Long-Lived Hole Spin/Valley Polarization Probed by Kerr Rotation inMonolayer WSe2Xinlin 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 EastAvenue, 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 photolumines-cence measurements are performed on MOCVD-grownmonolayer tungsten diselenide (WSe2). We observe a surpris-ingly long-lived Kerr rotation signal (∼80 ns) at 10 K, which isattributed to spin/valley polarization of the resident holes. Thispolarization is robust to transverse magnetic field (up to 0.3 T).Wavelength-dependent measurements reveal that only excitationnear the free exciton energy generates this long-lived spin/valleypolarization.

KEYWORDS: Tungsten diselenide, Kerr rotation, photoluminescence, exciton, spin polarization

Monolayer transition metal dichalcogenides (TMDs) canbe direct bandgap semiconductors with bandgaps

located at the K/K′ points.1−3 Spatial inversion symmetrybreaking and strong spin−orbit coupling result in spin-valleyinterlocking and polarization-dependent optical selection rulesfor carriers in the K/K′ valleys, thus making valley polarizationgeneration possible through optical orientation.1,4,5 In analogywith spintronics,6 valleytronics might be realized in TMDsusing the valley index to store information. One fundamentalquestion closely related to information storage in valleytronicsis the valley polarization lifetime. Time-resolved photo-luminescence (TRPL) was used to study the valley dynamicsin TMDs, and picosecond-scale spin/valley polarizationlifetimes were observed.7−9 The TRPL signal is proportionalto the number of optically generated carriers, which decreasesover time due to recombination.10 In contrast, time-resolvedKerr rotation (TRKR), a pump−probe technique, can monitorpolarization signal that persists beyond the recombination time.Recently, polarization lifetimes on the order of severalnanoseconds 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 WSe2and examine the effects of applied magnetic field and laserexcitation energy in order to elucidate the role of spin−orbitspin stabilization in WSe2 and show that this long-lived spin/valley signal is produced at laser energies near the free excitonenergy. We demonstrate how measurements as a function ofpump−probe spatial overlap can be used to more accuratelymeasure spin/valley relaxation times that exceed the laserrepetition period.

Monolayer WSe2 samples are grown on SiO2/siliconsubstrates by metal−organic chemical vapor deposition(MOCVD),14 where tungsten hexacarbonyl, dimethyl selenideare used as precursors. A measurement of sheet conductance asa function of backgate voltage confirms that the samples are p-type. The WSe2 samples are mounted in a liquid helium flowcryostat, which is placed between the two poles of anelectromagnet. A mode-locked Ti: Sapphire laser with a pulsewidth of 3 ps and a repetition rate of 76.00 MHz (periodicity13.16 ns) is used. The laser output is separated into pump andprobe paths, which are modulated by a photoelastic modulator

(switches between + λ4

and − λ4) and an optical chopper,

respectively. The relative delay between the pump and probepulses is varied by a mechanical delay line. Spin/valleypolarization is generated by the circularly polarized (σ+/σ−)pump pulse according to the valley dependent optical selectionrules (Figure 1a)1,15,16 and detected by the Kerr rotation of theprobe pulse. The spot size of the pump and probe beams on thesample 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, andSample 2 has an average grain size of 1 μm. All the data shownin the main text are from Sample 1 and the data for Sample 2can be found in Section 6 of the Supporting Information.

Received: April 28, 2016Revised: June 29, 2016Published: July 28, 2016

Letter

pubs.acs.org/NanoLett

© 2016 American Chemical Society 5010 DOI: 10.1021/acs.nanolett.6b01727Nano Lett. 2016, 16, 5010−5014

