key: cord-0668998-lmv9cfeg
authors: Scuri, Giovanni; Andersen, Trond I.; Zhou, You; Wild, Dominik S.; Sung, Jiho; Gelly, Ryan J.; B'erub'e, Damien; Heo, Hoseok; Shao, Linbo; Joe, Andrew Y.; Valdivia, Andr'es M. Mier; Taniguchi, Takashi; Watanabe, Kenji; Lonvcar, Marko; Kim, Philip; Lukin, Mikhail D.; Park, Hongkun
title: Electrically tunable valley dynamics in twisted WSe$_2$/WSe$_2$ bilayers
date: 2019-12-24
journal: nan
DOI: nan
sha: b72379c9cc758e5d9042cf42a3fdcf72e70e0e3e
doc_id: 668998
cord_uid: lmv9cfeg

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 WSe$_2$/WSe$_2$ 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 three 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.

*These authors contributed equally to this work. †To whom correspondence should be addressed: hongkun_park@harvard.edu, lukin@physics.harvard.edu 2 Valleys represent the crystal momentum states where bands have an extremum [1] [2] [3] [4] [5] [6] . Charge carriers or excitons in different valleys can exhibit markedly distinct properties [1] , including different spin, optical selection rules, and Berry curvature, leading to a wealth of new physical phenomena such as the valley Hall [7, 8] and Nernst effects [9, 10] . Moreover, the valley degree of freedom can enable new ways of encoding and processing information beyond traditional schemes based purely on charge [11] [12] [13] . The realization of such applications relies on efficiently initializing a large valley polarization and achieving long valley and exciton lifetimes.

Transition metal dichalcogenides (TMDs) are a promising platform for valleytronics as they host tightly bound excitons with coupled spin-valley properties that can be optically addressed via circularly polarized light [2, [14] [15] [16] . A major obstacle to harnessing these properties in monolayer TMDs is the short lifetimes of intralayer excitons (0.1-1 ps) resulting from the sizeable electronhole wavefunction overlap [17, 18] , as well as rapid valley mixing caused by exchange interactions [19] [20] [21] [22] [23] . Interlayer excitons in bilayer TMDs [13, 24, 25] , consisting of an electron and a hole residing in two distinct TMD layers, present a promising route for overcoming these limitations.

Because of the reduced wavefunction overlap, interlayer excitons can exhibit enhanced lifetimes that are 3 to 4 orders of magnitude longer than their intralayer counterparts [24, 25] .

Unfortunately, interlayer excitons in naturally occurring TMD bilayers exhibit rapid valley mixing because valleys of opposite chirality are degenerate in energy and momentum ( Fig. 1(a) , top) [1, 26, 27] . Moreover, natural bilayers are inversion symmetric (the two layers are rotated 180 o relative to each other), thus as a whole they do not exhibit net valley polarization [26, 28] unless the symmetry is broken, e.g., with an electric field [29] . Consequently, most valleytronic 3 studies involving interlayer excitons have focused on heterobilayers made of two different materials, such as WSe2/MoS2 [30] and MoSe2/WSe2 [12, 13, 31, 32] .

In this Letter, we show that the introduction of a twist angle between the layers can provide a new avenue for engineering the spin-valley properties of TMD bilayers, including homobilayers.

Previously, the twist angle has been used to modify the resonance energy of excitons [33, 34] and alter their properties due to moiré-induced spatial confinement and hybridization of bands [35] [36] [37] [38] [39] [40] .

Here, we tune the twist angle between the layers to control the momentum alignment of their respective valleys ( Fig. 1(a) , bottom), permitting long-lived interlayer exciton states with slow valley depolarization even at zero electric and magnetic fields. Importantly, we also demonstrate that the exciton and valley dynamics of twisted bilayers can be tuned via electrostatic doping.

