Moiré-trapped interlayer trions in a charge-tunable WSe_2/MoSe_2 heterobilayer
Mauro Brotons-Gisbert, Hyeonjun Baek, Aidan Campbell, Kenji Watanabe, Takashi Taniguchi, Brian D. Gerardot
MMoiré-trapped interlayer trions in a charge-tunable WSe /MoSe heterobilayer Mauro Brotons-Gisbert, ∗ Hyeonjun Baek, Aidan Campbell, Kenji Watanabe, Takashi Taniguchi, and Brian D. Gerardot † Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, UK Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan International Center for Materials Nanoarchitectonics, NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan (Dated: January 20, 2021)Transition metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices ofinteracting bosons with several degrees of freedom. Such heterobilayers can feature moiré patternsthat modulate their electronic band structure, leading to spatial confinement of single interlayerexcitons (IXs) that act as quantum emitters with C symmetry. However, the narrow emissionlinewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nomi-nally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we reportthe continuous evolution from a few trapped IXs to an ensemble of IXs with both triplet and singletspin configurations in a gate-tunable H -MoSe /WSe heterobilayer. We observe signatures of dipo-lar interactions in the IX ensemble regime which, when combined with magneto-optical spectroscopy,reveal that the narrow quantum-dot-like and broad ensemble emission originate from IXs trappedin moiré potentials with the same atomic registry. Finally, electron doping leads to the formation ofthree different species of localised negative trions with contrasting spin-valley configurations, amongwhich we observe both intervalley and intravalley IX trions with spin-triplet optical transitions. Ourresults identify the origin of IX emission in MoSe /WSe heterobilayers and highlight the impor-tant role of exciton-exciton interactions and Fermi-level control in these highly tunable quantummaterials. INTRODUCTION
Van der Waals heterobilayers consisting of verticallystacked monolayer transition-metal dichalcogenide semi-conductors (TMDs) form atomically sharp interfaceswith type-II band alignment [1, 2]. This enables theformation of interlayer excitons (IXs) - electron-holeCoulomb bound states between electrons and holes spa-tially separated in different monolayers. The reducedoverlap of the electron and hole wavefunctions gives riseto long IX radiative lifetimes (compared to intralayer ex-citons) [3, 4] that can be further tailored by the momen-tum mismatch between the carriers [5]. The spatial sep-aration of the IXs carriers also results in a large perma-nent electric out-of-plane dipole moment, which enablesa large tunability of the exciton energy by externally ap-plied electric fields [6–8]. The combination of long life-times and large binding energies [9, 10] position IXs inTMD heterostructures as an exciting platform to exploremany-body exciton-exciton phenomena such as dipolarinteractions of IXs in the low density regime [11, 12] orthe high-density regime, where signatures of coherent ex-citonic many-body quantum states and high-temperatureexciton (boson) condensation have been predicted [13–15]and observed [16, 17]. The robust and long-lived IXs inTMD heterobilayers also offer novel opportunities to re-alize atomically-thin optoelectronic devices such as lasers[18] and excitonic transistors that can operate at roomtemperature [19].Beyond the large permanent dipole moment and strongCoulomb interactions, the compelling concept of a moiré superlattice [20] emerges in TMD heterobilayers due tothe lattice mismatch and any relative twist angle betweenthe constituent monolayers. In MoSe /WSe heterobi-layers, the moiré superlattice results in a periodic poten-tial landscape for IXs [21] (with a periodicity that de-pends on the relative crystallographic alignment of thelayers) in which three trapping sites with three differ-ent local atomic registries arise [22–24]. Experimentalevidence of IXs trapped in a moiré-induced potentialhas been reported in MoSe /WSe heterobilayers withtwist angles near 0 ◦ , 21.8 ◦ and 60 ◦ at cryogenic tem-peratures [8, 25, 26]. These localized IXs present emis-sion linewidths below 100 µ eV [8, 25, 26] and photonantibunching [8], clear hallmarks of quantum-confinedexcitons. Moreover, the trapped IXs show well-definedmagneto-optical properties: the g -factors of the trappedIXs depend on the relative valley alignment (i.e., stack-ing configuration) between the layers hosting the carriers,while their optical selection rules are determined by theatomic registry of the trapping site [25, 26]. Together,these magneto-optical properties provide compelling ev-idence