The twist degree of freedom provides a powerful new tool for engineering the electrical and optical properties of van der Waals heterostructures. Here, we show that the twist angle can be used to control the spin-valley properties of transition metal dichalcogenide bilayers by changing the momentum alignment of the valleys in the two layers. Specifically, we observe that the interlayer excitons in twisted WSe₂/WSe₂ bilayers exhibit a high (>60%) degree of circular polarization (DOCP) and long valley lifetimes (>40  ns) at zero electric and magnetic fields. The valley lifetime can be tuned by more than 3 orders of magnitude via electrostatic doping, enabling switching of the DOCP from ∼80% in the n-doped regime to <5% in the p-doped regime. These results open up new avenues for tunable chiral light-matter interactions, enabling novel device schemes that exploit the valley degree of freedom

Andersen, Trond I.

Bérubé, Damien

Gelly, Ryan J.

Heo, Hoseok

Joe, Andrew Y.

Kim, Philip

Lončar, Marko

Lukin, Mikhail D.

Mier Valdivia, Andrés M.

Park, Hongkun

Scuri, Giovanni

Shao, Linbo

Sung, Jiho

Taniguchi, Takashi

Watanabe, Kenji

Wild, Dominik S.

Zhou, You

English

Caltech Authors - Main

1 
 
Supplemental Material for: Electrically Tunable Valley Dynamics in 
Twisted WSe2/WSe2 Bilayers 
Giovanni Scuri1*, Trond I. Andersen1*, You Zhou1,2*, Dominik S. Wild1, Jiho Sung1,2, Ryan J. 
Gelly1, Damien Bérubé3, Hoseok Heo1,2, Linbo Shao4, Andrew Y. Joe1, Andrés M. Mier 
Valdivia4, Takashi Taniguchi5, Kenji Watanabe5, Marko Lončar4, Philip Kim1,4, Mikhail D. 
Lukin1†, and Hongkun Park1,2† 
1Department of Physics and 2Department of Chemistry and Chemical Biology, Harvard University, 
Cambridge, Massachusetts 02138, USA 
3Department of Physics, California Institute of Technology, Pasadena, California 91125, USA 
4John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, 
Massachusetts 02138, USA 
5National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 
*These authors contributed equally to this work. 
†To whom correspondence should be addressed: hongkun_park@harvard.edu, 
lukin@physics.harvard.edu 
  
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I. MATERIALS AND METHODS 
Flakes of hBN, graphene and WSe2 were mechanically exfoliated from bulk crystals onto Si wafers 
(with 285 nm SiO2). Monolayer and bilayer WSe2 were identified using optical microscopy and 
later confirmed in photoluminescence measurements. The thicknesses of hBN flakes were 
determined with atomic force microscopy. The heterostructures were then assembled with the dry-
transfer method, using the tear-and-stack technique [1,2] to form twisted bilayer WSe2. Next, 
electrical contacts to the WSe2 and graphite gates were defined with electron-beam lithography 
and deposited through thermal evaporation (10 nm Cr+90 nm Au). Optical measurements were 
conducted in a 4 K cryostat (Montana Instruments), using a self-built confocal setup with an 0.75 
NA objective. The DOCP was measured with two polarizers in the excitation and collection paths, 
and a quarter wave plate directly above the objective. To eliminate any polarization-dependent 
instrument response, all DOCP measurements included excitation with (and collection of) both 𝜎𝜎+ 
and 𝜎𝜎− light. PL measurements were carried out using a 660 nm diode laser. A sub-picosecond 
pulsed laser (Coherent) and a streak camera (Hamamatsu) were used in the time-resolved PL 
measurements.  
 
