Introduction

Reassembled layered van der Waals heterostructures have revealed new phenomena beyond single material layers1. In particular, when two different monolayer transition metal dichalcogenides (TMDs) are properly aligned, the electrons can be confined in one layer while the holes are confined in the other layer1,2,3,4,5,6,7,8. Because the electron and hole wavefunctions in the two layers only have small overlap, excitons can have a longer lifetime of several nanoseconds, as compared to around picoseconds for excitons in monolayer. Such exciton is known as indirect exciton or interlayer exciton2,8. A long exciton lifetime is crucial for the generation of high-temperature macroscopically ordered exciton state, which forms the basis of a series of fundamental physics phenomena such as superfluidity9 and Bose–Einstein condensation10,11,12. Moreover, longer survival of excitons means longer distance of exciton transport, which is useful for excitonic devices13,14.

In another perspective, similar to monolayer TMDs, the properly aligned two-dimensional (2D) heterostructure has indirect exciton with valley degree of freedom. Valleys (K and K′) are located at the band edges in the corners of the hexagonal Brillouin zone15,16. The spins show opposite signs in the two valleys at the same energy which corresponds to spin-valley locking15,16. Moreover, these two valleys have opposite Berry curvature leading to different optical selection rules in each valley. By using a circularly polarized optical pumping and observing the locking between the output photon chirality and the valleys, the phenomena of valley polarization has been observed17,18,19,20,21. These unique properties put the valley degree of freedom as a possible candidate for opto-electronics and quantum computation with 2D material22,23,24. Leading to its application, a long valley polarization lifetime is a prerequisite and extensive efforts have been put towards particles and quasi-particles with longer lifetime in these ultra-thin systems. Previous lifetime measurement reveals that direct exciton lifetime is in the order of picosecond25,26,27, limiting its application to some extent. Localized excitons can have a lifetime of around nanosecond28,29 and indirect exciton can have ~100 ns lifetime30,31 and tens of nanosecond valley polarization lifetime8. We note that recent work also shows single charge carrier can have microsecond lifetime32. On the other hand, experimental evidence shows the existence of dark excitons, lying tens of millielectronvolts below the bright exciton in WSe233. Their decay time is measured to be nanoseconds in monolayer TMD34.

Here we report that, the dark excitons in 2D heterostructures can survive for microsecond timescale. With magnetic field suppressed valley mixing, they serve as a microsecond valley polarization memory for indirect excitons. This is two orders longer than the case without an applied magnetic field.

Results

Experimental observation of interlayer excitons

The schematics and the optical spectroscopy result of the MoSe2/WSe2 heterostructure on SiO2/Si substrate are shown in Fig. 1. In such heterostructures, electrons tend to go to the conduction band of MoSe2 and holes are confined in the valence band of WSe2, forming the indirect excitons (Fig. 1a). Our samples are prepared via a mechanical exfoliation and aligned-transfer method7. In this sample, the MoSe2 monolayer is stacked on top of the WSe2 monolayer in AA-stacking style (see Supplementary Note 4 and Supplementary Fig. 5 for the second harmonic generation experiment). The detail of the sample preparation can be found in the Methods section. A fluorescence image of the heterostructure was taken with a color camera under white light excitation (Fig. 1d). It is found that the heterostructure consists of two areas: dark area with low intensity luminescence (labeled as H1) and bright area with high intensity luminescence (labeled as H2). The photoluminescence (PL) of these two areas as well as the MoSe2 region under 633 nm continuous-wave (CW) laser excitation is shown in Fig. 1e. As can be seen from this figure, the interlayer exciton emission of ~1.34 eV emerges for the dark area H2. The interlayer exciton emission intensity is comparable to the intralayer exciton and the trion emission of MoSe2. The interlayer emission is missing for the H1 region where higher intensity of intralayer emission is observed. This can be attributed to the weak coupling between the two layers in this H1 region7. In the following measurements, we focused on the interlayer exciton emission in H2 area. An 850-nm long pass filter is used in the PL collection to filter out the contribution of other emission type.