To experimentally demonstrate twist-based spin-valley engineering, we fabricate optically addressable field-effect transistors that incorporate twisted WSe2/WSe2 bilayers (t-WSe2/WSe2) encapsulated in hexagonal boron nitride (hBN, Fig. 1(b) , Supplementary Section I [41] ). The devices feature top and bottom graphene gates for independent control of doping and vertical electric field. Using the tear-and-stack technique [42, 43] , we fabricate multiple such devices from high-quality exfoliated flakes, with target twist angles ranging from 0 o to 17 o . For comparison, we also make a device using a 2H-stacked natural bilayer (labeled as 180 o twist angle).

Figure 1(c) shows polarization-resolved photoluminescence (PL) spectra from t-WSe2/WSe2 at different twist angles (see Supplementary Fig. S1 for additional twist angles [41] ). These spectra are obtained with both of the graphene gates grounded, so that the TMD layers are intrinsic and 4 under zero vertical electric field. At all twist angles, including the natural 2H bilayer, the spectra show two sets of peaks: the higher energy peaks near 1.7 eV ( 0 ) are assigned to momentum direct (K-K) intralayer transitions [26, 28, 44] , and the lower energy peaks between 1.5 and 1.6 eV ( I ) are attributed to interlayer transitions [16, [44] [45] [46] . This assignment is based on our out-of-plane electric field dependence measurements ( Fig. 2(a) , Supplementary Section II and Supplementary   Fig. S2 [41] ), which show a zero (non-zero) linear Stark shift for intralayer (interlayer) excitons, consistent with previous studies [25, 44] . Despite their weaker binding energies [25] , the interlayer excitons have lower energies than the K-K intralayer excitons, indicating that they do not originate from the momentum direct K-K transition. Instead, the interlayer excitons arise from lower-energy transitions that are momentum indirect, as previously predicted for multilayer TMDs [16] .

As the twist angle is increased from 0 o to 17 o , the interlayer exciton peaks blueshift by almost 80 meV, consistent with reduced interlayer coupling [33, 34, [47] [48] [49] (Fig. 1(c) ). In all twisted structures, we observe four or five interlayer exciton peaks separated by 15-17 meV. We note that similar multi-peak structures in twisted MoSe2/WSe2 heterostructures have been attributed to the confinement of interlayer excitons in moiré supercells [36] . In t-WSe2/WSe2 studied here, the multiple peaks are observed even in natural bilayers (as in Ref. [44] ) and their spacing is independent of twist angle, suggesting a different origin. Since their energy separation is similar to the optical phonon energy in WSe2 [44, 50] , one possibility is that the peaks are phonon replicas [44] . Further experimental and theoretical studies are necessary to confirm this hypothesis, however. 5 The spin-valley properties of the interlayer excitons change drastically with the introduction of a twist angle between the two layers, as evidenced by the contrast between co-and cross-polarized emission signals ( co and cross , respectively) in PL measurements. Upon illumination with circularly polarized light, the natural bilayer emits almost equal co and cross , whereas t-WSe2/WSe2 emits much stronger co-polarized light ( Fig. 1(c) ). Defining the degree of circular polarization (DOCP) as co − cross co + cross , we find that while the neutral interlayer exciton DOCP remains close to zero in natural bilayers, it reaches values as high as 60% in twisted bilayers ( Fig. 1(d [41] ). Similar to previous studies [23, 52] , we observe a 15 ps delay between the co-and crosspolarized emission, which causes a dip in the DOCP until both polarization branches reach the slow decay regime (Fig. 3(d) ). Fitting the DOCP in this regime with a linear coupled model (see Supplementary Section IV [41] ), we extract a very long valley lifetime of 44 ns (dashed line in inset of Fig. 3(d) , lines corresponding to 5 ns and 10 ns shown for comparison), comparable to the best reported values in TMD heterobilayers [31] .

In the doped cases, we focus on shorter time scales, because the exciton population and DOCP decay very rapidly in the n-and p-doped regimes, respectively. Fitting the data with the linear coupled model [41, 52] 

, we find that the initial exciton decay rate is faster in the n-doped regime ( 1 =40 ps) than in the intrinsic and p-doped regimes ( 1 =0.1 ns).

Conversely, the valley lifetime is longer in the n-doped regime ( v =2.2 ns) than in the p-doped regime ( v =30 ps, similar to instrument response time).

