Quantum-Confined Stark Effect of Individual Defects in a van der

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Quantum-confined Stark effect of individual defects in a van der Waals heterostructure Chitraleema Chakraborty, Kenneth Matthew Goodfellow, Sajal Dhara, Anthony Yoshimura, Vincent Meunier, and Nick Vamivakas Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04889 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 8, 2017

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Quantum-confined Stark effect of individual defects in a van der Waals heterostructure Chitraleema Chakraborty,∗,†,‡ Kenneth M. Goodfellow,¶,‡ Sajal Dhara,¶,‡ Anthony Yoshimura,§ Vincent Meunier,§ and A. Nick Vamivakas∗,¶,k,†,‡ †Materials Science, University of Rochester, Rochester, NY 14627, USA ‡Center for Coherence and Quantum Optics, University of Rochester, Rochester, NY 14627, USA ¶Institute of Optics, University of Rochester, Rochester, NY 14627, USA §Department of Physics, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA kDepartment of Physics, University of Rochester, Rochester, NY 14627, USA E-mail: [email protected]; [email protected]

Abstract The optical properties of atomically thin semiconductor materials have been widely studied since the isolation of monolayer transition metal dichalcogenides (TMDCs). They have rich opto-electronic properties owing to their large direct bandgap, the interplay between the spin and the valley degree of freedom of charge carriers, and the recently discovered localized excitonic states giving rise to single photon emission. In this letter, we study the quantum-confined Stark effect of these localized emitters present near the edges of monolayer tungsten diselenide (WSe2 ). By carefully designing sequences of metallic (graphene), insulating (hexagonal boron nitride) and semiconducting (WSe2 ) two-dimensional materials, we fabricate a van der Waals heterostructure field effect device with WSe2 hosting quantum emitters that is responsive to external

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static electric field applied to the device. A very efficient spectral tunability up to 21 meV is demonstrated. Further, evaluation of the spectral shift in the photoluminescence signal as a function of the applied voltage enables us to extract the polarizability volume (up to 2000 Å3 ) as well as information on the dipole moment of an individual emitter. The Stark shift can be further modulated on application of an external magnetic field, where we observe a flip in the sign of dipole moment possibly due to rearrangement of the position of electron and hole wavefunctions within the emitter.

Keywords Quantum confined Stark effect, Monolayer tungsten diselenide, Defects, van der Waal’s heterostructure, Single photon emitter, Transition metal dichalcogenide Optically active semiconductor defects and quantum dots have gained attention in recent years for applications ranging from high-resolution metrology and optoelectronics to quantum information science. 1–5 From the perspective of quantum information science these materials are robust sources of quantum light and can efficiently interface spins with photons. 6 Recently, it has been discovered that the atomically thin semiconductors, in addition to their remarkable photo-physical properties, 7–9 also support quantum emitters at low temperatures in monolayer form and at the interfaces between monolayer and thicker flakes. 10–16 Although these excitons trapped in defects possess many desirable characteristics, there are many open questions concerning the origin of these defects. Further, the extent to which their electrical and optical properties can be tailored is still unknown. Controlling the excitonic wavefunction is a key step to understanding quantum physics and realizing devices with single emitters in these semiconductors. An externally applied electric or magnetic field is normally applied to manipulate the wavefunctions in a single emitter. We leverage the quantum-confined Stark effect to realize high-resolution voltage controlled optical spectroscopy demonstrating the tunablility of the electronic and optical properties of the defects embedded in a van der Waals heterosructure. 2


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Van der Waals heterostructures 17 are an emerging nano-optoelectronics device architecture enabling a wide variety of device functionality based on stacking two-dimensional materials. 18,19 In this work the monolayer WSe2 is incorporated in a heterostructure where it is encapsulated in between hexagonal boron nitride (h-BN) and placed between electricallycontacted few-layer graphene flakes both on top and bottom of the device (see Fig. 1b). With this device we are able to apply a vertical electric field to the defects and demonstrate quantum-confined Stark effect (QCSE). The physical origin of QCSE is in the separation of phototgenerated charges, creating a dipole that opposes the externally applied electric field. Here we study the permanent dipole moment arising due to spatial separation of electron and hole wavefunctions in an exciton trapped within a defect, and polarizability, which decides the extent to which an applied electric field can pull the electron-hole pair apart. Both of the parameters estimate the sensitivity of exciton energy to an applied field. If the polarizability is large in an emitter, its energy can be tuned over a wide range with moderate electric field; therefore, it is lucrative to have large polarizabilities for nanomaterial device applications involving single photon sources and detectors. We utilize QCSE and quantify the wide range of dipole moments and polarizabilities values from several defect emissions. Further, we also demonstrate that the dipole moment of the emitter can be inverted on application of a static magnetic field perpendicular to the flake. Thus, this provides an alternative pathway to control the charge distribution within the emitter and tune the electron-hole interaction. We anticipate this demonstration of the QCSE of defects in a van der Waals heterostructure will benefit their future study and application much like indium arsenide quantum dots. 20 Figure 1a displays the schematic ordering of the device. The flakes were mechanically exfoliated and stacked vertically using a PDMS-based all dry transfer method 21 onto prepatterned Cr/Au electrodes on a Si/SiO2 substrate. The few layer graphene (FLG) flakes as the outermost layers serve as semi-transparent conductive electrodes. Although not single layer graphene, the flakes are still thin enough to transmit a significant amount of signal from the underlying emitters. Qualitatively similar behavior has been seen on using graphene or

