letter pubs.acs.org/NanoLett
Long-Lived Hole Spin/Valley Polarization Probed by Kerr Rotation in Monolayer WSe2 Xinlin Song,† Saien Xie,‡ Kibum Kang,§ Jiwoong Park,§,∥ and Vanessa Sih*,⊥ †
Applied Physics Program, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States School of Applied and Engineering Physics and §Department of Chemistry and Chemical Biology, Cornell University, 245 East Avenue, Ithaca, New York 14853, United States ∥ Kavli Institute at Cornell for Nanoscale Science, 245 East Avenue, Ithaca, New York 14853, United States ⊥ Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States ‡
S Supporting Information *
ABSTRACT: Time-resolved Kerr rotation and photoluminescence measurements are performed on MOCVD-grown monolayer tungsten diselenide (WSe2). We observe a surprisingly long-lived Kerr rotation signal (∼80 ns) at 10 K, which is attributed to spin/valley polarization of the resident holes. This polarization is robust to transverse magnetic field (up to 0.3 T). Wavelength-dependent measurements reveal that only excitation near the free exciton energy generates this long-lived spin/valley polarization. KEYWORDS: Tungsten diselenide, Kerr rotation, photoluminescence, exciton, spin polarization
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Monolayer WSe2 samples are grown on SiO2/silicon substrates by metal−organic chemical vapor deposition (MOCVD),14 where tungsten hexacarbonyl, dimethyl selenide are used as precursors. A measurement of sheet conductance as a function of backgate voltage confirms that the samples are ptype. The WSe2 samples are mounted in a liquid helium flow cryostat, which is placed between the two poles of an electromagnet. A mode-locked Ti: Sapphire laser with a pulse width of 3 ps and a repetition rate of 76.00 MHz (periodicity 13.16 ns) is used. The laser output is separated into pump and probe paths, which are modulated by a photoelastic modulator λ λ (switches between + 4 and − 4 ) and an optical chopper, respectively. The relative delay between the pump and probe pulses is varied by a mechanical delay line. Spin/valley polarization is generated by the circularly polarized (σ+/σ−) pump pulse according to the valley dependent optical selection rules (Figure 1a)1,15,16 and detected by the Kerr rotation of the probe pulse. The spot size of the pump and probe beams on the sample is around 45 μm. We report results for two WSe2 samples. The growth temperature for Sample 1 and Sample 2 are 640 and 550 °C, respectively. Sample 1 has an average grain size of 2 μm, and Sample 2 has an average grain size of 1 μm. All the data shown in the main text are from Sample 1 and the data for Sample 2 can be found in Section 6 of the Supporting Information.
onolayer transition metal dichalcogenides (TMDs) can be direct bandgap semiconductors with bandgaps located at the K/K′ points.1−3 Spatial inversion symmetry breaking and strong spin−orbit coupling result in spin-valley interlocking and polarization-dependent optical selection rules for carriers in the K/K′ valleys, thus making valley polarization generation possible through optical orientation.1,4,5 In analogy with spintronics,6 valleytronics might be realized in TMDs using the valley index to store information. One fundamental question closely related to information storage in valleytronics is the valley polarization lifetime. Time-resolved photoluminescence (TRPL) was used to study the valley dynamics in TMDs, and picosecond-scale spin/valley polarization lifetimes were observed.7−9 The TRPL signal is proportional to the number of optically generated carriers, which decreases over time due to recombination.10 In contrast, time-resolved Kerr rotation (TRKR), a pump−probe technique, can monitor polarization signal that persists beyond the recombination time. Recently, polarization lifetimes on the order of several nanoseconds have been observed in MoS2,11 WS2,12 and WSe213 using TRKR. Here, we report an order of magnitude longer hole spin/valley polarization lifetime in monolayer WSe2 and examine the effects of applied magnetic field and laser excitation energy in order to elucidate the role of spin−orbit spin stabilization in WSe2 and show that this long-lived spin/ valley signal is produced at laser energies near the free exciton energy. We demonstrate how measurements as a function of pump−probe spatial overlap can be used to more accurately measure spin/valley relaxation times that exceed the laser repetition period. © XXXX American Chemical Society
Received: April 28, 2016 Revised: June 29, 2016
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DOI: 10.1021/acs.nanolett.6b01727 Nano Lett. XXXX, XXX, XXX−XXX