for the moiré potential as the origin of the IXtrapping. The important role the moiré potential playsin the confinement of IXs is further supported by thetwist-dependent IX diffusion in TMD heterobilayers, inwhich the diffusion length of the IX ensemble depends onthe moiré periodicity [27, 28]. However, the narrow emis-sion linewidths observed for single trapped IXs contrastwith the broad photoluminescence (PL) spectra observedin similar MoSe /WSe heterostructures [4–7, 16, 29–31],which show IX emission bands with linewidths of − a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n meV in the cleanest samples [6, 16, 30], two orders of mag-nitude broader than single trapped IXs. Such contrastingobservations have opened a debate regarding a unifiedpicture of the nature of IX emission in TMD heterobilay-ers, and in particular in the prototypical heterostructure:MoSe /WSe heterobilayers [32]. To date, clear experi-mental evidence which can marry these two regimes (nar-row linewidth trapped IX vs broad linewidth enesembleIX) is missing. Further, gate doping of MoSe /WSe heterobilayers has been shown to lead to the formationof charged IX (trions) with spin-singlet and spin-tripletconfigurations [7, 33]. However, the trapped or delocal-ized nature of IX trions, and all their possible spin-valleyconfigurations, have yet to be addressed.Here, we investigate the magneto-optical properties ofIXs in a gate-tunable MoSe /WSe heterobilayer. Wetune the density of IXs by scanning the excitation powerover five orders of magnitude and report a clear andcontinuous evolution from the narrow emission of single-trapped IXs to broad ensemble IX peaks, for which IXswith both spin-triplet and spin-singlet configuration areobserved. In the high excitation power regime, we ob-serve an energetic blue-shift of the IXs due to repul-sive dipolar interactions. We estimate the density ofIXs from the power dependent evolution of the IX PLand find that, even at the highest excitation powersemployed in our measurements (80 µ W), the estimateddensity of optically-generated IXs is more than two or-ders of magnitude smaller than the estimated density ofmoiré traps ( ∼ · cm − ) in our heterostructure.Polarization-resolved PL measurements under a verticalmagnetic field confirm that the narrow and broad IX PLpresent identical magneto-optical properties, confirmingthat both the quantum-dot-like and broad PL emissionfrom IXs arise from IXs trapped in moiré potentials withthe same atomic registry. Moreover, we investigate theformation of negatively-charged IX trions and find thatthe trion creation originates from on-site charging of thetrapping potentials. The magneto-optical properties ofthe negatively-charged IXs reveal three different nega-tive trion species with contrasting spin-valley configura-tions. Interestingly, we observe both intervalley and in-travalley IX trions with spin-triplet optical transitions,a consequence of the absence of a dark exciton state inMoSe /WSe heterobilayers. The identification of thevarious neutral and charged exciton species provides newinsight into multiple peaked IX spectra in heterobilayers,while the identification of the localized nature of IX en-semble emission in MoSe /WSe heterobilayers demon-strate the important role of the moiré potential in theirmagneto-optical properties. These findings highlight thenecessity to consider the spatial pinning of the IXs tothe moiré lattice in order to achieve an accurate descrip-tion of many-body exciton-exciton phenomena in TMDheterobilayers. MAGNETO-OPTICS OF SPIN-SINGLET ANDSPIN-TRIPLET NEUTRAL IXs
Figure 1(a) shows a sketch of the dual-gated heterobi-layer device we employ, which consists of a ML MoSe and a ML WSe vertically stacked with a twist angle ∆ θ ∼ . ± . ◦ (2 H stacking). The twist angle in ourheterobilayer is beyond the theoretically proposed criticalangle for lattice reconstruction [34–36], ensuring minimalmoiré domain formation. The heterobilayer was encapsu-lated by hexagonal boron nitride (hBN). Graphene layersact as electrical contacts for the top, bottom and heter-obilayer gates (see Ref. [8] for more details). First, weinvestigate the evolution of the low-temperature (T = 4K) confocal PL spectrum as a function of the IX den-sity (with all gates grounded). The density of optically-generated IXs in our sample can be varied by changingthe power of the continuous-wave excitation laser ( P exc )[37]. We excite resonantly to the 1 s state of the intralayerA exciton in ML MoSe ( λ = 759 nm), and scan P exc over 5 orders of magnitude. Figure 1(b) shows a colorplot of the full evolution of the PL spectrum at a repre-sentative spot in the grounded heterobilayer for 0.4 nW ≤ P exc ≤ µ W, while Fig. 1(c) presents linecuts ex-tracted from Fig. 1(b) for P exc of different orders ofmagnitude. At low excitation powers ( P exc ≤