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graphite as electrode material. 22 The large bandgap h-BN layers serve as tunneling barriers. Further, the h-BN layers also separate the WSe2 housing the single emitters from the FLG to minimize quenching of the emitted signal. 23,24 Figure 1b displays an optical micrograph of the device with the dashed white box outlining the heterojunction region as illustrated in the schematic of Fig. 1a. The sample was characterized at low temperature in an attoDRY-1000 cryostat at 4K equipped with a confocal microscope. The input light source used for photoluminescence (PL) studies was a continuous wave MOPA laser at 675 nm wavelength which was focused on the sample using a 0.82 numerical aperture objective. The same objective was used to collect the light emitted from sample. The signal was then directed to a spectrometer with a liquid nitrogen-cooled charge coupled device (CCD) array. An exemplary PL spectrum is shown in Fig. 1c. Apparent from the image are spectral lines from several emitters in the WSe2 . These defects emit at smaller energies than the 2D exciton transition of WSe2 , which is at 1.75 eV at 4 K. A zoom in of the spectral region highlighted with the grey box is shown in the inset of Fig. 1c demonstrating linewidths of the order of hundreds of µeV. Correlating the spectroscopic data with density functional theory calculations one likely class of defect match a subset of the optical transition energies observed from these emitters (Figure S1). The I-V graph of the device showing diode-like character is shown in Fig. 1d. For the following spectroscopic studies, the spatial regions of the sample exhibiting the sharp PL emission were first identified as sources of single photon emitters through second order autocorrelation measurements (Figure S2). Then, PL was recorded at these locations as a function of applied voltage. Figure 2a,c displays two exemplary spectral maps as the applied voltage is swept. Clear in the PL spectra is a rich variety of spectral responses exhibited by the emitting centers most likely due to different structure and size of the emitters. Such spectral shifts are a manifestation of the QCSE in defects present in 2D materials when assembled into this type of heterostructure device. In our earlier device 13 where the TMDC was directly contacted with the electrode and the back silicon contact was used to gate the

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device, slight blue shift of the charged delocalized excitons was observed likely due to band filling effects. However, PL energy shift of the localized excitons was not observed in such backgated device assembly. When sweeping the voltage on the device from negative to positive direction, we observe that along with a spectral shift there is a modulation of the linewidth and PL intensity from the emission lines. The data in Fig. 2b, and Fig. 2d illustrates this effect for the transitions identified by the red box in the adjacent spectral maps (see figure S3 for additional data sets). As the voltage is swept from negative to positive, the line width decreases with a corresponding increase in the PL intensity. This suggests a decrease in non-radiative processes such as tunneling. The spectral shift and linewidth modulation due to the external bias are distinctive features of the QCSE. Such observations reflect the buildup of an internal electric field or dipole that opposes the externally applied field also observed earlier with other confined excitonic systems. 25 To verify the observed shifts are due to the changing applied voltage bias and not due to random spectral shifts it was confirmed the PL spectral wandering was at most 150 µeV (Figure S4), which is much less than the voltage-controlled shift. The spectroscopic utility of the QCSE is that it reveals the exciton’s built in dipole moment and polarizability and these can be found by fitting the PL emission energy (E) to the following equation 1 E = E0 − µF − αF 2 2

(1)

where E0 is the zero-field transition energy, F is the local electric field acting at the defect, and µ and α are the dipole moment and polarizability, respectively, between the ground and excited states. Similarly to an approach followed previously, 26 F is calculated from the applied voltage (V) by the Lorentz local field approximation, F = V (ǫ + 2)/3/t, where ǫ is the dielectric constant and t is the thickness for the surrounding h-BN environment. Our devices are approximately 30 nm thick, and the dielectric constant of h-BN is taken to be 3. 27 6


