Highly Valley-Polarized Singlet and Triplet Interlayer Excitons in van der Waals Heterostructure

TL;DR

This paper demonstrates highly valley-polarized interlayer excitons in van der Waals heterostructures, revealing mechanisms for prolonged valley polarization and potential for valleytronic device applications.

Contribution

It reports the first observation of singlet and triplet interlayer excitons with over 80% valley polarization in WSe2/MoSe2 heterobilayers, clarifying valley depolarization mechanisms.

Findings

Over 80% valley polarization in interlayer excitons

Identification of direct band-gap exciton transition

Ultrafast charge separation and suppressed valley depolarization

Abstract

Two-dimensional semiconductors feature valleytronics phenomena due to locking of the spin and momentum valley of the electrons. However, the valley polarization is intrinsically limited in monolayer crystals by the fast intervalley electron-hole exchange. Hetero-bilayer crystals have been shown to have a longer exciton lifetime and valley depolarization time. But the reported valley polarization was low; the valley selection rules and mechanisms of valley depolarization remains controversial. Here, we report singlet and brightened triplet interlayer excitons both with over 80% valley polarizations, cross- and co-polarized with the pump laser, respectively. This is achieved in WSe2/MoSe2 hetero-bilayers with precise momentum valley alignment and narrow emission linewidth. The high valley polarizations allow us to identify the band minima in a hetero-structure and con_rm unambiguously the direct band-gap exciton transition, ultrafast charge separation, strongly suppressed valley depolarization. Our results pave the way for using semiconductor heterobilayers to control valley selection rules for valleytronic applications.

Equations

$$I_S/I_T=({\tau }_T/{\tau }_S)e^{(-\Delta E/k_{B}T)},$$

$$\rho =\frac{{\rho }_0}{1+2\frac{{\tau }_r}{{\tau }_v}}=(87.6\%\pm 7.9\%){\rho }_0.$$

Full text

Introduction

Monolayer transition metal dichalcogenide crystals (TMDCs) feature strong intrinsic spin orbital coupling (SOC) and broken inversion symmetry. Consequently, excitons from opposite momentum valleys couple with circularly polarized lights with opposite helicities mak_control_2012 ; xiao_coupled_2012 , enabling novel valleytronic phenomena and applications zhang_electrically_2014 ; wang_colloquium_2018 . However, strong inter-valley scattering due to the electron hole (e-h) exchange interaction leads to rapid valley depolarization on a picosecond scale yu_dirac_2014 ; glazov_exciton_2014 ; wang_valley_2014 ; lagarde_carrier_2014 ; zhu_exciton_2014 , posing intrinsic limits on valley polarization (VP) of monolayer excitons. Alternatively, interlayer excitons in hetero-bilayers may enable high VP since the e-h exchange interaction becomes suppressed due to reduced electron-hole wavefunction (fig. 1a-b) rivera_interlayer_2018 ; jin_ultrafast_2018 ; mak_opportunities_2018 . Recent theoretical work also suggests the possibility to control the exciton states and valley selection rules through moiré superlattices in hetero-bilayers yu_moire_2017 ; wu_theory_2018 . However, the reported VP of interlayer excitons has been low, comparable to that of intralayer ones and varying between 10$\%$ to 35$\%$, rivera_valley-polarized_2016 ; miller_long-lived_2017 ; hanbicki_double_2018 ; ciarrocchi_polarization_2019 ; tran_moire_2018 . Inconsistent valley selection rules and different mechanisms for the low VP have been proposed, such as slow charge separation rivera_valley-polarized_2016 , formation of indirect bandgap transitions and compromised optical selection rules even in rotationally aligned bilayers hanbicki_double_2018 ; ciarrocchi_polarization_2019 , and mixing among different mini-bands in a moiré lattice tran_moire_2018 . In many of these works, the interlayer exciton emission shows an inhomogeneous broadening of 20-50 meV, which may have masked the valley selection rules of individual exciton states and yielded inconsistent and controversial results. (see the Supplementary materials)

In this work, using rotationally aligned WSe2/MoSe2 hetero-bilayers with hexagon-Boron Nitride (hBN) encapsulation, we observe narrow linewidth of 6 meV, thereby resolving spin singlet and brightened spin triplet excitons with very high VPs over 80%, in opposite helicities. Compared to previous work rivera_valley-polarized_2016 ; miller_long-lived_2017 ; hanbicki_double_2018 ; ciarrocchi_polarization_2019 ; tran_moire_2018 ; seyler_signatures_2018 , the high VP enables us to identify ambiguously the $H_{h}^{h}$ atomic registry as the exciton band minimum with a direct-bandgap transition, where the triplet exciton, which is dark in monolayers, became bright and forms the interlayer exciton ground state. The high VP also confirms the preservation of valley selection rules, ultrafast charge transfer and suppressed intervalley scattering in hetero-bilayers. These results pave the way for using heterostructures to control spin and charge dynamics and manipulate the optical selection rules .