Fig. 1
figure 1

Sample characterization. a MoSe2 and WSe2 form a 2D heterostructures, where electrons are confined in one layer and holes are confined in the other layer. b Schematic of the interlayer exciton and dark exciton. The interlayer excitons are illustrated as solid black ellipses. The dark excitons are represented by the dashed ellipses. Red (blue) curves denote spin-up (spin-down) in the conduction and valence bands while the gray arrowed curves denote the dark exciton valley scattering. c Optical microscope image of the MoSe2/WSe2 heterostructure. Blue dashed line shows the area of MoSe2. White dashed lines show the region of heterostructure, which is separated into two areas labeled as H1 and H2 in d. d Fluorescence image taken with a color camera under white light excitation. It shows a bright (H1) and dark (H2) state in the two different place of heterostructure. e Photoluminescence in the monolayer MoSe2, heterostructure H1 region, and heterostructure H2 region under a 633 nm laser excitation. Peaks on MoSe2 are attributed to exciton (XMo) and trion (TMo) of MoSe2. In H1 area, another two weak peaks appear and are labeled as exciton (XW) and trion (TW) from WSe2. In H2 area, another peak around 1.34 eV emerges, which is attributed to interlayer exciton and labeled as Int

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Valley polarization with CW laser

We firstly carried out the measurement of valley polarization with a CW pump laser. The results are shown in Fig. 2. In order to increase the count of the interlayer exciton, an excitation laser with wavelength of 1.708 eV is used. This corresponds to the resonant excitation of the WSe2 charged exciton. The polarization states of the excitation and detection are set to the circular polarization σ+ or σ−, and the degree of circular polarization is extracted from these four polarization combinations. Please note that the emission polarization will have a small distortion away from circular polarization due to the existence of the Moire pattern35,36,37,38. However, circular polarization still acts as a good approximation for studying the dynamics of valley polarization here. The PL emission of different configurations at 0 T are shown in Fig. 2a, b. It is observed that the PL intensity of the co-polarization is always larger than that of the cross-polarization, corresponding to valley polarization. Next, we apply a magnetic field of −7 T perpendicular to the sample surface (out-of-plane direction, B z ). The results are shown in Fig. 2c, d. As can be seen from these figures, the emission difference between the case with co-polarization and cross-polarization excitation gets larger at B z  = −7 T compared to 0 T.

Fig. 2
figure 2

Valley polarization with CW laser excitation. a, b Valley polarization at 0 T. Right and left circularly polarized light are labeled as σ+ and σ−. Under σ+ laser excitation, σ+ PL output component is more than σ− and vice versa for σ− excitation. This shows evidence of valley polarization. c, d Valley polarization at −7 T. Valley polarization is enhanced by applying magnetic field perpendicular to the sample surface. e The valley polarization degree as a function of applied magnetic field in the z direction. The solid line is the fitting result following equation \(P^j = P_0^j \pm P_1^j\left( {1 - \frac{1}{{r^2 + r\sqrt {1 + r^2} + 1}}} \right)\), \(r = \left| B \right|{\mathrm{/}}\alpha\) where j indicates the excitation polarization, \(P_0^j\) is the residual degree of polarization at 0 T due to the valley polarization, \(P_1^j\) is the saturation level of degree of polarization, and α represents the intervalley scattering between the dark exciton. f, The valley polarization degree as a function of applied magnetic field in the y direction with B z  = 0T

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To quantify this difference, we measured the degree of polarization as a function of magnetic field in both B z (Faraday geometry) and B y directions (parallel to sample surface, Voigt geometry). Here we define the degree of polarization as \(P^j = \frac{{I_{\sigma _ + }^j - I_{\sigma _ - }^j}}{{I_{\sigma _ + }^j + I_{\sigma _ - }^j}}\), where \(I_{\sigma _ + }^j\) \(\left( {I_{\sigma _ - }^j} \right)\) is the σ+ (σ−) polarized PL intensity when excited with j polarization. The degree of polarization pumped by σ+ and σ− excitation versus magnetic field in the Faraday and Voigt geometry are shown in Fig. 2e, f. We can observe a dip of the degree of polarization at low magnetic field around 0 T in Faraday geometry. The valley polarization is around 17% at 0 T and quickly increases to ~35% at ~1 T. For Voigt geometry, the degree of polarization does not show any dependence on the magnetic field.

Regarding the Faraday geometry, our observation of increased valley polarization near 0 T is in line with the report in ref. 39 where it is attributed to the suppression of intervalley electron–hole exchange interaction. Similar with traditional semiconductor quantum wells and quantum dots, the valley depolarization in 2D material is caused by electron–hole exchange interaction40,41,42. The larger binding energy of excitons in monolayer TMDs further enhances such interaction, leading to valley depolarization and short valley polarization lifetime. The intervalley scattering can be understood in term of in-plane depolarizing field40. Hence, by increasing the magnitude of out-of-plane magnetic field, the valley depolarization can be suppressed28,41. This model can also explain why the degree of polarization saturates at high magnetic field. This saturation has also been observed in WSe2 exciton system43. The difference is that, unlike the bright exciton case reported there, the interlayer exciton shows a non-linear magnetic-dependence of valley polarization. Following this, we fit the degree of polarization with equation   \(P^j = P_0^j \pm P_1^j\left( {1 - \frac{1}{{r^2 + r\sqrt {1 + r^2} + 1}}} \right)\), \(r = \left| B \right|{\mathrm{/}}\alpha\) where j indicates the excitation polarization, \(P_0^j\) is the residual degree of polarization at 0 T, \(P_1^j\) is the saturation level of degree of polarization, and α represents the intervalley scattering term between the dark excitons where the dark exciton refers to the WSe2 dark exciton as illustrated in Fig. 1b. The experimental data fits very well with this model within the magnetic field range of our experiment.

The exchange interaction-based argument can also be used to explain why the degree of polarization does not show any magnetic field dependence under the Voigt geometry. In order to discuss this, it should be noted that the 2D material can be seen as an atomic-thin quantum well. It is known that the effect of in-plane magnetic field to the exchange interaction is proportional to the quantum well thickness44. Hence, the exchange interaction is practically independent of the magnetic field under the Voigt geometry which result in the magnetic field-independent degree of polarization.

Time-resolved experiment with pulsed laser excitation

To understand the dynamics of the interlayer exciton emission, we carried out time-resolved PL experiment with pulsed laser excitation. The laser has a repetition period of 8 μs and has the same wavelength as the one used in the CW experiment. The left panels of the Fig. 3a, b show the decay of the PL emission pumped by σ+ excitation at 0 T and −3 T, respectively. The middle panels show the calculated degree of polarization. We can see that, the degree of polarization \(P^{\sigma _ + }\) decays quickly to zero at 0 T, while it has an extra slow decay component and remains above 0.2 for up to 2.5 μs at −3 T. To quantify it, here we address two different types of degree of polarization: valley polarization and PL polarization. The former depends on the polarization state of the excitation, i.e. copolarization and cross-polarization give different PL intensity. It can be calculated as \(P_{{\mathrm{val}}} = \frac{{P^{\sigma _ + } - P^{\sigma _ - }}}{2}\). The latter one solely depends on the polarization of the PL emission and it does not depend on the excitation. It can be calculated as the average of the individual degree of polarization pumped by σ+ or σ− excitation: \(P_{{\mathrm{PL}}} = \frac{{P^{\sigma _ + } + P^{\sigma _ - }}}{2}\). Figure 3e, f shows the decay of valley polarization Pval at 0 and −3 T. valley polarization at 0 T has a decay time of 15 ± 0.3 ns, while it has a decay time of 1.745 ± 0.007 μs at −3 T. More detailed PL data, valley polarization and PL polarization at −3, 0 and 3 T are provided in Supplementary Figs. 1 and 2. More analysis can be found in Supplementary Note 1.

Fig. 3
figure 3

Time-resolved investigation of polarization in magnetic field. a, b Time-resolved PL of σ+-output and σ−-output pumped by a σ+-polarized pulsed laser in Faraday geometry at B z  = 0 T (a) and B z  = −3 T (b). c, d Degree of polarization extracted from σ+ excitation PL at B z  = 0 T (c) and B z  = −3 T (d). e, f Valley polarization calculated from σ+ excitation and σ−-excitation PL. The σ− excitation PL data is in the Supplementary Figs. 1 and 2. At B z  = 0 T, the degree of polarization disappears quickly and hardly seen after 50 ns and valley polarization has a decay time of 15 ± 0.3 ns. At B z  = −3 T, the difference between σ+ output and σ− output is clearly seen even at 200 ns. The valley polarization at B z  = −3 T has a decay time of 1.745 ± 0.007 μs

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Microscopic mechanism of long lifetime and valley polarization lifetime for interlayer excitons