10 nW),the PL spectrum reveals several discrete narrow emissionlines with energies in the range 1.39 - 1.41 eV, consistentwith recently reported values for neutral IXs trapped inthe moiré potential landscape [25, 26]. Magneto-opticalstudies in WSe /MoSe heterobilayers with 2 H stackinghave shown that the moiré-trapped IXs arise from opticaltransitions involving the lowest spin-orbit-split conduc-tion band of MoSe at ± K [8, 25, 26]. This observationleads to spin-triplet optical transitions for the trappedIXs (see Fig. 1(d)). Although such spin-flip transitionsare normally forbidden in ML TMDs [38], they can bebrightened due to the selection rules dictated by the re-sulting interlayer atomic registry of the heterostructures,as theoretically predicted [24] and experimentally shown[6, 31, 33, 39].For the lowest excitation powers employed, only a fewtens of IX are generated ( ∼
10 to 40 depending on thespatial position in the sample). Figure S1 shows the fullevolution of the PL spectrum measured at a second spa-tial location of the heterobilayer in a similar P exc range.The PL measured at both spatial locations shows thesame overall behavior under increasing excitation power.First, the emission intensity of the few discrete narrowlines saturates with increasing power (see Figs. S2(a)and S2(b)), hallmarks of few-level quantum-confined sys-tems. Simultaneously, as P exc increases, more trappingsites are populated with IX and we progressively losethe ability to resolve individual spectral lines, since theymerge into an IX ensemble band. The IX ensemble bandblue-shifts with increasing P exc . At excitation powers of FIG. 1: Power dependence of moiré-trapped IXs. (a)
Sketch of the dual-gated WSe /MoSe heterobilayer. Graphite layersare used as contacts for top, bottom, and heterobilayer, while hBN layers ( D =
18 nm) are used as dielectric spacers. (b)
Color plot with the full evolution of the low-temperature (T = 4 K) confocal PL spectrum of a representative spot in theundoped heterobilayer for 0.4 nW ≤ P exc ≤ µ W in logarithmic scale. (c)
Linecuts extracted from the color plot in (b)for P exc with different orders of magnitude. The spectra have been shifted vertically and normalized by the values indicatedin the figure for visualization purposes. (d) Schematics of the spin–valley configuration of the proposed optical transitionswith the corresponding selection rules for H hh atomic registry [24]. (e) Magnetic-field dependence of IX PL in the low- andhigh-excitation regimes (bottom and top panels, respectively) for σ + - and σ − -resolved confocal collection (left and right panels,respectively). (f ) Magnetic-field dependence of the Zeeman splitting measured for IX T and IX S at high P exc (top panel), andfor a representative moiré-trapped IX at low P exc . ∼ µ W, a second IX emission peak appears at higherenergy and continuously blue-shifts with increasing P exc .For the highest P exc used in our experiments (80 µ W),the two IX peaks exhibit linewidths between 5 and 10meV (depending on the spatial location on the sample)and consistently exhibit an energy splitting of ∼
24 meV.To unambiguously identify if these peaks arise fromband-edge states at ± K and disentangle the spin–valleyconfiguration of each IX emission band, we performhelicity-resolved magneto-optical spectroscopy measure-ments in the Faraday configuration ( B z ) under linearlypolarized ( π ) excitation at 1.63 eV (759 nm). Figure1(e) shows the magnetic-field ( B z ) dependence of IXPL in the low- and high-excitation regimes (bottom andtop panels, respectively) for σ + - and σ − -resolved con- focal collection (left and right panels, respectively). Aclear Zeeman splitting with increasing B z is observedfor the IX PL in both excitation regimes. The IX T ensemble band observed at high P exc shows the samepolarization dependence with B z as the few individu-ally resolved moiré-trapped IXs. However, the IX S en-semble band presents the opposite polarization. Figure1(f) shows the B z -dependence of the experimental Zee-man splitting ( ∆ E z ) values measured for IX T and IX S (top panel) and a representative single moiré-trapped IX(bottom panel), as extracted from Lorentzian fits of theexperimental data. The Zeeman splitting is defined as ∆ E z ( B z ) = E σ + ( B z ) − E σ − ( B z ) = gµ B B z , with g aneffective g -factor, µ B the Bohr magneton and E σ ± the B z -dependent energies of the IX transitions with σ ± po-larization. Linear fits reveal g -factors of − . ± . , . ± . , and − . ± . for IX T , IX S and themoiré-trapped single IX, respectively. Since the carrierspin, the valley index and the atomic