Figure 1b shows TRKR measurements at 10 K for differenttransverse magnetic fields. Two main features are observedhere: a long-lived polarization signal and no obvious magneticfield dependence or spin precession. We will focus on the timeevolution of the polarization first and then discuss the absenceof spin precession. The polarization decay curve can be fit usinga sum of three decaying exponentials. The characteristic time ofeach decay is labeled as τ1, τ2, and τ3 (τ1 < τ2 < τ3). Most of thepolarization signal decays within τ1, which is around 6 ps. Thisfast polarization decay may come from neutral excitonrecombination9 or electron−hole exchange interactions whichcause efficient valley depolarization.17−20 τ2 is around 200 psand the physical origin of this decay might be trionrecombination. TRPL shows that the trion polarization canpersist much longer than neutral excitons.9 τ3 is around 80 ns,which far exceeds the carrier recombination time. We attributethis long-lived signal to the spin/valley polarization of residentholes. Transfer of spin polarization from photoexcited carriersto resident carriers is not unusual. For instance, in n-type GaAs,hole spins depolarize much faster than electrons, and theelectron spin polarization can exist for a long time after therecombination of photoexcited carriers.21 The transfer ofpolarization from photoexcited carriers to resident carriershappens when one type of carrier (electron or hole) has at leastpartially depolarized before recombination.13 In such situations,the spin lifetime of the other type of carrier is only limited byspin relaxation processes instead of carrier recombination. InTMDs, the electron intervalley scattering time is on the orderof several picoseconds,22−25 which is much shorter than thehole scattering time due to the smaller spin splitting in theconduction band (CB). In contrast to the electrons, hole

intravalley scattering (flips spin) is unlikely because of the largespin splitting at the valence band (VB) edge.26,27 Intervalleyscattering from K to K′ is also unlikely to happen, because thisneeds both atomic scale scatterers and magnetic defects.Theories as well as experiments show that the hole polarizationlifetime is on the order of nanoseconds.13,15,22,28

During each TRKR scan, the optics on the mechanical delayline need to be translated by ∼1 m in order to cover the delayscan range (5 ns), and this may cause the signal to change ifthere is any variation in the pump beam spot size and positionat the sample. As a result, errors will be introduced to thepolarization lifetime extracted from TRKR, especially when thelifetime is much longer than the scan range. An alternatetechnique to find the long lifetime is to compare the Kerrrotation amplitude at two delay times that span a large temporaldifference but are physically close (Supporting InformationSection 1). Delay times of −200 ps (which corresponds to12.96 ns since the previous pump pulse) and 1 ns are chosen. τ2is much shorter than 1 ns so that only the contribution fromthe long-lived component is included (the excitons and trionshave already recombined at 1 ns). The Kerr rotation signal ismeasured by scanning the position of the pump beam relativeto the probe beam on the sample (Figure 1c). Thismeasurement clearly shows that even at −200 ps delay time,there is still a large pump-induced polarization signal. Theheight of the curve at −200 ps is only slightly smaller than thatat 1 ns, indicating that most of the long-lived polarizationpersists over 13 ns. The polarization lifetime we get using thisoverlap 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 1band Supporting Information Section 6). This is in contrast tothe measurements conducted on traditional III−V semi-conductors such as GaAs21 and GaN,29 where an oscillatoryKerr rotation signal is observed at the Larmor frequency due toelectron spin precession. TMDs are known to have large VBspin splitting (Δ) due to the strong spin−orbit coupling fromthe d orbitals of the transition metal atoms and the spatialinversion asymmetry.1,5 For WSe2, the VB spin splitting isaround 400 meV.26,27,30 The spin splitting creates an effective

longitudinal magnetic field ( ∼ ∼μΔB 10

geff3

BT), which is

much larger than the applied transverse magnetic field.Therefore, the hole spins are “pinned” along this large effectivemagnetic field and have little response to the applied field. Wenote that some recent TRKR measurements on TMDs did seea small oscillatory component on top of the overall Kerrrotation signal. This small oscillatory signal was attributed tothe spin precession of localized carriers, which may not beaffected by the effective field.11,12,31 Within the signal-to-noiseratio of our measurements, we are unable to observe theoscillatory signal from localized carriers. Although in n-typeMoS2, the spin lifetime decreases rapidly in a small transversemagnetic field,11 field-dependent lifetime is not observed in ourWSe2 samples (Figure 1d) and WS2 samples.12 This may bedue 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 Kerrrotation signal at each temperature (Supporting Informationsection 3). Figure 2a shows TRKR measurements at 5, 30, and75 K. The polarization signal decays faster at highertemperature. To see this more clearly, overlap Kerr rotationmeasurements are also performed as shown in Figure 2b. It is

Figure 1. (a) Schematic band structure along with the valley opticalselection rules and electron scattering processes for monolayer WSe2.Both the conduction band and valence band spin splittings are shown.γve and γs

e 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 polarizationlifetime (τ3) measured at different magnetic fields using pump−probeoverlap Kerr rotation technique (50 K). No obvious trend in themagnetic field dependence is observed.

