Electrically controlled quantum confinement of neutral excitons in 2D semiconductors
Deepankur Thureja, Atac Imamoglu, Alexander Popert, Kenji Watanabe, Takashi Taniguchi, David J. Norris, Martin Kroner, Puneet A. Murthy
EElectrically controlled quantum confinement of neutral excitons in 2D semiconductors
Deepankur Thureja,
1, 2
Atac Imamoglu, ∗ Alexander Popert, Kenji Watanabe, Takashi Taniguchi, David J. Norris, Martin Kroner, and Puneet A. Murthy † Institute for Quantum Electronics, ETH Zurich, Zurich, Switzerland Optical Materials Engineering Laboratory, Department of Mechanicaland Process Engineering, ETH Zurich, Zurich, Switzerland National Institute for Materials Science, Tsukuba, Ibaraki, Japan
Achieving fully tunable quantum confinement of excitons has been a long-standing goal in opto-electronics and quantum photonics. We demonstrate electrically controlled 1D quantum confinementof neutral excitons by means of a lateral p-i-n junction in a monolayer transition metal dichalco-genide semiconductor. Exciton trapping in the i-region occurs due to the dc Stark effect induced byin-plane electric fields. Remarkably, we observe a new confinement mechanism arising from the re-pulsive polaronic dressing of excitons by electrons and holes in the surrounding regions. The overallconfinement potential leads to quantization of excitonic motion, which manifests in the emergenceof multiple spectrally narrow, voltage-dependent resonances in reflectance and photoluminescencemeasurements. Additionally, the photoluminescence from confined excitonic states exhibits high de-gree of linear polarization, highlighting the 1D nature of quantum confinement. Electrically tunablequantum confined excitons may provide a scalable platform for arrays of identical single photonsources and constitute building blocks of strongly correlated photonic many-body systems.
Confining particles to lengthscales comparable to theirde Broglie wavelength leads to discrete eigenstates, whichreveals their quantum mechanical nature, an effect knownas quantum confinement. The experimental realizationof this fundamental effect has enabled the direct obser-vation and manipulation of individual quantum statesand their superpositions in various branches of physics,from condensed matter to ultracold atoms and trappedions. In semiconductor systems, quantum confinementis typically achieved by modulation of material proper-ties [1, 2], which has led to groundbreaking discoveriessuch as integer and fractional quantum hall effects in2D electronic gases [3, 4], photon antibunching and en-tanglement in quantum dots [5, 6], and Bose–Einsteincondensation of exciton-polaritons in microcavities [7].However, this approach crucially lacks in-situ tunabilityof the confining potentials, particularly along the planardimensions. For instance, creating ensembles of identi-cal, individually controlled quantum dots or wires withdeterministic position is extremely challenging using ma-terial modulation. This has hindered the application ofthese methods for quantum information processing andrealizing strongly correlated photonic states.Electrically induced quantum confinement provides aremedy to this problem, but has so far been shown onlyfor charged particles [8–12]. Achieving electrically tun-able quantum confinement of neutral excitons (boundelectron-hole pairs) would provide the crucial advantageof optical addressability of individual quantum states,and therefore has been a long-standing goal of opto-electronics and quantum photonics. Here, we exploitthe unique properties of monolayer Transition MetalDichalcogenide (TMD) semiconductors to demonstrate ∗ [email protected] † [email protected]
1D quantum confinement of neutral excitons with fullelectrical control.Neutral excitons are intrinsically more challenging toelectrically confine than charged particles. One possibleroute for exciton confinement involves the dc Stark ef-fect which ensures that the lowest energy excitons seean attractive potential around the maximum of an inho-mogeneous electric field distribution. However, achiev-ing quantum confinement in such a potential requiresthat the energy splitting between discrete motional ex-citonic states ( (cid:126) ω ) exceed the exciton line broadeningΓ as well as the characteristic energy of thermal fluctu-ations k B T . For excitons in GaAs heterostructures orTMD monolayers at T = 4 K, this implies (cid:126) ω (cid:38) (cid:96) = (cid:112) (cid:126) /m X ω (cid:46)
10 nm for an exciton mass m X ∼ elec-tron mass m e . Unless the exciton binding energy is muchlarger than (cid:126) ω , the requisite applied fields will lead tofast ionization of the excitons, drastically reducing theirradiative efficiency.Previous experiments have mainly approached thisproblem by relying on indirect excitons, where the elec-tron and hole comprising an exciton are spatially sepa-rated in different quantum wells, giving rise to a perma-nent electric dipole moment that couples more stronglyto the applied fields. In III-V semiconductor heterostruc-tures with coupled quantum wells, different potentiallandscapes have been demonstrated for indirect excitons,such as ramps, lattices, and harmonic traps [13–17]. Evenin these systems however, the requirement to suppress ex-citon ionization [18] prevented the observation of quan-tum confinement. Moreover, because the quantum wellstypically need to be buried deep within the heterostruc-ture, the electric field gradients that can be applied usinglithographically patterned gates outside the structure arelimited.We solve these problems by realizing a lateral p-i-n a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b FIG. 1.