orbital involved inthe optical transitions are associated to a magnetic mo-ment [25, 40–42], the measured g -factors provide valuableinformation about the nature of the transitions. Takinginto account the reported effective masses of m ∗ h = 0 . m and m ∗ e = 0 . m for holes in the topmost valenceband of WSe [43] and electrons in the lowest conductionband of MoSe at at ± K [44, 45] (with m the free elec-tron rest mass), we estimate theoretical g -factor values of − . and . for IX T and IX S transitions, respectively[26]. The good agreement between the experimental andcalculated g -factor values confirms the spin-valley con-figurations of both excitonic transitions and corroboratesthe identification of IX T and IX S in the high excitationregime (see Fig. 1(d) for a level schematic, the opticaltransitions, and the corresponding selection rules [24]), inagreement with recent works [6, 31, 33, 39]. These resultsbring to light a striking property of these IX transitions:unlike counterpart ML TMDs [38, 46], TMD heterobilay-ers do not host dark excitons (i.e. spin-forbidden opticaltransitions). In the rest of the work, we focus on theproperties of the IX ensemble emission peaks with differ-ent spin configurations (IX T and IX S ) observed at highIX densities. DIPOLAR INTERACTIONS OF AN ENSEMBLEOF TRAPPED IXs
To understand the link between the individually re-solved moiré-trapped IX and the ensemble IX emission,we focus on the power-dependent blue-shifts observed inthe PL energy of both IX T and IX S . The peak blue-shiftsoriginate from the repulsive dipolar exciton-exciton inter-action of IXs, which arises as a consequence of the largepermanent electrical dipole moment induced by the spa-tial separation of the exciton carriers [47–50]. The power-dependent energy shifts for IX T ( ∆ E T ) and IX S ( ∆ E S )can be expressed as ∆ E S,T ( P exc ) = E S,T ( P exc ) − E S,T ,with E S,T ( P exc ) and E S,T being the energy of the cor-responding exciton species at P exc and vanishing exci-tation, respectively. Such excitation-dependent energyshifts can be quantitatively estimated using the plate ca-pacitor formula [47, 48]: ∆ E S,T ( P exc ) = 4 πN S,T ( P exc ) e d/(cid:15), (1)where N S,T is the exciton density of the corresponding IXconfiguration, e is the electron charge, d is the interlayerdistance, and (cid:15) is the dielectric constant. Figure 2(a)shows the ratio of integrated PL intensities between theIX T and IX S peaks as a function of P exc extracted fromFig. 1(b) (black dots). The inset shows the evolution ofthe integrated PL intensities for each individual peak in the same P exc range. In the range of P exc for which bothpeaks coexist, we observe the intensity ratio decreasesfrom ∼
105 to ∼ P exc . To evaluate thePL intensities of the two IX species peaks quantitatively,we employ a rate equation model (see supplementary in-formation). The solid lines in Fig. 2(a) represent fitsof the experimental data for both the PL intensity ratio(red) and the PL intensities of the IX T (blue) and IX S (green) peaks to the rate equation model. The fits allowus to confidently estimate the power-dependent relativedensities of IXs with spin-singlet ( N S ) and spin-triplet( N T ) configurations. Next, we show in Fig. 2(b) theexperimentally-measured energy splitting between IX S and IX T ( ∆ E S − T ), where we observe that increasing P exc gives rise to a reduction of ∆ E S − T by up to 3 meV, wellbeyond the uncertainty associated to the experimentaldetermination of the energy splitting. From Eq. (1), thedensity-dependent ∆ E S − T can be calculated as ∆ E S − T = ∆ E S − T + ∆ N S − T ( P exc )4 πe d/(cid:15), (2)with ∆ E S − T = E S − E T and ∆ N S − T ( P exc ) = N S ( P exc ) − N T ( P exc ) . From Eq. (2) it is straightfor-ward to see that the decrease of ∆ E S − T with increasing P exc has its origin in the higher density of IX T in therange of P exc used in our experiments, which leads to ∆ N S − T ( P exc ) < . Figure 2(b) shows the fit of the ex-perimental ∆ E S − T (black dots) to Eq. (2) (red solidline), where we have used the relative IX densities shownin 2(b), and have assumed d = 0.7 nm [12] and (cid:15) = 7 . (cid:15) [51], with (cid:15) the vacuum permittivity. The inset showsa comparison of the experimental and calculated energyshift for each individual exciton band. The good agree-ment between the experimental and calculated values al-lows us to estimate the order of magnitude of the absolutedensities for IXs ( N IX ) with both spin configurations.This analysis sheds light on the nature of the IX PLemission bands observed at high P exc . The stacking an-gle in our heterostructure ( ∆ θ = 56 . ± . ◦ [8]) givesrise to an estimated density N total ∼ . · cm − of moiré