The observed polarization properties and their doping dependence can be understood from the band structure of t-WSe2/WSe2 bilayers. In natural (2H) bilayer WSe2, recent angle-resolved photoemission spectroscopy measurements [53, 54] and density functional theory calculations [44, 55] suggest that the conduction band minimum (CBM) and valence band maximum (VBM) are located at the Q and K points, respectively. Our results suggest that this is also the case in t-WSe2/WSe2. In particular, the electric field dependent PL measurements display an interlayer exciton Stark shift that corresponds to an electron-hole separation of =0.37 nm (Fig. 2(a) ). This value is smaller than the interlayer separation of 0 =0.6 nm [25] but larger than 0 /2 as expected 7 for a K (hole) to Q (electron) transition, where the hole is localized in a single layer and the electron is partially delocalized between the layers (see Supplementary Section II for further discussion [41] ).

A key difference in the band structures of natural and twisted WSe2 bilayers is that the Q and K points are spin-degenerate in the former, but not in the latter [56] . Therefore, electrons and holes in natural bilayer WSe2 do not need to acquire any energy or momentum to change spin, enabling rapid depolarization ( Fig. 4(a) ). In contrast, valley depolarization of neutral interlayer excitons in twisted structures requires both carriers to scatter with phonons, acquire energy and flip their spins [23, 51] (Fig. 4(b) ). This is a much slower process, and the dynamics are instead likely governed by electron-hole exchange interactions [12, 51, 57] . However, this process is also slow, because the interlayer excitons are indirect both in real and momentum space. In our experiment, we show that the valley depolarization rate is much slower than the exciton decay rate (Fig. 3) , leading to the large observed DOCP (Fig. 1(d) ).

The observed hierarchy of valley lifetimes in the three doping regimes, i.e. τv(intrinsic) > τv(ndoped) > τv(p-doped), is also well described by our band-structure considerations. In the p-and ndoped regimes, the depolarization dynamics of charged interlayer excitons are dominated by intervalley scattering [12, 51, 57] , and in contrast to the intrinsic regime, only one of the carriers needs to scatter, due to the additional resident charge in the opposite valley. Positively charged excitons, which already have resident holes in both the K and K' valleys, only require scattering of the electron to depolarize (Fig. 4(c) ). Conversely, only the hole needs to scatter in negatively charged excitons (Fig. 4(d) ). These considerations indicate that the valley lifetime should be 8 shorter in the doped regimes than in the intrinsic regime, as observed here. Our results in Figure   3 (d) suggest that the depolarization mechanism for holes is slower than for electrons in our twisted structures, consistent with the large spin-orbit coupling at the K point VBM and the resultant strong spin-valley locking for holes [26] .

The strong asymmetry in degree of circular polarization shown in Figure 2 is a result of the interplay between the depolarization and exciton decay dynamics. In the hole doped regime, the depolarization timescale is shorter than 1 (30 ps and 0.1 ns, respectively), resulting in a low DOCP (<5%). In the electron doped regime, on the other hand, v is much longer than 1 (2.2 ns and 40 ps, respectively) so the observed DOCP is very large (>80%).

In conclusion, we have shown that the twist angle provides a new route for engineering the chiral 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) 25 exhibits no Stark shift, and is therefore attributed to intralayer excitons. The lower-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 [25] . This is further supported by the fact that the extracted electron-hole separation, = 0.37 nm (0.36 nm in 2 o twist device), is significantly smaller than the full interlayer separation ( 0 = 0.6 nm) [25] 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 [33, 61] , causing ≤ 0 /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.

To confirm the stark contrast in DOCP between natural and twisted bilayer WSe2, we fabricate an hBN-encapsulated TMD heterostructure that contains both natural (180 o ) and twisted (∼0 o ) 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) ). 26 

To fit the full time-dependence of the photoluminescence in the intrinsic regime, we use a biexponential decay convoluted with the system response, ( ), as measured from the response of our sub-picosecond laser:

Here, 1 and 2 are the fast and slow decay timescales, with corresponding amplitudes 1 and 2 .