Exciton confinement in lateral p-i-n junctions. ( A ) Schematic side view of the device. Applying a voltagebias between the top and bottom gates leads to inhomoge-neous in-plane electric fields (dashed black lines) along theedge of the gate, which are strongest in the p-i-n regime wherethe monolayer is electron doped (red) and the region under-neath the top gate is hole doped (blue). The band structureof the semiconductor near the edge of the top gate is illus-trated in ( B ). ( C ) The spatial dependence of the in-plane fieldstrength F x (blue line) and the total charge density σ (dashedblack line) obtained from electrostatic simulations. ( D ) Thetotal confining potential for excitons (black line) stems fromthe dc Stark effect due to the in-plane electric field (blue line)and the repulsive polaronic dressing of the exciton by itinerantholes and electrons in the neighbouring doped regions. Theenergy shifts arising from each of these effects are indicatedin D . The tight potential leads to quantization of excitonicmotion with level separation (cid:126) ω ∼ − . diode in a TMD monolayer embedded in a van der Waals(vdW) heterostructure. Here, p, i and n refer to p-doping, insulating, and n-doping of adjacent spatial re-gions of the device. The electrostatic landscape of the p-i-n structure naturally creates a narrow i-region for neu-tral excitons with strong inhomogeneous in-plane elec-tric fields, without requiring lithographic patterning atnanoscopic scales. We take advantage of the following keyfeatures of TMD heterostructures: (i) the ultra-strongexciton binding energy characteristic of all TMD mono-layers [19] renders the excitons resilient against ioniza-tion even under very strong applied electric fields up to ∼ . A . We consider a device which in-cludes a TMD monolayer encapsulated by insulating di-electric spacer layers and two metallic gate electrodes(top gate, TG; bottom gate, BG) with partial spatialoverlap as shown. This gate structure allows to sepa-rately define adjacent p- and n-doped regions, and gen-erate in-plane electric fields along the top gate edge. Theband diagram in this scenario is illustrated in Fig. 1 B ,which shows the position of the Fermi level relative tothe conduction (CB) and valence (VB) bands and definesthe doping in different regions. Electrostatic simulationsof such a p-i-n device provide a quantitative picture ofthe spatial and voltage dependence of the charge density( σ ( x )) and in-plane electric field ( F x ) distribution in thevicinity of the TG, as shown in Fig. 1 C [20]. The simu-lations indicate that a neutral junction region as narrowas 30 nm can be achieved in realistic devices with highlyinhomogeneous in-plane electric fields and steep chargedensity gradients.Exciton confinement in the i-region of this device pri-marily arises from the strong in-plane electric field ( F x )which polarizes the excitons along x and lowers their en-ergy due to a dc Stark shift ∆ E S = − α | F x | , where α is the exciton polarizability [21]. Since F x vanisheson either side of the i-region (Fig. 1 C ), excitons expe-rience an attractive confining potential towards the lo-cal maximum in F x ( x ). In addition, we have discov-ered a new mechanism of confinement that stems frominteractions of neutral excitons with itinerant holes andelectrons present on either side of the i-region [22, 23].Excitons generated in the i-region become repulsive po-larons as they enter the n- or p- doped regions, wherethey experience an effective, charge-density ( σ ( x )) de-pendent positive mean field shift ∆ E P ∼ g · σ ( x ), whichincreases their energy. The proportionality constant g isthe exciton-electron coupling strength empirically deter-mined from optical spectroscopy measurements of doped2D heterostructures. Therefore, a gradient in charge den-sity results in a force applied on excitons, as shown in [24].In our case, the steep charge density gradient on bothsides of the i-region (Fig. 1 C ) leads to a tightly confiningrepulsive potential barrier even for exciton energies largerthan the free, zero-momentum, exciton energy ( E X ).The total potential for excitons in the p-i-n configura-tion, V ( x ) = − αF x ( x ) (cid:124) (cid:123)(cid:122) (cid:125) dc Stark Shift + g · σ ( x ) (cid:124) (cid:123)(cid:122) (cid:125) Polaron shift , (1)is the sum of the dc Stark shift (blue line) and repul-sive polaron shift contributions. This potential providesconfinement only for excitons - which are bound electron-hole pairs - whereas unbound electrons or holes experi-ence a repulsive potential that accelerates them towards FIG. 2. van der Waals heterostructure for exciton confinement. ( A ) Optical micrograph of the sample studied in thiswork. The dashed white line corresponds to the outline of the monolayer MoSe flake. The inset shows an AFM scan of the splitgate (inset scale bar: 200 nm). ( B ) Typical broadband