trapping sites with three different local atomicconfigurations: ( H hh , H Xh and H Mh [22], where H µh de-notes an H -type stacking with either h the hexagon cen-tre, X the chalcogen site or M the metal site verticallyaligned with the hexagon centre ( h ) of the hole layer. N total yields a density N moir ´ e = N total / ∼ . · cm − of moiré sites with the same atomic registry, as in-dicated by the black dashed line in Fig. 2(c). Figure 2(c)shows that, even for the highest excitation powers usedin our experiments, the estimated densities of optically-generated IXs are more than two orders of magnitudesmaller than N moir ´ e ; less than 1 % of the moiré sites arefilled with IXs. The orange shaded area in Fig. 2(c)represents the estimated N moir ´ e for MoSe /WSe heter-obilayers with stacking angles ranging from 54 ◦ to 59 ◦ ,showing that this conclusion holds true even for largeuncertainties in the determination of the stacking angle. FIG. 2: Dipolar interactions of an ensemble of trapped IXs. (a)
Ratio of integrated PL intensities between the IX T and IX S peaks (IX T /IX S ) as a function of P exc extracted from Fig. 1(b) (black dots). The inset shows the evolution of the integrated PLintensities for each individual peak in the same P exc range. The red, blue and green solid lines represent fits of the experimentaldata to the rate equation model described in the Suppl. Mat. (b) Energy splitting between IX S and IX T ( ∆ E S − T ) as afunction of the excitation power (black dots). The inset shows the energy shifts of the individual peaks. The red solid linerepresents a fit of the experimental ∆ E S − T to Eq. (2), while the green and blue solid lines are fits of the measured ∆ E S,T toEq. (1). (c)
Estimated power-dependent densities of IXs with spin-singlet (green) and spin-triplet (blue) configurations. Theblack dashed line indicates the density of moiré traps estimated for our heterostructure, while the orange shaded area representsthe density of sites for MoSe /WSe heterobilayers with stacking angles ranging from 54 ◦ to 59 ◦ . (d) Sketch depicting thetransition between the low- and high-excitation power regimes for IXs (red spheres) trapped in the moiré sites of a MoSe /WSe heterobilayer. At low P exc , only a few IXs are a localized in the moiré sites lying inside the circular confocal collection spot(not to scale). As P exc increases, more and more optically-generated IXs are trapped in the moiré sites, giving rise to a broadPL emission band originating from an ensemble of moiré-trapped IXs. Even at the highest P exc used in this work, less than of moiré sites contain trapped IXs. We note that the highest N IX achieved in our exper-iments corresponds to the lowest N IX investigated byWang et. al. , who reported an optically driven Motttransition from IXs to a charge-separated electron andhole plasmas in a 3 R -MoSe /WSe heterobilayer with asimilar moiré period ( ∆ θ = 4 ◦ ) for N IX > · cm − (i.e., for N IX > N moir ´ e ) [37].Our results represent a bridge between the quantum-dot like [8, 25, 26] and the broad PL emission peaks [4–7, 16, 29, 31] previously observed for IX ensembles inMoSe /WSe heterobilayers at different excitation pow- ers. Figure 2(d) shows a sketch depicting the transitionbetween the low- and high-density regimes. At low P exc ,only a few IXs (red spheres) are localized in the moirésites lying inside our circular confocal collection spot (notto scale). The spatial and spectral isolation of thesetrapped excitons is likely aided by dipolar repulsion,which minimizes the probability for excitons to populateneighboring moiré sites. As P exc increases, more andmore optically-generated IXs are trapped in the moirésites, giving rise to a broad PL emission band originat-ing from the ensemble of moiré-trapped IXs. Even at the FIG. 3: Interalyer exciton trions in WSe /MoSe . (a), (b), Gate-voltage controlled PL of IXs in the neutral ( < V g ≤ . V) and electron doping regime ( V g ≥ . V) at B z = 0 T, and P exc = 20 nW (a) and P exc = 40 µ W (b) at 4 K. (c) , Linecutsextracted from the color plots in (a) and (b) (black and red solid lines, respectively) in the neutral ( V g = 0 V) and electrondoping regimes ( V g = 0 . V). The spectra have been normalized by the values indicated in the figure, and the linecuts at V g = 0 . V have been shifted vertically for visualization purposes. The dashed vertical lines indicate the central energies ofthe different ensemble peaks, illustrating the power-induced blue-shift ( ∆ E ( P exc ) ) and the energy splittings arising from thebinding energies of the charged IXs with spin triplet ( ∆ E IX T ) and spin singlet ( ∆ E IX S ) configuration. highest P exc used in this work, less than 1 % of moiré sitescontain