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evident that less polarization signal survives at −200 pscompared with 1 ns when the temperature is increased. Thepolarization lifetimes extracted from both TRKR and overlapKerr rotation measurements are shown in Figure 2c. Thedecrease of lifetime at higher temperatures may be related tophonon-assisted intervalley scattering, because the averageoccupation number of acoustic and optical phonons increases.28

Increasing the temperature should not significantly facilitatehole polarization relaxation due to spin−orbit stabilization.12Even at 100 K, we still observe a lifetime ∼10 ns. Similarphenomena have also been reported on WSe2

13 in which evenat room temperature, hole valley lifetime is still aroundhundreds of picoseconds. Further experiments such astemperature-dependent transport measurements would providemore information about the underlying relaxation mechanisms.Extensive experiments on gallium arsenide have shown that thespin relaxation time can vary by several orders of magnitudedepending on the carrier density and mobility of the sample.32

Despite the long lifetime, we are unable to performmeasurement on this long-lived hole polarization for temper-atures higher than 100 K due to the low signal-to-noise ratio.Figure 2d shows that the Kerr rotation signal decreases at high

temperatures. Note that a smaller Kerr signal at highertemperature does not necessarily mean less hole polarization.Polarization-resolved photoluminescence shows approximately40% valley polarization even at room temperature in MoS2.

7

The decrease of Kerr signal at higher temperature may comefrom absorption band edge broadening or other factors that areunrelated to the spin/valley polarization magnitude.Temperature-dependent photoluminescence (PL) measure-

ments are also done to provide more information about thislong-lived hole polarization. Besides the peak at roomtemperature, a new peak at the low energy side starts toappear at 120 K and finally becomes the dominant peak below50 K (Figure 3a). We attribute the higher energy peak to free

excitons (FX) and the lower energy one to localized excitons(LX) originating from disorder or defect effects.33 At lowtemperatures, free excitons are more likely to be trapped andbecome localized. This explains the disappearance of the FXpeak 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 tohigher energy as the temperature is decreased, which iscommonly seen in semiconductors. The peak positions can be

Figure 2. (a) TRKR measurements at different temperatures. Thevertical axis is in logarithmic scale and the curves are shifted for clarity.(b) Overlap Kerr rotation measurements with corresponding Gaussianfits at different temperatures. The black and red data points are from 1ns and −200 ps (12.96 ns) delay time, respectively. (c) Temperature-dependent polarization lifetime extracted from TRKR (red triangles)and overlap Kerr rotation measurements (black dots). (d) Temper-ature-dependent Kerr rotation amplitude. The Kerr rotationamplitudes are obtained from the overlap Kerr rotation measurementsat 1 ns delay time using the wavelengths which maximize the Kerrrotation at each temperature.

Figure 3. (a) Normalized PL spectra versus photon energy at differenttemperatures. All the spectra are measured with an excitationwavelength of 532 nm. The blue line is the fit using thetemperature-dependent semiconductor band gap formula. The redline is a guide to the eye for the localized exciton peak shift. (b) PLspectrum (black curve) and Kerr rotation amplitude (green curve)versus photon energy at 65 K. Gaussian fits for the free exciton (bluedotted line) and localized exciton PL emission (red dotted line), whichare 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 peakpositions (green squares) versus temperature. The blue line is a fitusing the band gap formula.