Results

An optical image of the hBN-encapsulated WSe2/MoSe2 hetero-bilayer is shown in fig. 2a. The twist angle between WSe2 and MoSe2 is measured to be 58.7∘ $\pm$0.7∘ by angle-dependence of the second harmonic generation from the two monolayers and from the bilayer jiang_valley_2014 ; hsu_second_2014 (see Supplementary Materials for details). The intra-layer and inter-layer exciton resonances are clearly identified in reflection contrast and photoluminescence (PL) measurements (fig. 2b). The absence of interlayer excitons in the reflectance contrast spectrum is expected because of smaller oscillator strengths due to the reduced e-h spatial overlap. In PL, however, the intralayer exciton emission is quenched while the interlayer excitons is much brighter. This observation suggests fast separation of the electron and hole into the two stacked monolayers compared to the intralayer exciton recombination. It also confirms the two monolayer are aligned close to (multiples of) $60^{\circ}$, so that the momentum mismatch between electron and hole is small nayak_probing_2017 . We can still observe weak intralayer exciton emission from MoSe2, suggesting slower hole transfer between the two layers.

Importantly, the linewidth of the interlayer exciton emission is only about 6 meV, showing greatly reduced inhomogeneous broadening thanks to encapsulation, which enables us to resolve individual exciton transitions. In contrast, in hetero-bilayers without hBN encapsulation and with a larger linewidth of 40 meV, VP of the interlayer exciton emission remained less than $35\%$; the helicity varied from sample to sample rather than reflecting the any underlying individual transitions (see Supplemental Figure 2).

We further examine the properties of the interlayer excitons and their dependence on the intralayer excitons via PL excitation spectroscopy. We scan a continuous-wave excitation laser with $\sigma^{+}$ circular polarization across the WSe2 and MoSe2 intralayer exciton resonances, while monitoring the interlayer exciton emission with co-circular ($\sigma^{+}/\sigma^{+}$) and counter-circular ($\sigma^{+}/\sigma^{-}$) polarizations, as shown in the left and right columns, respectively, in fig. 3a.

The data clearly show two interlayer exciton states with opposite and high VPs: a strong emission peak at 1.400 eV co-polarized with the pump, label as the T-state (bottom row), and a much weaker emission peak at 1.425 eV, cross-polarized with the pumped, label as the S-state (top row). Both states show significantly enhanced emission intensities and VPs as the excitation wavelength coincide with the WSe2 and MoSe2 intralayer exciton resonances (fig. 3a and fig. 4a), which confirms that T and S states are interlayer excitons with VPs inherited from the intralayer excitations. The two states are separated by 25 meV, corresponding to the MoSe2 conduction band splitting associated with SOC larentis_large_2018 ; liu_electronic_2015 , which suggests that the higher-energy S-state is the bright singlet interlayer exciton, while the lower-energy T-state is the brightened triplet interlayer exciton (fig. 1b,c).

To understand the intensity difference between the S-state and T-state, and further confirm their origin, we measure the temperature dependence of the emission from 5 K to 150 K with a $\sigma^{+}$ excitation laser at 1.72 eV. The spectrum is shown in supplementary material. The resonance energies of both states redshift as temperature increases, which are well described by standard temperature dependence of semiconductor bandgap: $E_{g}(T)=E_{g}(0)-S\hbar\omega[coth(\hbar\omega/2k_{B}T-1)]$, where $E_{g}(0)$ is the exciton resonance energy at T=0 K, S is the dimensionless coupling constant, and $\hbar\omega$ is the average phonon energyodonnell_temperature_1991 . From the fits, we extract for triplet and (singlet) state, the $E_{g}(0)=1.400\pm 0.001(1.425\pm 0.001)eV$, $S=1.9\pm 0.3(2.2\pm 0.2)$, $\hbar\omega=15.3\pm 3.1meV$ for both. The separation $\Delta E$ between the two states stays consistently between 22 meV and 25 meV (inset of fig. 3b). With a constant $\Delta E$, the population in the two states should follow the Boltzman distribution of the population at equilibrium; the ratio of their total emission intensities $I_{S}/I_{T}$ is then given by:

[TABLE]

where $\tau_{S,R}$ is the decay time of the S- and T-state. The equation eq. 1 fits the data very well. From the fit, we obtain $\Delta E=24.1$ meV$\pm 3.6$  meV, consistent with the measured S- and T-state separation as well as the conduction band splitting of MoSe2 larentis_large_2018 ; liu_electronic_2015 . The fitted ratio $\tau_{T}/\tau_{S}=14.1\pm 4.7$ suggests the singlet state recombines much faster than the triplet state, also consistent with the calculation yu_brightened_2018 .