trapped IXs. This behaviour agrees well with themagneto-optical properties measured for single confinedIXs and the IX T ensemble PL band. The polarization se-lection rules of moiré-trapped excitons are dictated by thelocal atomic registry of the moiré trapping site [22, 24].The same optical selection rules observed for both sin-gle confined IXs and the IX T ensemble PL band indicatethat only moiré sites with a local atomic registry H hh areresponsible for the IX trapping [8, 25, 26, 39]. Moreover,the optical selection rules of the IX S ensemble PL peaksfurther corroborate this affirmation, since H hh is the onlylocal atomic registry in H -stacked TMD heterobilayersthat results in opposite circularly-polarized transitionsfor IXs with spin-triplet and spin-singlet configurations[24]. We note that for MoSe /WSe heterobilayers with R -stacking (i.e. ∆ θ ∼ ◦ ), the magneto-optical selec-tion rules suggest that the PL emission at high excitationpower arises from spin-singlet and spin-triplet IXs witha local stacking registry R Xh [6, 33]. SPIN-VALLEY CONFIGURATIONS OFNEGATIVE IX TRIONS IN 2 H -MoSe /WSe In this section, we investigate the formation of neg-atively charged trapped IXs with both spin-triplet andspin-singlet configuration. The Fermi energy in ourWSe /MoSe heterobilayer can be continuously tunedwith an external gate voltage V g . The color plots of Figs. 3(a) and 3(b) show the effects of electron dop-ing on the PL of the trapped IXs at low ( P exc = 20 nW) and high ( P exc = 40 µ W) excitation powers, respec-tively. The V g -dependent evolution of the IX PL showsthe same overall behaviour for both low and high IX den-sity regimes. For < V g (cid:46) . V, the PL spectrum isdominated by neutral excitons: IX T at low IX density(Fig. 3(a)), and both IX T and IX S at high IX density(Fig. 3(b)). At high IX density, the IX T and IX S ensem-ble peaks present linewidths of ∼ . meV and ∼ meV,respectively, on par with the cleanest MoSe /WSe sam-ples [6, 16, 30]. For V g (cid:38) . V, new red-shifted peaksappear at energies ∼ ∼
4) meV below the IX T (IX S )peaks, indicating the formation of negatively charged IXtrions with different spin configurations (see linecuts inFig. 3(c)). The measured energy differences betweenthe neutral and charged exciton peaks are attributed tothe binding energies of the charged IXs, in good agree-ment with recently reported values for MoSe /WSe het-erostructures with R stacking [7, 33]. The new trionpeaks coexist with IX T and IX S for a short range ofapplied voltages until IX T and IX S eventually vanishwith increasing V g . We note the observation of IX tri-ons in the quantum emitter (low-excitation) regime isnovel. At high excitation powers, the PL spectrum inthe n -doped region shows broad emission shoulders inboth the low- and high-energy tails of the IX trion peakwith spin-triplet configuration (IX − T,inter ). In order tospectrally resolve the emission bands, we plot the PL ofIXs for n doping ( V g = 2 V) as a function of P exc (see FIG. 4: Interalyer exciton trions in WSe /MoSe . (a) Color plot with the full evolution of the PL spectrum of negative IXtrions for 0.2 nW ≤ P exc ≤ µ W at V g = 2 V in logarithmic scale, in which four different peaks can be resolved (as indicatedby the arrows). (b)
PL spectrum acquired for the intermediate P exc value indicated by the white dashed line in (a) (2 µ W) at V g = 2 V, fitted to four lorentzian peaks corresponding to various exciton species: IX − T,inter (blue), IX − T,intra (gray), IX − S,inter (green), and IX − (cid:48) T (red). (c) Schematic representation of the charge configurations for IX − T,inter (left), IX − T,intra (middle) andIX − S,inter (right) showing the optical transitions that involve a hole in the the topmost valence band of WSe at K . Fig. 4(a)). Figure 4(b) shows the PL spectrum acquiredfor an intermediate P exc value of 2 µ W at V g = 2 V,as indicated by the white dashed line in Fig. 4(a). Atthis excitation power, we clearly resolve four emissionpeaks. The brightest peak in the spectrum (at ∼ − T,inter ). At higher emission energies,we observe two additional peaks with an energy splittingof ∼