reflectance spectra of the encapsulated TMD monolayer as a functionof V BG , taken at a position away from the TG (marked by ∗ in A ). This shows the exciton resonance in the charge neutralregime and the attractive and repulsive polaron branches that emerge in the electron and hole doped regimes. ( C ) Applyinga negative V TG depletes the region below the TG leaving only a narrow 1D channel for electron transport, which is effectivelypinched off at large negative V TG . Source-drain measurements as a function of V TG for different V BG show a nonlinear step-likerise in current, indicating confinement of electrons in the 1D channel. the n- and p-doped regions respectively. The excitonconfinement strength achieved with such a potential de-pends on the geometry of the device and the excitonicproperties of the material. We calculate the potentialshape using the following parameters in our simulations: α = 6 . / V (for MoSe ) [21], m X = 1 . m e [25–27], g = 1 . µ eV µ m , and h-BN thickness of 30 nm. InFig. 1 D , we show the overall potential (black line) andthe dc Stark contribution (blue line) using the in-planeelectric field and charge density distribution obtained forbottom gate voltage V BG = 4 . V TG = − V . Interestingly, at large charge densities( σ (cid:38) cm − ), the polaronic confinement is almosta factor of 3 larger than the dc Stark shift confinement.The discrete eigenstates in the confining potential have alevel separation (cid:126) ω x ≈ − . (cid:96) ≈ − encapsulated by ∼
30 nmthick h-BN flakes and contacted with palladium elec-trodes which enable doping of the monolayer. An opticalmicrograph of the heterostructure is shown in Fig. 2 A .The global doping level is tuned by applying voltage onthe gold BG that almost encompasses the entire MoSe flake. A 13 nm-thick gold TG in the shape of a narrowstrip running across the flake allows to locally modifythe charge density underneath. The thin TG is opti-cally transparent, allowing to probe optical properties inthe region underneath the gate and along its edge. A100 nm wide gap in the TG is created to investigate elec-tron transport through nano-constrictions. By applyingvoltages of opposite polarity to the TG and BG, it is pos-sible to simultaneously generate hole and electron dopedregions in the monolayer MoSe . To study the optical properties of the sample at liquidhelium temperature, we perform broadband reflectanceand photoluminescence (PL) spectroscopy through a highnumerical aperture lens focused at different positions onthe sample. In Fig. 2 B , we show typical reflectancespectra as a function of V BG taken at position awayfrom the TG, which is marked with a star-symbol inFig. 2 A . In the charge neutral region ( − . (cid:46) V BG (cid:46) − . E X = 1642 meV. As the monolayer is globally dopedwith electrons ( V BG > − . V BG < − . C , we show source-drain (S-D) current through the split-gate channel, as a function of V TG for different Fermi energies set by V BG and fixed S-Dvoltage V SD = 2 V. The fact that the 100 nm wide channelcan be completely pinched off at a certain V TG demon-strates that a region of width ∼
50 nm around the TGcan be depleted of electrons. As expected, for larger V BG corresponding to larger global Fermi energy, the channelpinch-off occurs at more negative V TG . As the channel isopened by increasing V TG , we observe a non-linear step-like increase in the current, indicating the strong electronconfinement in the transverse ( y ) direction of the meso-scopic 1D channel [9, 11, 28].In order to study the modification of excitonic statesdue to confinement in the narrow depleted region aroundthe TG as discussed above, we measure the optical re-sponse of the TMD monolayer by positioning the opticalspot on the edge of the TG (see top left inset in Fig. 3 C ).We emphasize that due to the diffraction-limited spotsize of our optical setup, our measurements correspondto the combined optical response of three distinct spatialregions: (I) the electron-doped region away from the TGthat is affected only by the BG, (II) the region directlyunderneath the TG, and (III) the narrow region betweenI and II. The contribution of region I to the total opticalresponse remains unchanged as V TG is varied. Therefore,to discern the influence of the TG alone, we measure V TG -dependent spectra for fixed values of V BG and subtractthe reflectance spectrum obtained for V TG = 0 V fromthe total signal to obtain the normalized differential re-flectance, ∆ RR = R ( V TG ) − R ( V TG = 0) R ( V TG = 0) . (2)In Fig. 3 A , we present ∆ R/R as a function of V TG at fixed V BG = 4 V. First, we identify the typical doping-dependent optical response from region II directly under-neath the TG (Fig. 2 B ). This includes a neutral regime( X : − (cid:46) V TG (cid:46) − − : V TG (cid:38) − + : V TG (cid:46) − + shows that, when region I is electron-doped, hole dopingof region II