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intravalley scattering (flips spin) is unlikely because of the large spin splitting at the valence band (VB) edge.26,27 Intervalley scattering from K to K′ is also unlikely to happen, because this needs both atomic scale scatterers and magnetic defects. Theories as well as experiments show that the hole polarization lifetime is on the order of nanoseconds.13,15,22,28 During each TRKR scan, the optics on the mechanical delay line need to be translated by ∼1 m in order to cover the delay scan range (5 ns), and this may cause the signal to change if there is any variation in the pump beam spot size and position at the sample. As a result, errors will be introduced to the polarization lifetime extracted from TRKR, especially when the lifetime is much longer than the scan range. An alternate technique to find the long lifetime is to compare the Kerr rotation amplitude at two delay times that span a large temporal difference but are physically close (Supporting Information Section 1). Delay times of −200 ps (which corresponds to 12.96 ns since the previous pump pulse) and 1 ns are chosen. τ2 is much shorter than 1 ns so that only the contribution from the long-lived component is included (the excitons and trions have already recombined at 1 ns). The Kerr rotation signal is measured by scanning the position of the pump beam relative to the probe beam on the sample (Figure 1c). This measurement clearly shows that even at −200 ps delay time, there is still a large pump-induced polarization signal. The height of the curve at −200 ps is only slightly smaller than that at 1 ns, indicating that most of the long-lived polarization persists over 13 ns. The polarization lifetime we get using this overlap Kerr rotation technique is ∼90 ns (at 10 K, 0 T). The TRKR signal in our WSe2 samples does not appear to change when applying a transverse magnetic field (Figure 1b and Supporting Information Section 6). This is in contrast to the measurements conducted on traditional III−V semiconductors such as GaAs21 and GaN,29 where an oscillatory Kerr rotation signal is observed at the Larmor frequency due to electron spin precession. TMDs are known to have large VB spin splitting (Δ) due to the strong spin−orbit coupling from the d orbitals of the transition metal atoms and the spatial inversion asymmetry.1,5 For WSe2, the VB spin splitting is around 400 meV.26,27,30 The spin splitting creates an effective Δ longitudinal magnetic field (Beff ∼ gμ ∼ 103 T), which is
Figure 1. (a) Schematic band structure along with the valley optical selection rules and electron scattering processes for monolayer WSe2. Both the conduction band and valence band spin splittings are shown. γev and γes are the electron phonon-assisted intervalley scattering rate (preserves spin) and intravalley scattering rate (flips spin) respectively. (b) Degenerate pump−probe TRKR measurements at 10 K with 0, 0.1, and 0.2 T transverse magnetic field. Curves are shifted for clarity. (c) Pump and probe overlap Kerr rotation measurements at 1 ns and −200 ps (12.96 ns) delay time (10 K). (d) The long polarization lifetime (τ3) measured at different magnetic fields using pump−probe overlap Kerr rotation technique (50 K). No obvious trend in the magnetic field dependence is observed.
Figure 1b shows TRKR measurements at 10 K for different transverse magnetic fields. Two main features are observed here: a long-lived polarization signal and no obvious magnetic field dependence or spin precession. We will focus on the time evolution of the polarization first and then discuss the absence of spin precession. The polarization decay curve can be fit using a sum of three decaying exponentials. The characteristic time of each decay is labeled as τ1, τ2, and τ3 (τ1 < τ2 < τ3). Most of the polarization signal decays within τ1, which is around 6 ps. This fast polarization decay may come from neutral exciton recombination9 or electron−hole exchange interactions which cause efficient valley depolarization.17−20 τ2 is around 200 ps and the physical origin of this decay might be trion recombination. TRPL shows that the trion polarization can persist much longer than neutral excitons.9 τ3 is around 80 ns, which far exceeds the carrier recombination time. We attribute this long-lived signal to the spin/valley polarization of resident holes. Transfer of spin polarization from photoexcited carriers to resident carriers is not unusual. For instance, in n-type GaAs, hole spins depolarize much faster than electrons, and the electron spin polarization can exist for a long time after the recombination of photoexcited carriers.21 The transfer of polarization from photoexcited carriers to resident carriers happens when one type of carrier (electron or hole) has at least partially depolarized before recombination.13 In such situations, the spin lifetime of the other type of carrier is only limited by spin relaxation processes instead of carrier recombination. In TMDs, the electron intervalley scattering time is on the order of several picoseconds,22−25 which is much shorter than the hole scattering time due to the smaller spin splitting in the conduction band (CB). In contrast to the electrons, hole
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much larger than the applied transverse magnetic field. Therefore, the hole spins are “pinned” along this large effective magnetic field and have little response to the applied field. We note that some recent TRKR measurements on TMDs did see a small oscillatory component on top of the overall Kerr rotation signal. This small oscillatory signal was attributed to the spin precession of localized carriers, which may not be affected by the effective field.11,12,31 Within the signal-to-noise ratio of our measurements, we are unable to observe the oscillatory signal from localized carriers. Although in n-type MoS2, the spin lifetime decreases rapidly in a small transverse magnetic field,11 field-dependent lifetime is not observed in our WSe2 samples (Figure 1d) and WS2 samples.12 This may be due to the larger spin splittings in WSe2 and WS2 than MoS2. We also investigate the temperature dependence of the polarization signal. The laser is tuned to maximize the Kerr rotation signal at each temperature (Supporting Information section 3). Figure 2a shows TRKR measurements at 5, 30, and 75 K. The polarization signal decays faster at higher temperature. To see this more clearly, overlap Kerr rotation measurements are also performed as shown in Figure 2b. It is B
DOI: 10.1021/acs.nanolett.6b01727 Nano Lett. XXXX, XXX, XXX−XXX
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temperatures. Note that a smaller Kerr signal at higher temperature does not necessarily mean less hole polarization. Polarization-resolved photoluminescence shows approximately 40% valley polarization even at room temperature in MoS2.7 The decrease of Kerr signal at higher temperature may come from absorption band edge broadening or other factors that are unrelated to the spin/valley polarization magnitude. Temperature-dependent photoluminescence (PL) measurements are also done to provide more information about this long-lived hole polarization. Besides the peak at room temperature, a new peak at the low energy side starts to appear at 120 K and finally becomes the dominant peak below 50 K (Figure 3a). We attribute the higher energy peak to free
Figure 2. (a) TRKR measurements at different temperatures. The vertical axis is in logarithmic scale and the curves are shifted for clarity. (b) Overlap Kerr rotation measurements with corresponding Gaussian fits at different temperatures. The black and red data points are from 1 ns and −200 ps (12.96 ns) delay time, respectively. (c) Temperaturedependent polarization lifetime extracted from TRKR (red triangles) and overlap Kerr rotation measurements (black dots). (d) Temperature-dependent Kerr rotation amplitude. The Kerr rotation amplitudes are obtained from the overlap Kerr rotation measurements at 1 ns delay time using the wavelengths which maximize the Kerr rotation at each temperature.
Figure 3. (a) Normalized PL spectra versus photon energy at different temperatures. All the spectra are measured with an excitation wavelength of 532 nm. The blue line is the fit using the temperature-dependent semiconductor band gap formula. The red line is a guide to the eye for the localized exciton peak shift. (b) PL spectrum (black curve) and Kerr rotation amplitude (green curve) versus photon energy at 65 K. Gaussian fits for the free exciton (blue dotted line) and localized exciton PL emission (red dotted line), which are obtained by fitting the PL spectrum with the sum of two Gaussians, are also shown. (c) Localized exciton peak positions (red triangles), free exciton peak positions (blue dots) as well as Kerr rotation peak positions (green squares) versus temperature. The blue line is a fit using the band gap formula.
evident that less polarization signal survives at −200 ps compared with 1 ns when the temperature is increased. The polarization lifetimes extracted from both TRKR and overlap Kerr rotation measurements are shown in Figure 2c. The decrease of lifetime at higher temperatures may be related to phonon-assisted intervalley scattering, because the average occupation number of acoustic and optical phonons increases.28 Increasing the temperature should not significantly facilitate hole polarization relaxation due to spin−orbit stabilization.12 Even at 100 K, we still observe a lifetime ∼10 ns. Similar phenomena have also been reported on WSe213 in which even at room temperature, hole valley lifetime is still around hundreds of picoseconds. Further experiments such as temperature-dependent transport measurements would provide more information about the underlying relaxation mechanisms. Extensive experiments on gallium arsenide have shown that the spin relaxation time can vary by several orders of magnitude depending on the carrier density and mobility of the sample.32 Despite the long lifetime, we are unable to perform measurement on this long-lived hole polarization for temperatures higher than 100 K due to the low signal-to-noise ratio. Figure 2d shows that the Kerr rotation signal decreases at high
excitons (FX) and the lower energy one to localized excitons (LX) originating from disorder or defect effects.33 At low temperatures, free excitons are more likely to be trapped and become localized. This explains the disappearance of the FX peak and the emergence of the LX peak. Both the FX and LX peak (Supporting Information Section 2) shift with temperature. The FX peak monotonically shifts to higher energy as the temperature is decreased, which is commonly seen in semiconductors. The peak positions can be C
DOI: 10.1021/acs.nanolett.6b01727 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters fit using a standard temperature-dependent semiconductor band gap formula34 ⎡ ⎛ ℏω ⎞⎤ Eg (T ) = Eg (0) − S⟨ℏω⟩⎢coth⎜ − 1⎟⎥ ⎢⎣ ⎝ 2kBT ⎠⎥⎦
where Eg(0) is the band gap at 0 K, S is a dimensionless coupling constant and ⟨ℏω⟩ is an average phonon energy. The best fit gives Eg(0) = 1.704 eV, S = 3.5 and ⟨ℏω⟩ = 0.052 eV. By extending the fit, we are able to determine the FX emission energy below 50 K (the blue line in Figure 3a,c). The LX peak first shifts to lower energy with decreasing temperature then shifts back to higher energy. This abnormal behavior has been reported on other WSe2 samples33 and InGaN/GaN quantum wells.35 In order to investigate the origin of the Kerr signal, we perform wavelength-dependent overlap Kerr rotation measurements at different temperatures and compare the Kerr signal peak positions (Supporting Information Section 3) with the PL peak positions. Figure 3b is one typical comparison at 65 K. The mismatch between the main PL emission peak (∼1.63 eV) and the Kerr signal peak (∼1.71 eV) is obvious. However, if we decompose the PL emission peak into the FX (Figure 3b blue dotted line) and LX (Figure 3b red dotted line) emission peaks, we find that the Kerr signal peak position agrees well with the FX peak position. There’s no Kerr signal when the laser energy is tuned close to the LX emission energy. The Kerr, FX, and LX peak positions at different temperatures are summarized in Figure 3c. It is clear that only light with energy close to the free exciton emission energy can generate hole polarization even when the free exciton emission is absent at low temperature. Figure 4 depicts a model to explain the peak position mismatch between the PL emission and Kerr rotation at temperatures below 50 K. For laser energies close to the FX emission energy, circularly polarized light generates polarization in both the conduction and valence band (Figure 4b). The electrons depolarize first due to fast intervalley scattering processes (Figure 4c) and the holes nonradiatively decay to the defect states (Figure 4d). The electrons and holes then radiatively recombine emitting light with energy smaller than the FX emission energy (Figure 4e). Therefore, the resident holes can stay polarized long after recombination (Figure 4f). However, when the laser energy is tuned close to the LX emission energy the holes are pumped to the defect states, and therefore the valley dependent optical selection rules do not hold and almost no spin/valley polarization is generated. Another possibility is that very few photoexcited carriers are excited at the LX emission energy due to the low excitation efficiency. In both cases, the holes are not polarized (Supporting Information Section 4). Thus, no Kerr rotation signal is observed with pump energy close to the LX emission energy. In conclusion, we generate and observe a long-lived (∼80 ns) hole polarization using optical orientation. A model is also proposed for long-lived resident hole polarization despite PL dominated by defect-assisted recombination at low temperature. This long-lived and field-independent spin/valley polarization from resident carriers may open doors for valleytronic devices in the future.
Figure 4. Schematic showing the carrier dynamics for excitation close to the FX emission energy at temperatures below 50K. (a) Some defect states (unfilled circles) are located close to the VB edge. Before photoexcitation, the defect states are almost empty and the resident holes are not polarized. (b) Circularly polarized light (σ+) generates spin-up electrons and holes in the K valley. (c) The electrons depolarize because of fast intervalley scattering. (d) The holes in both valleys nonradiatively decay to the defect states (filled circles). (e) The holes in the defect states radiatively recombine with the electrons in the CB, emitting light at the LX emission energy. (f) The resident holes are still polarized after recombination. Thus, the long-lived polarization signal can be observed.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b01727. Details of finding τ3 from the Kerr rotation overlap measurements; fits of PL spectrum at different temperatures; details of determining the Kerr rotation peak; TRKR scans around zero delay time; measurements on pump power dependence; TRKR data on Sample 2 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS X.S. and V.S. would like to acknowledge helpful discussions with Hanan Dery. The work at the University of Michigan is supported by the Defense Threat Reduction Agency Basic Research Award No. HDTRA 1-13-1-0013 and the National Science Foundation Materials Research Science and Engineering Center program DMR-1120923. The work at the Cornell University is supported by AFOSR (FA2386-13-1-4118, FA9550-16-1-0031) and Nano Material Technology Development Program through the National Research Foundation of D
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(31) Yang, L.; Chen, W.; McCreary, K. M.; Berend, J. T.; Lou, J.; Crooker, S. A. Nano Lett. 2015, 15, 8250−8254. (32) Dzhioev, R. I.; Kavokin, K. V.; Korenev, V. L.; Lazarev, M. V.; Meltser, B. Y.; Stepanova, M. N.; Zakharchenya, B. P.; Gammon, D.; Katzer, D. S. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 245204. (33) Yan, T.; Qiao, X.; Liu, X.; Tan, P.; Zhang, X. Appl. Phys. Lett. 2014, 105, 101901. (34) O’Donnell, K. P.; Chen, X. Appl. Phys. Lett. 1991, 58, 2924− 2926. (35) Cho, Y.-H.; Gainer, G. H.; Fischer, A. J.; Song, J. J.; Keller, S.; Mishra, U. K.; DenBaars, S. P. Appl. Phys. Lett. 1998, 73, 1370−1372.
Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (2012M3A7B4049887).
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