To understand the VPs of the singlet and triplet exciton emission, we analyze the optical selection rules for the heterostructure, as illustrated in fig. 1. As the two monolayers with a lattice mismatch of $\delta a$ are stacked together with a $60^{\circ}$ twist angle, a moiré superlattice is formed with a period of $a/\delta_{a}$ (fig. 1a). The atoms in the two monolayers are displaced from each other except at the three special positions in the moiré super-cell, as illustrated in fig. 1a. At these points, the atomic registry recovers the three fold rotation symmetry, and therefore, the VPs are restored for the excitonic transitions. The three points also correspond to potential extrema in the superlattice potential, as was predicted by density function theory (DFT) calculation and confirmed by the scanning tunneling spectroscopy (STM) in MoS2/WSe2 hetero-bilayers wu_theory_2018 ; yu_moire_2017 ; zhang_interlayer_2017 .

At the $H_{h}^{h}$ registry (fig. 1a), the exciton singlet (triplet) state couples to circularly polarized light with the opposite (same) helicity as that of the intralayer exciton in the same valley yu_brightened_2018 , which fully agrees with our observation. At the $H_{h}^{X}$ and $H_{h}^{M}$ registries, the singlet and triplet excitons couple to light with either the opposite helicity than as observed or with an out-of-plane polarization. The measured high VP suggests the emission comes from excitons localized at the $H_{h}^{h}$ registry. The relatively high T-state emission intensity compared to the S-state or intralayer excitons suggests that the $H_{h}^{h}$ registry corresponds to the potential minimum in the moiré lattice.

The high VPs and their dependence on the excitation wavelength also shed light on the charge and spin relaxation processes in the heterostructure. We first analyze more closely the VP of the interlayer excitons. The VP depends sensitively on the excitation energy. As shown in fig. 4a, the S- and T-state, exhibiting positive and negative helicity respectively, both reaching maximum absolute values of VP of $0.8$ when the excitation laser is resonant with the WSe2 intralayer exciton energy.

With the pump fixed at the WSe2 intralayer exciton resonance, we measure the interlayer exciton VP under both $\sigma^{+}$ (red lines) and $\sigma^{-}$ (black lines) polarized pumping (fig. 4b). With both pump polarizations, we measure bright co-polarized T-state emission and weaker cross-polarized S-state emission, both with the absolute values of VP up to $0.8$. These pronounced features including two interlayer exciton states with alternate helicities and high VP, are consistently observed across the whole sample, confirming the high uniformity of the heterostructure (see Supplementary Material). Similar results are also reproduced in a few other high quality MoSe2/WSe2 hetero-bilayers (see Supplementary Material).

The very high VP measured is possible only if we have a high intralayer VP that is well preserved by the interlayer excitons. Preserving the intralayer VP requires rapid relaxation from intralayer excitons to the interlayer exciton states at the high symmetry points, and slow valley depolarization of the intervalley excitons compared to their recombination time. As illustrated in fig. 1b, resonantly excited WSe2 intralayer excitons have a high initial VP. Before they can recombine or scatter to the opposite valley on the pico-second time scale, the conduction band electrons rapidly transfer to lower energy states in the overlapping MoSe2 layer, conserving spin and momentum hong_ultrafast_2014 ; schaibley_directional_2016 ; jin_ultrafast_2018 , followed by energy relaxation to the band edge. The valence band hole is already at the band edge and stays in WSe2. Once the electron and hole are separated into two layers, the exchange interaction and therefore the valley-depolarization is suppressed. The electrons can thermalize to the lower conduction band with flipped spins. This process can happen efficiently in heterobilayers because of the conduction-band spin hybridization in the absence of the mirror symmetry yu_brightened_2018 . The electrons and holes, both in the same valley, form spin singlet and triplet states at moiré potential minima at the $H_{h}^{h}$ registries and radiatively recombine, emitting light with VP inherited from intravalley excitons.

The interlayer exciton VP is lower when pumped at the MoSe2 exciton resonance. It is expected due to a lower initial intralayer exciton VP in MoSe2 wang_polarization_2015 ; macneill_breaking_2015 . The formation of the interlayer excitons may also be slower as it requires both inter-valley scattering and flipping of the electron spin (see illustration in fig. 1c).