12 meV. These two peaks show a similar integratedPL intensity across the entire range of P exc (see Fig. S3),suggesting that their corresponding charge configurationsinvolve the same band-edge energy levels. We attributethe low energy and high energy peaks of this doublet tointravalley (IX − T,intra ) and intervalley (IX − S,inter ) trionswith spin-triplet and spin-singlet configuration, respec-tively. Figure 4(c) shows a schematic representation ofthe charge configurations for IX − T,inter (left), IX − T,intra (middle), and IX − S,inter (right) with optical transitions that involve a hole in the the topmost valence band ofWSe at K .The PL spectrum in Fig. 4(b) also shows a broademission peak at lower energies than IX − T,inter (IX − (cid:48) T ).Although its origin is not yet fully understood, this fea-ture has also recently observed in the reflectivity of n -doped ML WSe [52, 53] and the PL of n -doped MoS [54, 55] and attributed to either a Mahan-like exci-ton [54] or an exciton-plasmon-like excitation [52, 53].We find that contrary to the behaviour of IX − T,inter ,IX − S,inter and IX − T,intra , the integrated emission intensityof IX − (cid:48) T increases with the carrier concentration (see Fig.S4). Moreover, increasing the electron concentration alsoleads to a linear increase of the energy splitting betweenIX − T and IX − (cid:48) T (see Fig. S4).Finally, the charge configurations for the differentcharged exciton species depicted in Fig. 4(c) highlight astriking difference between IX − S,inter and IX − T,intra . Un-like IX − S,inter , in which the photon emission arises fromelectron-hole recombination between the topmost VBand the top spin-split CB, the absence of a dark excitonground state in MoSe /WSe heterostructures enablesthe electron-hole recombination between the topmost VBand the bottommost spin-split CB for IX − T,intra . This be-haviour contrasts with intravalley negative trions in W-based TMDs, in which both intravalley and intervalleynegative trions present electron-hole recombination in-volving the same top spin-plit CB [56]. Moreover, sinceIX − S,inter is the only trion species in which the electron-hole recombination involves the top spin-split CB, the V g -dependent relative integrated PL intensities of the dif-ferent trion species should provide an estimate of the en-ergy splitting between the spin-split CBs in MoSe [33].We observe that the PL intensity from IX − S,inter overtakesthe combined PL intensity from IX − T,inter and IX − T,intra at V g ∼ ∼
21 meV, in good agreement withthe calculated spin-orbit splitting of MoSe conductionbands at ± K (23 meV) [57]. Therefore, the spin-valleyconfigurations depicted in Fig. 4(c) for the different trionstates suggest that, contrary to intravalley negative tri-ons in W-based TMDs, although IX − S,inter and IX − T,intra involve the topmost CB, they should present differentmagneto-optical properties.
MAGNETO-OPTICS OF NEGATIVE IX TRIONS
To investigate the magneto-optical properties of thedifferent trion peaks, we measure PL as a function of B z at P exc = 40 µ W and V g = σ + - (purple) and σ − -polarized (orange) col-lection in the range ≤ B z ≤ T. The results reveala clear Zeeman splitting for the three IX trion species:a positive vertical B z field leads to a red-shift of the σ + -polarized emission for both IX − T,inter and IX − T,intra ,while it induces a slight blue-shift of the σ + -polarizedemission for IX − S,inter . Such contrasting behaviour canalso be seen in the experimental Zeeman splitting ofeach IX trion species as shown in Fig. 5(b): IX − T,inter and IX − T,intra present negative slopes (negative g -factor),whereas X − S,inter exhibits a positive one. Linear fitsof the measured Zeeman splittings reveal g -factors of − . ± . , − . ± . and . ± . for IX − T,inter ,IX − T,intra and IX − S,inter , respectively. The extracted val-ues show that IX − T,inter and IX − S,inter have g -factors withopposite signs and different magnitudes, as previously ob-served for IX T and IX S in the results shown in Fig. 1(f).More importantly, the fits also reveal that IX − T,inter andIX − T,intra present g -factors with the same sign and very FIG. 5: Magneto-optical properties of interlayer exciton tri-ons in the IX denisty regime. (a)
Magnetic field dependenceof the IX trions PL for σ + - (purple) and σ − -polarized (or-ange) collection in the range ≤ B z ≤ T under V g =
1V and P exc = 40 µ W. (b) Zeeman splitting of each IX exci-ton species (dots) as extracted from fits of the experimentaldata shown in (a). The solid lines represent linear fits of theexperimental data. similar magnitude, which confirms that the electron-holerecombination in these trions involve the same exact con-duction and valence band states, confirming the originof the IX − T,intra peak. We note that the particular bandalignment and optical selection rules in 2 H -MoSe /WSe heterobilayers allow the formation of intervalley and in-travalley IX trions by optical pumping of both the up-per and lower CBs of MoSe even in the neutral dopingregime (see Suppl. Note 6). These results suggest theimportance of revisiting the interpretation of multiple IXemission peaks in previous reports. Finally, the fits re-veal a dependence of the trions g -factors with the carrierconcentration. Figure S7 shows the evolution of the g -factors of the brightest peak in our spectra (IX − T,inter ) asa function of electron doping. Similar to the case of the g − factor of quasiparticles in a 2D electron gas [58], andintralayer exciton polarons in ML TMDs [59–61], we ob-serve a change of g with increasing electron doping. Thischange in the effective g -factors with increasing carrierdoping has been attributed to many-body interactionsand phase space filling effects [60, 61].Figure 5(b) also shows the measured Zeeman splittingfor the excitonic feature IX − (cid:48) T . The observed negativeslope in the Zeeman splitting of this peak with increas-ing B z reveals similar selection rules to IX − T,inter . How-ever, similar to the exact origin of IX − (cid:48) T , the extracted g -factor of − . ± . is not yet understood. Finally,we note a quadratic red-shift of the central energy of theZeeman-split peaks of the IX ensemble peaks with in-creasing magnetic field (see Fig. S8), which is absentfor low IX densities, highlighting the importance of thestrong exciton-exciton interactions at high IX densities. CONCLUSION AND PERSPECTIVES
In summary, we investigate neutral and negativelycharged IXs trapped in moiré confinement potentials ina gate-tunable 2 H -WSe /MoSe heterostructure. Thehomogeneous linewidths of the ensemble IX peaks wefind in our sample ( ∼ T ) and spin-singlet (IX S ) configu-rations are identified. The IX ensemble peaks energet-ically blue-shift with increasing density due to dipolarrepulsion. From this effect, we are able to estimate N IX and find that even at the highest IX density we mea-sure, N IX << N moir ´ e . We discover that the magneto-optical properties of the trapped IX are identical, re-gardless of their density: both the narrow quantum-dot-like and broad ensemble IX emission originate from IXslocalised in moiré potential traps with the same localatomic registry ( H hh ). Moreover, the optical selectionrules of the IX S ensemble further corroborate this af-firmation, since H hh is the only local atomic registry in H -stacked TMD heterobilayers that results in oppositecircularly-polarized transitions for IXs with spin-tripletand spin-singlet configurations.Next, the Fermi energy was tuned to create negativelycharged moiré trapped IX, which we observe in both thelow- and high-density IX regimes. To our knowledge, the observation of charged moiré trapped IX in the low-density regime is novel, and an exciting avenue for futureinvestigations. Binding energies for the on-site negativelycharged IX are found to be 7 meV (4 meV) for the spin-triplet (spin-singlet) trion configuration. Our magneto-optical measurements at high IX densities reveal a finestructure for negative IX trions with spin-triplet con-figuration; we clearly resolve intravalley (IX − T,intra ) andintervalley (IX − T,inter ) IX trions. We note that, usingmoderate excitation powers, the formation of intervalleyand intravalley IX trions is observed even in the neutraldoping regime. This creates a multi-peaked PL spec-trum consisting of six possible neutral and charged IXspecies (IX T , IX S , IX − T,intra , IX − T,inter , IX − S,intra , andIX − (cid:48) T ). These results suggest it could be fruitful to re-visit previous interpretations of multiple peaked IX spec-tra from MoSe /WSe heterobilayers in previous reports,particularly those using ungrounded devices and high ex-citation powers.We remark that the unified picture of narrow linewidthIX emitters and broad ensemble IX peaks reconcilescontrasting IX spectra reported from nominally similarWSe /MoSe heterobilayer samples. This provides fur-ther valuable evidence about the nature of quantum emit-ters in moiré heterostructures, complementing previousresults [8, 25, 26]. So, although the narrow linewidthpeaks have an inhomogeneous energy distribution simi-lar to defect-related single photon emitters in 2D mate-rials, the properties of the moiré quantum emitters areidentical to the ensemble IX and arise from the intrinsicsymmetry of the moiré confining potential at the specificatomic registry. Further, in the low-excitation regime,spatial isolation of trapped IX is likely aided by dipolarrepulsion, which minimizes the probability for excitonsto populate neighboring moiré sites. Finally, in the high-excitation regime, the results highlight the importance ofconsidering the spatial pinning of the ensemble IXs to themoiré lattice in order to achieve an accurate descriptionof many-body exciton-exciton phenomena in TMD het-erobilayers: the dipole interactions will depend on, andcan be tuned by, the twist angle. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] M.-H. Chiu, C. Zhang, H.-W. Shiu, C.-P. Chuu, C.-H.Chen, C.-Y. S. 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