is possible even without direct electrical con-tacts. We speculate this to be an optical doping effectstemming from exciton-dissociation, as discussed in [20].In addition to the expected optical response, we ob-serve a plethora of narrow and discrete spectral lineson the hole-doped side for V TG (cid:46) − V TG . These narrow linesare consistently found at all positions investigated alongthe edge of the TG, but disappear as we move away fromthe TG edge. PL measurements at the same positionon the sample, shown in Fig. 3 C , also reveal red shiftingdiscrete emission lines similar to the reflectance spectra.The PL spectrum at V TG = − C , which show a series of four lines that becomemonotonously weaker with increasing energy. As a func-tion of V TG , the PL counts of each line also decreases withmore negative voltage, ultimately becoming too weak todiscern for V TG < − B , we show spectral linecuts taken at V TG = − . − . − . V ( x ), Eq. (1)) for those volt-ages obtained from electrostatic simulations. We quan-titatively analyze the discrete lines by fitting a superpo-sition of Lorentzian functions to the reflectance spectra[20]. The resonance frequencies of the discrete states inreflectance (blue circles) and PL (red circles) thus ob-tained are plotted in Fig. 3 D . The fits reveal a level sep-aration (cid:126) ω x ∼ . V TG = − ∼ µ eV,which is more than an order of magnitude narrowerthan the linewidth of the 2D exciton X (Γ ∼ B ) away from the TG. Interestingly, we observeadditional fine structure of some of the discrete states ata V TG (cid:46) − D , [20]).The lowest energy narrow resonances that red shift withdecreasing V TG are fully consistent with the presence ofan attractive potential due to dc Stark effect that low-ers the neutral exciton energy in a spatially dependentway. Further evidence for confinement is provided bythe dramatic reduction of the linewidth of the individ-ual states compared to the free exciton. This is expectedto stem from two factors: (i) reduced radiative decay of1D excitons as compared to their 2D counterparts, and(ii) lower inhomogeneous broadening as the exciton mo-tion is restricted to a smaller spatial area due to confine-ment. We remark that the reduced electron-hole wave-function overlap originating from the permanent in-planeelectric dipole moment induced by the in-plane electricfield should result in a further reduction of the radiativedecay rate.Remarkably, we also observe quantized modes with en-ergy higher than the 2D exciton energy E X , that splitfrom the repulsive-polaron branch of the p-doped region(RP + ). We attribute these resonances to the additionalexciton confinement due to repulsive exciton-charge in-teractions in the neighboring n- and p-doped regions (seethe second term in Eq. (1)). This interaction-inducedpolaronic confinement is in fact dissipative in naturedue to the non-radiative decay of repulsive polarons intothe lower attractive branch, the rate of which increaseswith charge density. Specifically, the dissipation arisesfrom the spatial component of the excitonic wavefunc-tion which leaks into the charged regions. As a conse-quence, the linewidth of the confined states increases aswe progress up the ladder of states, accompanied by a lossof oscillator strength. To the best of our knowledge, thisis the first example of a trapping mechanism that relies onmany-body interactions between a mobile impurity anda surrounding medium. Understanding the dynamics ofexcitons in such non-Hermitian confining potentials con-stitutes an interesting problem for future investigations.A comparison of the reflectance and PL measurements(Fig. 3 D ) reveals a pronounced discrepancy in the volt-age dependence of confined exciton resonances for V TG (cid:46) − − < V TG < − FIG. 3.
Optical signatures of quantum confined excitons. ( A ) The normalized differential reflectance ∆ R/R (Eq.1) asa function of V TG , taken at the TG edge at V BG = 4 V. The top left inset of C shows a schematic of the TG, with the positionof the optical spot marked by the red disk. In addition to the typical features associated with the neutral exciton (X ) andrepulsive polaron (RP + and RP − ) from underneath the top gate, we observe narrow discrete spectral lines that red shift as afunction of V TG compared to the exciton or RP + energy at that voltage. ( B ) Spectral linecut at V TG = − . − . − . V ( x ) for excitons at the corresponding voltages(see Eq.(1)). ( C ) Photoluminescence spectrum at V BG = 4 V as a function of V TG shows discrete red shifting emission lines.Spectral linecut at V TG = − D ) Energy of discrete resonances ( E ) with respect to the freeexciton energy ( E X ), obtained from Lorentzian fits of the reflectance (blue circles) and PL (red diamonds) data show a levelseparation of order (cid:126) ω x ∼ . V TG = − min ∼ µ eV). changes at the onset of strong hole-doping under thegate at V TG ