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Valley-polarized exciton dynamics in a 2D semiconductor heterostructure

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Science  12 Feb 2016:
Vol. 351, Issue 6274, pp. 688-691
DOI: 10.1126/science.aac7820

Stacking to prolong valley lifetime

In the material MoSe2, which, like graphene, has a two-dimensional honeycomb crystal lattice, the electronic structure has two “valleys.” Electrons can be distinguished by the valley they reside in, making them act as potential information carriers. However, electrons easily lose this information by scattering into the other valley. Rivera et al. placed single layers of MoSe2 and WSe2 on top of each other and shone circularly polarized light on the structure. The light caused excitons—pairs of electrons and holes—to form so that the hole and electron came from the same valley but different layers. The valley-specific character of such excitons persisted far longer than would be possible in a single layer of either material.

Science, this issue p. 688

Abstract

Heterostructures comprising different monolayer semiconductors provide an attractive setting for fundamental science and device technologies, such as in the emerging field of valleytronics. We realized valley-specific interlayer excitons in monolayer WSe2-MoSe2 vertical heterostructures. We created interlayer exciton spin-valley polarization by means of circularly polarized optical pumping and determined a valley lifetime of 40 nanoseconds. This long-lived polarization enables the visualization of the expansion of a valley-polarized exciton cloud over several micrometers. The spatial pattern of the polarization evolves into a ring with increasing exciton density, a manifestation of valley exciton exchange interactions. Our work introduces van der Waals heterostructures as a promising platform from which to study valley exciton physics.

Van der Waals heterostructures of two-dimensional (2D) materials provide an exciting platform for engineering artificial material systems with distinct properties (1). A beautiful example is the demonstration of the Hofstadter butterfly physics in moiré superlattice structures composed of graphene and hexagonal boron nitride (24). As the library of 2D crystals is explored further, the range of possible new phenomena in condensed matter physics becomes ever more diverse. For example, heterostructures of 2D semiconductors [namely, transition metal dichalcogenide monolayers (MX2)] have been assembled with type-II band alignment (58), in which electrons and holes energetically favor different layers (Fig. 1A). These heterostructures form atomically thin p-n junctions that can be used for photon-energy harvesting (915) and host interlayer excitons (XI), with the Coulomb-bound electron and hole located in different monolayers (1417). This species of exciton has a lifetime far exceeding those in monolayer MX2, and the vertical separation of holes and electrons entails a permanent out-of-plane electric dipole moment, providing an optical means to pump interlayer electric polarization and facilitating electrical control of interlayer excitons (17).

Fig. 1 Interlayer exciton spin-valley polarization in MoSe2-WSe2 heterostructures.

(A) Side view of MoSe2-WSe2 heterostructure device. Boxed region depicts the interlayer exciton, with holes (h+) and electrons (e) located in WSe2 and MoSe2, respectively. (B) Optical image of device, with WSe2 on top of MoSe2. Scale bar, 2 μm. (C) Circular polarization–resolved PL spectra of the interlayer exciton showing the generation of strong valley polarization. (D) Illustration of the Dirac points in the hexagonal Brillouin zone of a MoSe2-WSe2 heterobilayer, with small twisting angle. The +K (red) and −K (blue) valleys at the conduction band minimum (in MoSe2) and valence band maximum (in WSe2) are nearly aligned in momentum space. (E) Schematic of the interlayer exciton in the +K valley. First, σ+ circularly polarized light (black wavy lines) excites intralayer excitons in the +KM and +KW valleys. Fast interlayer charge hopping (blue dotted lines) forms the interlayer exciton in the +K valley. The optical selection rules in the +KW and +KM valleys produce co-polarized PL.

The interlayer excitons in 2D heterostructures are similar to spatially indirect excitons in III-V quantum wells (1822). In both systems, the electron-hole wave function overlap is reduced in the out-of-plane direction, suppressing the magnitude of exciton oscillator strength and the electron-hole exchange interaction. This leads to greatly enhanced population and spin lifetimes for spatially indirect excitons as compared with their direct exciton counterparts.