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Figure 3a presents the optical transition energy as a function of applied voltage taken from a defect exhibiting a linear Stark shift. We have observed a giant energy shift of 21 meV from this emitter which is comparable to Stark shifts obtained from InAs/GaAs quantum dots in a heterostructure device. 28 About 15 percent of the studied defects show a Stark shift within this order of magnitude. The dipole moment (µ) of this emitter is calculated to be -2.4 D, where 1 D = 3.33 × 10−30 C·m. Predominently linear Stark effects have been observed from about 31 percent of the emitters. This kind of behavior is expected from defects which lack a center of symmetry. Figure 3b shows a defect with a strong linear and quadratic component; the polarizability volume is α=1592 Å3 . The polarizability volume is the polarizability divided by a factor of 4πǫ0 . The changes in polarizability are expected to be of the order of the defect center volume. 26 Among the defects exhibiting Stark shift, 50 percent demonstrated a combination of linear and quadratic shifts (see figure S5 for statistical analysis). The rest shows an asymmetric shift centered about zero. Such emitters exhibit different magnitude of dipole moment and polarizabilities for either direction of electric field (Figure S6). An important observation made possible by the QCSE is that almost all of the studied emitters have a built-in dipole moment. This is evidenced from the contribution from the linear component in Eq. (1). The nonzero shift at zero electric field demonstrates a finite built-in dipole moment that has magnitude that varies from 0.15 D to 8.5 D. For comparison a nitrogen vacancy (NV) defect center has dipole moment distribution between -1.5 D to 1.5 D. 26 From the dipole moment values we determine that the electron-hole separation within the emitter ranges from 3 pm to 177 pm. Next, we calculated the distribution of total shift in energy (△E=Emax -Emin ) per unit voltage change (△V=V(Emax )-V(Emin )) for several defects and plotted them in Fig. 3c. In Fig. 3c and d, the magnitude of the shift per unit voltage and hence the dipole moment obtained from fitting increases with decreasing energy (increasing wavelength). Also the polarizability volume (Fig. 3e) increases with decreasing energy. This reflects the fact that the defects emitting at lower energy (longer wavelength) would have a larger volume than a defect emitting at higher energy (shorter wavelength).

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As a consequence, the confinement is less pronounced and applied electric fields are more effective at displacing the electron and hole wavefunctions resulting in larger QCSE (see figure S7 for an extended discussion). Moreover, in fig. 3f, we also see that the polarizability volume (α) and dipole moment (µ) are correlated and present a nearly linear relationship. This suggests that the built-in field among the several emitters is roughly constant as by classical definition of dipole moment, µ = α.F, where F is the built-in field. Such correlations have been also observed in InAs/GaAs quantum dots and have been attributed to a roughly constant lateral extent of the excitons irrespective of the quantum dots. 29 However, details of the lateral excitonic confinement is not well understood for the case of these defects and requires further study. Finally we studied the effect of a magnetic field perpendicular to the plane of the heterostructure (Faraday geometry). First the Zeeman effect was studied at zero electric field which showed an increase in the splitting of the doublet features, consistent with previous results from magneto-optical spectroscopy. 10–13 The g-factors for several emitters are calculated to be ∼ 8 (see figure S8). For each magnetic field, we study the Stark shift of the doublet as a function of the applied electric field. Both the peaks of the doublet exhibit similar Stark effect. In Fig. 4a, the Stark shift for different magnetic fields is plotted for the lower energy peak of the doublet for clarity. Figure 4b shows the peak energies extracted at zero electric field. From the linear and quadratic dependence of the Stark shift, the dipole moment (Fig. 4c) and polarizability (Fig. 4d) are extracted from the fits. At zero magnetic field, the emitter has a positive dipole moment (electron-hole separation) value of 0.04 D (0.8 pm) which then decreases and becomes negative with the maximum value of -0.2 D (4 pm) at magnetic field of 7 T. Along with a change of an order of magnitude, a flip in the sign of the dipole moment was also observed as the magnetic field increased from zero. However, the polarizability of the emitter retained the same order of magnitude with magnetic field. This effect has been attributed to the altering of the confinement potential of the electrons and holes in the quantum dot. 30 Magnetic field can induce carrier redistribution in the quantum

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emitters which can lead to changes in the permanent dipole moment of the emitter and hence the orientation of the dipole with respect to the electric field. Thus, this has shown another pathway of controlling the charge distribution in the defect. In summary, we have explored the different trends of quantum-confined Stark effect on single defects in atomically thin WSe2 . Based on the varied linear and quadratic nature it is clear that atomically thin WSe2 supports different types of optically active defects. The van der Waals heterostructure field effect type devices has allowed efficient control of the electronic resonances and provided insight into the defect’s optical properties. Application of an external magnetic field can alter the QCSE by manipulating the alignment of electronhole wavefunctions. This has been demonstarted through the inverion of dipole moment as a function of magnetic field. This device concept can be used in future to resonantly tune the transition of an emitting center for strongly interacting with another local emitter 31,32 or a cavity mode. 33 Devices capable of producing an in-plane electric field may help to reveal more information about properties like defect orientation. Future work utilizing polarizationresolved methods along with voltage controlled spectroscopy will allow for the understanding of the interaction between the WSe2 defects and WSe2 excitons, paving the way for new devices based on confined valleytronics. Further more, precise manipulation of the fine structure splitting from the doublets within such heterostructure devices can also be very useful for solid state quantum information processing, such as, polarization entangled photon pair generation. 34

Acknowledgement This work was supported by NSF EFRI EFMA-1542707, NSF CAREER DMR 1553788, AFOSR FA9550-16-1-0020 and University of Rochester University Research Award.

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Supporting Information Available The supplementary information provides the following: Density functional theory predictions, intensity autocorrelation, symmetric variation of peak width and intensity of a defect displaying a quadratic Stark shift, spectral diffusion versus Stark shift, statistics of different varieties of Stark shift, variety of Stark shift trends from different defects, energy shift with applied voltage for defects in different spectral range, magneto-optical studies. This material is available free of charge via the Internet at http://pubs.acs.org/.

Competing financial interests The authors declare no competing financial interests.

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