Below we analyze the origin of the long exciton lifetime and valley polarization lifetime. To this end, the experimental result for B = −7, 0, 7 T at low temperature (T = 2.3 K) in the case of σ− polarization excitation and σ− polarized PL detection are shown in Fig. 4a. First we consider the case at high magnetic field. The decay has both the slow and fast decay components. The slow decay in the order of τ1 ~ 1 μs suggests the dark exciton involvements, which will be further confirmed by the magnetic field dependence measurement shown below. The fast decay  part includes two parts, one of which is exponential decay and the other one is power-law decay. Hence, we fit the decay with three components as

$$I = A_1{\rm e}^{ - \frac{t}{{\tau _1}}} + A_2 {\rm e}^{ - \frac{t}{{\tau _2}}} + \frac{B}{{t + t_0}},$$
(1)

where τ1 and τ2 are related to the lifetimes of the slow and fast decay, respectively. A1, A2, B and t0 are other fitting parameters related to the initial population and rate constants. The value of τ1 is ~1 μs while τ2 has a value of ~10 ns.

Fig. 4
figure 4

Theoretical model and experimental data fitting. a Sample of the experimental data (temperature, T = 2.3 K) and the fitting to the theoretical model. The data is obtained using σ− polarized pulsed excitation and σ− polarized PL detection. Semi-log plot is used. b, c The two conversion pathways from the WSe2 dark exciton to the interlayer exciton. In the first pathway (A-B-D), the spin flip happens before the interlayer charge transfer while in the second one (A-C-D), the interlayer charge transfer happens before the spin flip. The conversion rate in the first path has an exponential magnetic field dependence while it is constant for the second path. d Scattering rate from dark exciton to interlayer exciton versus magnetic field. The dark-to-interlayer scattering rates in K valley (σ− PL) and K′ valley (σ+ PL) are plotted against magnetic field and fitted using exponential function

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For the small magnetic field case, instead of Eq. (1), a more complete model has to be used. In this more complete model, each valley has one WSe2 dark exciton state and two type of interlayer exciton states. The first type of the interlayer exciton decays following power law while the second type undergoes exponential decay. The dark exciton can scatter to the interlayer exciton of the second type. Additionally the dark exciton in one valley can scatter to become dark exciton in the other valley. This model is equivalent to Eq. (1) when this dark exciton intervalley scattering rate is negligible. The complete description of this model is given in the Supplementary Note 2 and Supplementary Fig. 3.

As can be seen from Fig. 4a, both the experimental data fits well with the theoretical model. The dark-to-interlayer exciton scattering rate is found to be in the MHz regime. This suggests that the dark exciton lifetime should be in the order of μs which is exceptionally long compared to the lifetime of other exciton types. The maximum value of the dark exciton intervalley scattering rate is found to be ~100 MHz at B z  = 0 T. It decreases quickly with increasing magnetic field. Note that this scattering rate is much smaller than the intralayer bright exciton intervalley scattering rate which can be attributed to the fact that the exchange interaction between dark excitons is much smaller compared to that between bright excitons. However, here we need to consider microsecond time scale. For this time scale, the valley depolarization of dark exciton need to be taken into account.

The dark-to-interlayer scattering rate has an exponential dependence on the magnetic field (Fig. 4d). This can be understood by analyzing the scattering mechanism from the dark exciton to the interlayer exciton. The dark exciton can scatter to become an interlayer exciton by following two different paths. These two paths are illustrated in Fig. 4b, c. In the first path (A-B-D path in Fig. 4b, c), the conduction band electron undergoes spin flipping before the charge transfer happens while in the second path (A-C-D path in Fig. 4b, c) the charge transfer happens before the spin flipping. Following the first path, the dark exciton will transform into an intermediate bright exciton before transforming into an interlayer exciton. According to previous measurement, charge transfer from the bright monolayer exciton to the interlayer exciton is very fast ~100 fs7. Therefore, we can safely neglect the charge transfer time. This means that the contribution of the first path to the dark-to-interlayer scattering rate will be approximately the same as the dark-to-bright exciton scattering rate. As can be seen from Fig. 4c this scattering rate at temperature T can be written as \(r_0{\rm e}^{ - ({\mathrm{\Delta }}E_0 + g\mu _{\mathrm{B}})/k_{\mathrm{B}}T}\), where ΔE0 is the energy difference between the dark exciton and bright exciton at 0 T and r0 is the bright-to-dark exciton scattering rate. This shows that this contribution from the first path has an exponential dependence on magnetic field. On the contrary, the second path does not have strong magnetic field dependence because the transition only happens from a higher energy level to a lower energy level. Hence, its contribution to the dark-to-interlayer scattering rate is constant.