MX2 heterostructures possess several features distinct from quantum well systems. First, the monolayers’ band edges are at doubly degenerate corners of the hexagonal Brillouin zone, so XI has an internal degree of freedom specified by the combination of electron and hole valley indices (23). Second, the twist angle between the crystal axes of constituent monolayers leads to a displacement of the conduction and valence band edges in momentum space, making the XI dark—momentum indirect—at its minimum energy and bright only at finite center-of-mass velocities. The location of the XI light cones depends on the twist angle between the monolayers, allowing for control over the optoelectronic properties (2426), such as the dipole strength and interlayer exciton lifetime (27). Third, the constituent MX2 monolayers exhibit valley-contrasting physical properties such as spin-valley locking, optical selection rules (2830), and Berry curvature (23). The inheritance of valley physics in twisted MX2 heterostructures is predicted to give rise to previously unknown optical and transport properties of XI (27), allowing the possibility of excitonic optoelectronic circuits with valley functionalities and providing a platform for investigating excitonic superfluidity and condensation (31).

We observed long valley lifetime and valley drift-diffusion of XI in MoSe2-WSe2 heterostructures with small twist angles. Our devices consist of a pair of exfoliated monolayers of WSe2 and MoSe2, which are stacked by means of dry transfer (32) on a 285-nm insulating layer of SiO2 on a silicon substrate. We used standard electron beam lithography techniques to fabricate metallic contacts (V/Au) on the heterostructure, and the silicon substrate functions as a global backgate, as shown in Fig. 1A (33). The optical brightness of the XI depends sensitively on the relative alignment of the two constituent monolayers. Theory shows that for twist angles near zero or 60°, there exist light cones at small kinematic momenta in which the XI can directly interconvert with photons (27). In such heterostructures, the XI can radiatively recombine after scattering into these light cones through, for example, exciton-phonon or exciton-exciton interactions (27). In our study, we focused on this type of heterostructure. To fabricate such samples, we identified the armchair axes of individual monolayers by means of polarization-resolved second-harmonic generation and then aligned these axes (fig. S1). This yields heterostructures with twist angles near zero or 60° (33). As such, the XI can be observed in photoluminescence (PL), even at room temperature (fig. S2). All data in the main text are taken at a temperature of 30 K from the device shown in the optical microscope image in Fig. 1B, with WSe2 stacked on MoSe2, and the excitation laser energy in resonance with the A exciton of WSe2 (1.72 eV).

We first performed polarization-resolved PL at zero gate voltage (Vg = 0 V). We applied circularly polarized continuous-wave laser excitation and separately detected the right circular (σ+) and left circular (σ) PL. The σ+ (black) and σ (red) components of the XI PL under circularly polarized excitation are shown in Fig. 1C. These results show that XI emission is strongly copolarized with the incident light. Denoting the degree of polarization by Embedded Image, where I± is the intensity of the σ± PL components, we observed Embedded Image. Similar results were obtained from several other samples (fig. S3). We also performed measurements in the linear basis, which do not show appreciable polarization (fig. S4).

The observation of circularly polarized PL demonstrates that the XI can retain memory of the excitation light helicity, which is a consequence of the valley optical selection rules in 2D heterostructures (27). In the following, we discuss the generation of valley polarization in heterostructures near AA-like stacking (twist angle near 0°) (Fig. 1D), but similar conclusions can be drawn for heterostructures near AB-like stacking (twist angle near 60°) (fig. S5) (33). The valley configuration of XI is specified by the valley indices of its electron and hole. With the spin-valley locking in monolayer MX2, a universal assignment of the valley index is applicable in the twisted heterostructures, and here we denote the valley with electron spin up as +K and spin down as −K in both layers. First, σ+ excitation creates valley-polarized intralayer excitons in the +KW valley in WSe2 and +KM valley in MoSe2. Next, charge carriers relax to the heterostructure band edges through interlayer charge transfer on subpicosecond time scales (11, 15) to form XI. Because of the large momentum difference, interlayer hopping between +KW and −KM valleys is strongly suppressed. Conversely, the +KW and +KM valleys have small momentum mismatch, and the spin-conserving interlayer hopping between these valleys becomes the dominant relaxation channel. Therefore, the σ+ excitation leads to valley-polarized XI (Fig. 1E). The situation for σ excitation can be obtained through time reversal. The radiative recombination of the valley-polarized XI is facilitated by the interlayer coupling, which allows emission of photons that are co-polarized with the excitation source (27).

We found that the degree of XI valley polarization can be electrically controlled by the gate. Shown in Fig. 2A are polarization-resolved PL spectra at selected Vg under σ+ excitation with ~50-ps laser pulses. There is a strong gate dependence of the valley polarization, which is greatest at +60 V and highly suppressed at −60 V (the full data set is provided in fig. S6). In Fig. 2B, we show the decay of co-polarized (Fig. 2B, black) and cross-polarized (Fig. 2B, red) interlayer exciton PL, as well as the degree of polarization (Fig. 2B, blue), at the same Vg values as in Fig. 2A (the full data set is provided in fig. S7). The valley polarization lifetime increases with Vg, reaching 39 ± 2 ns at +60 V, as determined by fitting a single exponential decay. We also measured long valley lifetimes in heterostructures with the opposite stacking order (MoSe2 on WSe2) (fig. S8).

Fig. 2 Gate-tunable interlayer exciton valley polarization and lifetime.

All plots are for σ+ pulsed laser excitation with co-polarized and cross-polarized PL shown in black and red, respectively. (A) Polarization-resolved interlayer exciton PL at selected gate voltages. (B) Time-resolved interlayer exciton PL at selected gate voltages. The blue curve (right axis) shows the decay of valley polarization. Solid lines are single exponential fits to valley polarization decay, with lifetimes of 39 ± 2, 10 ± 1, and 5 ± 2 ns for gate voltages of +60, 0, and −60 V, respectively.

These measurements imply a strong suppression of intervalley scattering for the XI and a valley lifetime several orders of magnitude longer than that of intralayer excitons in monolayers, in which valley depolarization occurs on picosecond time scales (3436). Our measurement also shows that the initial PL polarization of XI is ~40% at +60 V. The imperfect initial valley polarization of XI is likely due to valley depolarization of intralayer excitons in the constituent monolayers, which mediate the XI formation. Because the XI is dark at the minimum of the energy dispersion (27), caused by the finite twisting angle and slight lattice mismatch between the two layers, it effectively provides a reservoir from which the XI are scattered into the light cones and luminesce. The momentum-indirect nature of XI is supported by temperature-dependent measurements, which show enhanced lifetime at low temperature (fig. S9). This complicated exciton-light coupling is likely responsible for the subtle but intriguing features in Fig. 2B, such as the increase of PL lifetime accompanying the decrease of valley polarization lifetime. However, future studies are required to gain a clear understanding of the microscopic mechanism for the observed gate-dependent PL dynamics of the XI.

The long valley lifetime of the XI allows visualization of their lateral drift and diffusion. A sequence of spatial maps of the XI PL polarization under pulsed excitation (40 MHz repetition rate) at Vg = 60 V is displayed in Fig. 3A for selected average excitation powers. The spatial pattern of ρ shows the evolution of a ring with a diameter that increases with excitation intensity (the full data set is available in fig. S10). The pattern of polarization stands in contrast to the spatial distribution of the emission. The polarization-resolved PL intensity spatial maps are shown in Fig. 3B at 20 μW, where both σ+ and σ PL components display an approximately Gaussian profile centered at the excitation spot. For direct comparison of the different spatial profiles, Fig. 3C gives the average PL intensity and ρ as a function of the distance from the beam center for the 40 μW case. The data show the drift-diffusion of σ+ (Fig. 3C, black) and σ (Fig. 3C, red) polarized excitons away from the laser spot (0.7 μm full-width at half maximum) (Fig. 3C, dashed line) as well as the ring of larger ρ (Fig. 3C, blue), demonstrating the striking difference between the spatial distribution of polarization and the total density of XI.