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fit using a standard temperature-dependent semiconductorband gap formula34

ωω= − ⟨ℏ ⟩ ℏ −

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟⎤⎦⎥⎥E T E S

k T( ) (0) coth

21gg

B

where Eg(0) is the band gap at 0 K, S is a dimensionlesscoupling constant and ⟨ℏω⟩ is an average phonon energy. Thebest fit gives Eg(0) = 1.704 eV, S = 3.5 and ⟨ℏω⟩ = 0.052 eV. Byextending the fit, we are able to determine the FX emissionenergy below 50 K (the blue line in Figure 3a,c). The LX peakfirst shifts to lower energy with decreasing temperature thenshifts back to higher energy. This abnormal behavior has beenreported on other WSe2 samples33 and InGaN/GaN quantumwells.35

In order to investigate the origin of the Kerr signal, weperform wavelength-dependent overlap Kerr rotation measure-ments at different temperatures and compare the Kerr signalpeak positions (Supporting Information Section 3) with the PLpeak 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 wedecompose the PL emission peak into the FX (Figure 3b bluedotted line) and LX (Figure 3b red dotted line) emission peaks,we find that the Kerr signal peak position agrees well with theFX peak position. There’s no Kerr signal when the laser energyis tuned close to the LX emission energy. The Kerr, FX, and LXpeak positions at different temperatures are summarized inFigure 3c. It is clear that only light with energy close to the freeexciton emission energy can generate hole polarization evenwhen 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 attemperatures below 50 K. For laser energies close to the FXemission energy, circularly polarized light generates polarizationin both the conduction and valence band (Figure 4b). Theelectrons depolarize first due to fast intervalley scatteringprocesses (Figure 4c) and the holes nonradiatively decay to thedefect states (Figure 4d). The electrons and holes thenradiatively recombine emitting light with energy smaller thanthe FX emission energy (Figure 4e). Therefore, the residentholes can stay polarized long after recombination (Figure 4f).However, when the laser energy is tuned close to the LXemission energy the holes are pumped to the defect states, andtherefore the valley dependent optical selection rules do nothold and almost no spin/valley polarization is generated.Another possibility is that very few photoexcited carriers areexcited at the LX emission energy due to the low excitationefficiency. In both cases, the holes are not polarized(Supporting Information Section 4). Thus, no Kerr rotationsignal is observed with pump energy close to the LX emissionenergy.In conclusion, we generate and observe a long-lived (∼80 ns)

hole polarization using optical orientation. A model is alsoproposed for long-lived resident hole polarization despite PLdominated by defect-assisted recombination at low temper-ature. This long-lived and field-independent spin/valley polar-ization from resident carriers may open doors for valleytronicdevices in the future.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.6b01727.

Details of finding τ3 from the Kerr rotation overlapmeasurements; fits of PL spectrum at different temper-atures; details of determining the Kerr rotation peak;TRKR scans around zero delay time; measurements onpump power dependence; TRKR data on Sample 2(PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: vsih@umich.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSX.S. and V.S. would like to acknowledge helpful discussionswith Hanan Dery. The work at the University of Michigan issupported by the Defense Threat Reduction Agency BasicResearch Award No. HDTRA 1-13-1-0013 and the NationalScience Foundation Materials Research Science and Engineer-ing Center program DMR-1120923. The work at the CornellUniversity is supported by AFOSR (FA2386-13-1-4118,FA9550-16-1-0031) and Nano Material Technology Develop-ment Program through the National Research Foundation of

Figure 4. Schematic showing the carrier dynamics for excitation closeto the FX emission energy at temperatures below 50K. (a) Somedefect states (unfilled circles) are located close to the VB edge. Beforephotoexcitation, the defect states are almost empty and the residentholes are not polarized. (b) Circularly polarized light (σ+) generatesspin-up electrons and holes in the K valley. (c) The electronsdepolarize because of fast intervalley scattering. (d) The holes in bothvalleys nonradiatively decay to the defect states (filled circles). (e) Theholes in the defect states radiatively recombine with the electrons inthe CB, emitting light at the LX emission energy. (f) The residentholes are still polarized after recombination. Thus, the long-livedpolarization signal can be observed.

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Korea (NRF) funded by the Ministry of Science, ICT, andFuture Planning (2012M3A7B4049887).

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