This model is used for both the co-and cross-polarized emission components (with separate fit parameters), and 0 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, v :

Here, co and cross are the co-and cross-polarized exciton populations, and 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, ( ), 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) ). 

Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides

Spin and pseudospins in layered transition metal dichalcogenides

Valley-Valley Splitting in Inversion Layers on a High-Index Surface of Silicon

Valley filter and valley valve in graphene

Valley Splitting of

AlAs Two-Dimensional Electrons in a Perpendicular Magnetic Field

Valley Susceptibility of an Interacting Two-Dimensional Electron System

The valley Hall effect in MoS2 transistors

Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport

The valley Nernst effect in WSe2

Thermally Driven Pure Spin and Valley Currents via the Anomalous Nernst Effect in Monolayer Group-VI Dichalcogenides

Valley-dependent optoelectronics from inversion symmetry breaking

Valleytronics in 2D materials

Interlayer valley excitons in heterobilayers of transition metal dichalcogenides

Control of valley polarization in monolayer MoS2 by optical helicity

Valley polarization in MoS2 monolayers by optical pumping

Atomically thin MoS2: A new direct-gap semiconductor

Exciton radiative lifetime in transition metal dichalcogenide monolayers

Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides

Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides

Valley depolarization due to intervalley and intravalley electronhole exchange interactions in monolayer MoS2

Many-Body Effects in Valleytronics: Direct Measurement of Valley Lifetimes in Single-Layer MoS2

Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers

Long-Lived Valley Polarization of Intravalley Trions in Monolayer WSe2

Observation of long-lived interlayer excitons in monolayer MoSe2-WSe2 heterostructures

Electrical control of interlayer exciton dynamics in atomically thin heterostructures

Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe2

Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers

Exciton dynamics in WSe2 bilayers

Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2

Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures

Valley-polarized exciton dynamics in a 2D semiconductor heterostructure

Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures

Tailoring the Electronic Structure in Bilayer Molybdenum Disulfide via Interlayer Twist

Evolution of interlayer coupling in twisted molybdenum disulfide bilayers

Moiré Intralayer Excitons in a MoSe2/MoS2 Heterostructure

Evidence for moiré excitons in van der Waals heterostructures

Observation of moiré excitons in WSe2/WS2 heterostructure superlattices

Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures

Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers

Identification of spin, valley and moiré quasi-angular momentum of interlayer excitons

See Supplemental Material for additional details regarding experimental methods, exciton characterization based on Stark shifts and fitting models used for the time dependent PL data

van der Waals Heterostructures with High Accuracy Rotational Alignment

Unconventional superconductivity in magic-angle graphene superlattices

Electrical Tuning of Interlayer Exciton Gases in WSe2 Bilayers

Emerging photoluminescence in monolayer MoS2

The role of momentum-dark excitons in the elementary optical response of bilayer WSe2

Probing Evolution of Twist-Angle-Dependent Interlayer Excitons in

MoSe2/WSe2 van der Waals Heterostructures

Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures

Interlayer Coupling in Twisted WSe2/WS2 Bilayer Heterostructures Revealed by Optical Spectroscopy

Intrinsic transport properties of electrons and holes in monolayer transition-metal dichalcogenides

Excitons in atomically thin transition metal dichalcogenides

Generation and Evolution of Spin-, Valley-, and Layer-Polarized Excited Carriers in Inversion-Symmetric WSe2

Visualizing electrostatic gating effects in two-dimensional heterostructures

Time-resolved XUV ARPES with tunable 24-33 eV laser pulses at 30 meV resolution

Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides

Tunable Berry curvature and valley and spin Hall effect in bilayer MoS2

Light-valley interactions in 2D semiconductors

Visible-frequency hyperbolic metasurface

Separation of valley excitons in a MoS2 monolayer using a subwavelength asymmetric groove array

Coherent steering of nonlinear chiral valley photons with a synthetic Au-WS2 metasurface

Nature and evolution of the band-edge states in MoS2: From monolayer to bulk