Fig. 3 Drift-diffusion of valley-polarized interlayer exciton gas.

All plots are for σ+ pulsed laser excitation. (A) Spatial map of valley polarization under 1 to 60 μW excitation. Sample outline is shown in white overlay. Scale bar, 2 μm. (B) Spatial maps of σ+ (left) and σ (right) interlayer exciton PL normalized intensity under 20 μW excitation. (C) Polarization-resolved spatial profiles of σ+ (black) and σ (red) components of interlayer exciton PL under 40 μW excitation. The spatial distribution of valley polarization is shown in blue, and the laser excitation profile is shown in gray. Line cuts are radially averaged through the excitation center, and curves are added as guides to the eye.

One possible explanation for the observed polarization ring is density-dependent intervalley scattering. However, consideration of the valley polarization as a function of excitation intensity suggests otherwise (fig. S11). Rather, the observed spatial patterns in the valley polarization can be understood as manifestations of valley-dependent many-body interactions in the dense interlayer exciton gas (33). The spin-valley polarized XI, which possess out-of-plane dipoles, interact through dipole-dipole and exchange interactions, both of which are repulsive. Because of the small interlayer separation of ~7 Å, we estimate that the exchange interaction is stronger than the dipole-dipole repulsion (33). Because the exchange interactions are appreciable only between excitons of the same valley species (33), in a cloud of valley-polarized interlayer excitons the majority valley excitons experience stronger mutually repulsive force (fig. S13A), leading to more rapid expansion than that of the minority valley excitons (fig. S13B). On the other hand, the density gradient of excitons will also give rise to diffusion, which is valley-independent and does not produce a ring pattern. Therefore, the relative strength of the diffusion and valley-dependent drift controls the pattern of the spatial polarization. If the interlayer exciton density is large enough that the valley-dependent repulsive interaction dominates the expansion of the exciton gas, higher valley polarization can appear away from the excitation center (fig. S15). Indeed, a pronounced ring in the polarization is generated at sufficiently high excitation intensity, as seen in Fig. 3A.

A temperature difference between the majority and minority XI could, in principle, cause them to expand at different speeds. However, under excitation by polarized laser pulse, the minority excitons are created at the excitation spot through intervalley relaxation. Because the relaxation of this internal degree of freedom does not change the kinetic energy of the exciton, the majority and minority XI are expected to have the same initial temperature before the expansion of the exciton cloud. This precludes valley-dependent temperature as a driving force for the ring formation.

Supplementary Materials

www.sciencemag.org/content/351/6274/688/suppl/DC1

Materials and Methods

Figs. S1 to S15

References (3745)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
Acknowledgments: We thank D. Cobden and F. Wang for helpful discussion. This work is mainly supported by the U.S. Department of Energy (DOE), Basic Energy Sciences (BES), Materials Sciences and Engineering Division (DE-SC0008145 and SC0012509). The spectroscopy work is partially supported by NSF-EFRI-1433496. H.Y. and W.Y. were supported by the Croucher Foundation (Croucher Innovation Award), and the Research Grants Counciland University Grants Committee of Hong Kong (HKU17305914P, HKU9/CRF/13G, AoE/P-04/08). J.Y. and D.G.M. were supported by the DOE, BES, Materials Sciences and Engineering Division. X.X. acknowledges a Cottrell Scholar Award and support from the State of Washington–funded Clean Energy Institute. Device fabrication was performed at the University of Washington Microfabrication Facility and NSF-funded Nanotech User Facility. Data described in this paper are presented in the supplementary materials and are available upon request. X.X. and W.Y. conceived and supervised the project. P.R. and K.L.S. fabricated the samples and performed the experiments, assisted by J.R.S. P.R., K.L.S., and X.X. analyzed data. H.Y. and W.Y. provided theoretical support and performed the simulation. J.Y. and D.G.M. synthesized and characterized the bulk crystal. P.R., K.L.S., X.X., W.Y., and H.Y. cowrote the paper. All authors discussed the results.
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