Based on our explanation above, the g-factor of the conduction band electron can be obtained from the magnetic dependence of the dark-to-interlayer exciton scattering rate at a fixed temperature. This can be used to check the sanity of our model. For K valley, the value 1.07 ± 0.079 is found while it is equal to   −1.11 ± 0.095 for K′ valley. These g-factor values agree well with the theoretical prediction of the conduction band g-factor for WSe2 when the out-of-plane effective spin g-factor has negative sign45. From the fitting in Fig. 4d, it can also be seen that the dark-to-interlayer exciton scattering rate saturates to a finite value of ~1 MHz at a big magnetic field as predicted by the model. Additionally, the value of the energy level difference between the bright and dark exciton at zero magnetic field (ΔE0) can also be calculated from the temperature dependence of k1. The detail of the experimental data and the theoretical fitting of the temperature dependence of k1 is shown in Supplementary Note 3 and Supplementary Fig. 4. The obtained energy level difference is in line with the value reported in ref. 46. All of these results shows the sanity of our model.

Discussion

The fact that there are two types of interlayer exciton and that the time-resolved PL signal follows a multi-exponential decay has been reported before2,30,31. The component with slow exponential decay of this PL signal has been attributed to the extrinsic defect30 and also to a transition that is indirect in both real space and momentum space31. However, these two possible explanations cannot be used to explain the magnetic dependence of the slow decay rate that is observed in our data. Instead, we attribute this slow decay component to slow conversion rate from the dark exciton to the bright exciton. By doing so, the magnetic field dependence of this decay rate can be explained. Experimental demonstration of interlayer excitons on additional samples can be found in Supplementary Notes 5 and 6, Supplementary Figs. 7, 8 and 9.

In summary, we have experimentally demonstrated the long valley polarization lifetime in the order of microsecond in 2D heterostructures. This is primarily induced by magnetic field suppressed valley mixing for dark excitons. The long lifetime of the dark exciton put the dark exciton as a reservoir for the interlayer exciton in a long time scale. The long lifetime of exciton in 2D heterostructures makes 2D heterostructure to be a promising candidate for the realization of ultralong-distance exciton transport and exciton devices13,14. The possibilty to realize superfluidity9 in 2D heterostructures with a long exciton lifetime may provide future platform towards low-energy dissipation valleytronic devices.

Methods

Spectroscopy experiment setup

A homemade fiber-based confocal microscope is used for performing the polarization-resolved PL spectroscopy. Polarizers and quarter wave plates are installed on the excitation and detection arms of the confocal microscope for polarization-selective excitation and PL detection. The PL emission is directed by an multi-mode optical fiber into a spectrometer (Andor Shamrock) with a CCD detector for spectroscopic recording. The sample is loaded into a magneto cryostat and cooled down to ~2.3 K. Cryostat with vector magnet provides possibility to study dynamics in different magnetic field directions. The vector magnetic field ranges from −7 to +7 T in the out-of-plane direction (z-axis) and −1 to +1 T in the in-plane direction (x-axis and y-axis). The wavelength of the excitation is 726 nm (1.708 eV) for both the CW and pulsed laser experiment (pulse width 100 ps).

Preparation of the heterostructures

We fabricated MoSe2/WSe2 heterostructures via a mechanical exfoliation and aligned-transfer method7. Bulk WSe2 and MoSe2 crystals (from HQ graphene) were used to produce WSe2 and MoSe2 monolayer flakes and they were precisely stacked with a solvent-free aligned-transfer process. We first prepared a WSe2 monolayer on SiO2 (300 nm)/Si substrate and a MoSe2 monolayer on a transparent polydimethylsiloxane (PDMS) substrate. After careful alignment (for both relative position and stacking angle) under the optical microscope with the aid of an XYZ manipulation stage, we then stacked the two monolayer flakes together, forming a PDMS/MoSe2/WSe2–SiO2/Si structure. Finally, we removed the top PDMS layer and obtained a MoSe2/WSe2 heterostructure on SiO2/Si substrate. For the controlled alignment of stacking angle, the armchair axes were guided according to their sharp edges from optical images, e.g., a stacking angle of 0° (60°) (<±2°) can be identified from Fig. 1a.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.