II. EXCITON CHARACTERIZATION BASED ON DC STARK SHIFT 
Upon applying a vertical electric field, excitons experience a Stark shift given by ΔE = 𝐸𝐸𝑧𝑧 ⋅ 𝑒𝑒 ⋅ 𝑑𝑑, 
where E is the exciton energy, 𝐸𝐸𝑧𝑧 is the applied electric field, d is the (vertical) electron-hole 
separation, and e is the elementary charge. Since interlayer excitons have an out-of-plane dipole 
moment (d), unlike intralayer excitons, the two species can be distinguished through electric field 
dependent PL measurements (Fig. 2(a) and Fig. S2). In all of our devices, the higher-energy feature 
(∼ 1.7 eV) exhibits no Stark shift, and is therefore attributed to intralayer excitons. The lower-
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energy peaks, on the other hand, show a clear shift, and are therefore assigned to interlayer 
excitons.  
The interlayer excitons are expected to be momentum indirect, because their PL energy is lower 
than that of the direct intralayer exciton, even with their weaker binding energy [3]. This is further 
supported by the fact that the extracted electron-hole separation, 𝑑𝑑 = 0.37 nm (0.36 nm in 2o twist 
device), is significantly smaller than the full interlayer separation (𝑑𝑑0~0.6 nm) [3] that would be 
expected if both carriers were at the K point. It is also not consistent with the Γ-K transition, 
because the wavefunction at the Γ-point is completely delocalized between the two layers [4,5], 
causing 𝑑𝑑 ∼ 𝑑𝑑0/2. Instead, the extracted electron-hole separation is consistent with the K to Q 
transition, where the hole is localized in a single layer and the electron is partially delocalized [6]. 
 
III. SPATIAL DEPENDENCE OF DOCP IN A SAMPLE CONTAINING BOTH NATURAL 
AND TWISTED BILAYER REGIONS 
To confirm the stark contrast in DOCP between natural and twisted bilayer WSe2, we fabricate an 
hBN-encapsulated TMD heterostructure that contains both natural (180o) and twisted (∼0o) bilayer 
regions (Fig. S3(a)). The device was made from a single exfoliated WSe2 flake that had both a 
bilayer and a monolayer region, the latter of which was torn and stacked on top of itself. Integrating 
only the interlayer exciton emission (photon energies below 1.6 eV), we find that the natural 
bilayer area exhibits almost no DOCP, while the twisted region has a DOCP close to 50% almost 
everywhere, except in sporadic defect spots (Fig. S3(b)). 
 
 
 
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IV. FITTING OF LIFETIME DATA 
To fit the full time-dependence of the photoluminescence in the intrinsic regime, we use a 
biexponential decay convoluted with the system response, 𝑠𝑠(𝑡𝑡), as measured from the response of 
our sub-picosecond laser: 
𝑝𝑝(𝑡𝑡) = �𝐴𝐴1𝑒𝑒−𝑡𝑡/𝜏𝜏1 + 𝐴𝐴2𝑒𝑒−𝑡𝑡/𝜏𝜏2� ∗ 𝑠𝑠(𝑡𝑡 − 𝑡𝑡0).  
Here, 𝜏𝜏1 and 𝜏𝜏2 are the fast and slow decay timescales, with corresponding amplitudes 𝐴𝐴1 and 𝐴𝐴2. 
This model is used for both the co- and cross-polarized emission components (with separate fit 
parameters), and 𝑡𝑡0 accounts for the observed delay between the two. The fits are shown as dotted 
lines in Fig. 3(a), with corresponding DOCP in Fig. 3(d). 
In the n- and p-doped regimes, we focus on shorter timescales due to their shorter exciton and 
valley lifetimes, respectively. At these timescales, we only observe a single exponential decay and 
therefore fit with a linear coupled model, which also allows for extracting the valley lifetime, 𝜏𝜏v:  
?̇?𝑝co = −𝑝𝑝co𝜏𝜏1 − 𝑝𝑝co − 𝑝𝑝cross𝜏𝜏v + (1 − 𝛼𝛼) ⋅ 𝑠𝑠(𝑡𝑡),  
?̇?𝑝cross = −𝑝𝑝cross𝜏𝜏1 − 𝑝𝑝cross − 𝑝𝑝co𝜏𝜏v + 𝛼𝛼 ⋅ 𝑠𝑠(𝑡𝑡). 
Here, 𝑝𝑝co and 𝑝𝑝cross are the co- and cross-polarized exciton populations, and 𝛼𝛼 is the proportion 
of cross-polarized excitons due to imperfect excitation. In order to account for the system response, 
we use the measured laser pulse, 𝑠𝑠(𝑡𝑡), as the laser input. The fits and corresponding DOCP are 
shown with dashed lines in Fig. 3(b)-(d). This model was also used for fitting in the intrinsic regime 
at longer timescales (inset of Fig. 3(d)). 
  
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V. INTRA- AND INTERLAYER K-Q EXCITONS 
The wavefunction at the Q-point in twisted bilayer WSe2 is expected to be more layer delocalized 
than that at the K-point, but still not fully delocalized as in the case of natural bilayers (Fig. S6(a)). 
Hence, there are two candidate K-Q exciton species: the intralayer species, where the electron 
wavefunction is more localized in the same layer as the hole (Fig. S6(b)), and the interlayer species 
where the electron is more localized in the opposite layer (Fig. S6(c)). The intra- (inter-) layer K-
Q exciton is expected to exhibit an electron-hole separation that is smaller (greater) than 
𝑑𝑑𝑜𝑜
2
~0.3 nm. Thus, the extracted electron-hole separation of 0.37 nm in our work indicates that the 
interlayer K-Q exciton dominates in PL. In this section, we explain why this is also to be expected 
theoretically. 
Crucially, the bands are not layer degenerate in twisted bilayers, even at zero electric field. This 
important difference from natural bilayers arises from the broken inversion symmetry, and is most 
easily understood by starting from the limit of zero twist angle, i.e. AB (3R) stacking. In that case, 
the W-atoms in the top layer are vertically aligned with Se-atoms in the other layer, while the W-
atoms in the bottom layer are not. This difference in atomic environment renders the bands non-
degenerate between the two layers, as shown both theoretically (Refs. [6-8]) and experimentally 
(Ref. [9]). In particular, theoretical studies suggest that the lowest conduction band at the Q-point 
and the highest valence band at the K-point are preferentially localized in opposite layers, thus 
promoting the interlayer species. Our observations suggest that this effect is stronger than the 
difference in binding energy between the intra- and interlayer K-Q species, thus causing the 
interlayer exciton to be the lowest energy state. 
Proceeding to non-zero twist angles, the system now exhibits a smooth periodic variation between 
AB- and BA-stacked points (the moiré pattern), and at large twist angles, the wavefunctions 
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become delocalized over multiple moiré cells. Nevertheless, as shown in Refs. [10,11], the 
delocalized hole wavefunction of the highest band at the K-point is still concentrated near the 
AB(BA)-stacked sites in the bottom (top) layer. Conversely, the lowest CB Q-bands are expected 
to be preferentially concentrated near the BA(AB)-stacked sites in the bottom (top) layer. Since 
the intralayer exciton consists of an electron and hole that are concentrated in different parts of the 
sublattice, the wavefunction overlap is very small (Fig. S6(b)). In the case of interlayer excitons, 
on the other hand, the electron is predicted to be in the same domain and layer as the hole almost 
40% of the time (Fig. S6(c)) [6]. Hence, it is expected that the interlayer K-Q species has both 
higher binding energy and stronger oscillator strength than the intralayer counterpart, and is thus 
the exciton species responsible for the lower energy peaks observed in our experiment.   
7 
 
 
Fig. S1: Photoluminescence from additional samples. Colored (grey) curves show PL from 
bilayer (monolayer) WSe2, including additional twist angles of 0.5o, 4.5o and 5o not displayed in 
the main text. The devices with 4.5o and 5o twist angles show the same interlayer exciton blue-
shift as was presented for the 17o sample in the main text.  
 
8 
 
 
Fig. S2: Electric field dependence of PL in device with 2o twist angle. While the intralayer 
exciton (∼ 1.7 eV) does not shift observably with electric field, the interlayer excitons (∼ 1.5 −1.6 eV) exhibit a clear Stark shift (dashed white lines). The corresponding electron-hole separation 
is 0.36 nm, similar to the value extracted in the 17o device (0.37 nm). 
  
9 
 
 
Fig. S3: Spatial map of DOCP. (a) Optical image of an hBN-encapsulated heterostructure that 
contains both natural (180o, lower right) and twisted (∼0o, upper left) bilayer regions. (b) Spatial 
dependence of average interlayer exciton DOCP (photon energy below 1.6 eV). Consistent with 
PL spectra shown in the main text, the twisted bilayer region exhibits much higher DOCP than the 
natural bilayer region. 
  
10 
 
 
Fig. S4: Doping dependence of DOCP in device with 2o twist angle. (a) Polarization-resolved 
photoluminescence spectra from 2o-twisted bilayer WSe2 at gate voltages VG=-4 V (left) and VG=4 
V (right). Solid and dashed curves show co- and cross-polarized emission, respectively. (b) DOCP 
calculated from PL spectra in (a). As in the 17o device presented in the main text, the interlayer 
DOCP is much higher in the n-doped regime than in the p-doped regime. (c) Full gate dependence 
of DOCP. (d) DOCP of the brightest interlayer exciton peak as a function of gate voltage. Since 
this device exits the intrinsic regime at relatively low gate voltages, plateaus are only observed in 
the p- and n-doped regimes. 
 
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Fig. S5: Exciton lifetime in additional samples. (a)-(b) Time-resolved PL measurements from 
devices with 0o (a) and 5o (b) twist angles (colored dots). Dotted black lines are biexponential fits 
convoluted with the system response. The extracted fast and short timescales are 𝜏𝜏1=110 (60) ps 
and 𝜏𝜏2=2.0 (3.3) ns for the device with 0o (5o) twist angle. 
  
12 
 
 
Fig. S6. Electron (blue, Q-point) and hole (red, K-point) wavefunctions in natural and twisted 
bilayers (only the bottom layer hole wavefunction is shown for simplicity). (a) In natural 
bilayers, the wavefunction at the Q-point is completely delocalized between the layers, causing the 
inter- and intralayer K-Q exciton to be equivalent. The expected electron-hole separation is half 
the interlayer spacing (𝑑𝑑 = 𝑑𝑑0/2). (b)-(c) In twisted bilayers, the hole wavefunction is 
concentrated near the AB(BA)-stacked sites in the bottom (top) layer. In contrast, the electron 
wavefunction is preferentially concentrated near the BA(AB)-stacked sites in the bottom (top) 
layer. Thus, the electron-hole wavefunction overlap is expected to be larger for the interlayer 
exciton (c) than the intralayer exciton (b). 
  
13 
 
References: 
[1] K. Kim et al., van der Waals Heterostructures with High Accuracy Rotational Alignment, 
Nano Letters 16, 1989 (2016). 
[2] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, 
Unconventional superconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018). 
[3] L. A. Jauregui et al., Electrical control of interlayer exciton dynamics in atomically thin 
heterostructures, Science 366, 870 (2019). 
[4] J. E. Padilha, H. Peelaers, A. Janotti, and C. G. Van de Walle, Nature and evolution of the 
band-edge states in MoS2: From monolayer to bulk, Physical Review B 90, 205420 (2014). 
[5] A. M. van der Zande et al., Tailoring the Electronic Structure in Bilayer Molybdenum 
Disulfide via Interlayer Twist, Nano Letters 14, 3869 (2014). 
[6] V. Enaldiev, V. Zólyomi, C. Yelgel, S. Magorrian, and V. Fal'ko, Stacking domains and 
dislocation networks in marginally twisted bilayers of transition metal dichalcogenides, 
arXiv:1911.12804  [Phys. Rev. Lett. (to be published)]. 
[7] W. Li, T. Wang, X. Dai, X. Wang, C. Zhai, Y. Ma, and S. Chang, Bandgap engineering of 
different stacking WS2 bilayer under an external electric field, Solid State Communications 225, 
32 (2016). 
[8] X. Fan, W. T. Zheng, J.-L. Kuo, D. J. Singh, C. Q. Sun, and W. Zhu, Modulation of 
electronic properties from stacking orders and spin-orbit coupling for 3R-type MoS2, Scientific 
Reports 6, 24140 (2016). 
[9] A. Weston et al., Atomic reconstruction in twisted bilayers of transition metal 
dichalcogenides, arXiv:1911.12664. 
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[10] H. Yu, M. Chen, and W. Yao, Giant magnetic field from moiré induced Berry phase in 
homobilayer semiconductors, National Science Review 7, 12 (2020). 
[11] F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Topological Insulators in 
Twisted Transition Metal Dichalcogenide Homobilayers, Physical Review Letters 122, 086402 
(2019). 
 


Electrically Tunable Valley Dynamics in Twisted WSe₂/WSe₂ Bilayers

https://authors.library.caltech.edu/103531/3/Supplemental_Material_FINAL_refs.pdf

Electrically Tunable Valley Dynamics in Twisted WSe₂/WSe₂ Bilayers

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