To compare the intervalley exciton depolarization time with the recombination time, we perform polarization resolved and time-resolved PL using a femto-second pulsed excitation laser resonant with WSe2 intralayer exciton. As shown in fig. 4c, fitting the data with single exponential function, we observe a short PL decay time $\tau_{r}=2.3\pm 0.3$ ns, but a much longer valley depolarization time $\tau_{v}=32.5\pm 4.1$ ns. The VP $\rho$ of the integrated PL can be related to the initial VP $\rho_{0}$ by lagarde_carrier_2014 ; wang_valley_2014 :

[TABLE]

Therefore $87.6\%$ of the initial VP is retained for interlayer excitons. The measured VP of $81.3\%\pm 4.9\%$ suggests an initial $\rho_{0}^{inter}=92.8\%\pm 8.9\%$ for the interlayer excitons. Assuming a near-perfect initial VP of $\rho_{0}^{intra}$ for the resonantly pumped WSe2 excitons, substituting $\rho_{0}^{inter}$ and $\rho_{0}^{intra}$ into eq. 2, we deduce that the initial charge separation takes place more than ten times faster than the intralayer exciton valley depolarization rate.

Conclusions

In summary, we observe emission from two interlayer exciton states with very high VPs and opposite helicities in WSe2/MoSe2 hetero-bilayers with a $60^{\circ}$ twist angle. The high VP and short lifetimes confirm they are direct bandgap excitons as opposed to indirect ones between the $Q$ and $\Gamma$ valleys ciarrocchi_polarization_2019 ; hanbicki_double_2018 . We identify the two exciton states as spin singlet and triplet excitons localized at the $H^{h}_{h}$ atomic registry based on their helicities yu_brightened_2018 , energy separation and temperature dependence of the emission intensities. The relative oscillator strengths of the two states are also obtained from the temperature dependence, which is consistent with the singlet and triplet assignment yu_brightened_2018 rather than two minibands in a moiré lattice wu_theory_2018 ; yu_moire_2017 . We are able to identify and measure highly valley-polarized singlet and tripilet excitons thanks to the very small inhomogeneous broadening of about 6 meV with hBN encapsulation. This is in sharp contrast to other reports in the literature with an inhomogeneous linewidth of 20-50 meV rivera_valley-polarized_2016 ; miller_long-lived_2017 ; tran_moire_2018 and VPs below 35% when different exciton states cannot be clearly resolved.

The high VPs show rapid electron transfer between the two monolayers at timescales an order of magnitude shorter than the WSe2 intralayer exciton depolarization time, and a long interlayer exciton valley depolarization time compared to the recombination time. A valley depolarization time of about 33 ns is measured, suggesting strongly suppressed inter-valley exchange interactions thanks to both electron-hole separation into the two monolayers and discretized spin singlet and triplet states. The VP in these heterobilayers can be altered by using different twist angles and materials and can be further controlled by electric fields or strain yu_moire_2017 . A heterostructure moiré lattice may enable further control of spin orbital coupling and open doors to other novel topological states.

Materials and Methods

Heterostructure fabrication. Monolayers of MoSe2, WSe2 and thin flakes of hBN are first mechanically exfoliated onto 300 nm SiO2 on Si wafers. We then use the dry transfer method to pick up and stack up the crystals to create the heterostructure, with the MoSe2 and WSe2 armchair aligned under a microscope, followed by annealing in vacuum kim_van_2016 .

Experimental setup For low temperature measurements, the sample is kept in a 4K cryostat (Montana Instrument). The excitation and collection are carried out with a home-built confocal microscope with an objective lens with numerical aperture (NA) of 0.45. For reflection contrast measurement, white light from a tungsten halogen lamp is focused on the sample with beam size of 10 $\mu$m in diameter. The spatial resolution is improved to be 2 $\mu$m by using pinhole combined with confocal lens. For PL measurements, a continuous wave Ti:sapphire laser (MSquared-Solstis, bandwidth $<$50 kHz, power held at 80 $\mu$W) is focused by the same objective with beam size of 2 $\mu$m. The signal is detected using a Princeton Instruments spectrometer with a cooled charge-coupled camera for time-integrated measurements. For time-resolved measurements, we use a single photon detector synchronized with the laser with a time resolution below 200 ps.

Author Contributions

H.D., L.Z.conceived the experiment. G.W.B, L.Z. fabricated the device. L.Z., R.G. performed the measurements. L.Z. and H.D. performed data analysis. J.H., E.P., Y.C, K.K assisted the fabrication. H.D. and E.T. supervised the projects. L.Z and H.D. wrote the paper. All authors discussed the results, data analysis and the paper.

Acknowledgment

We thank Allan H. MacDonald, Fengcheng Wu, Wei Xie, Wencan Jin and Kai Chang for helpful discussions. All authors acknowledge the support by the Army Research Office under Awards W911NF-17-1-0312.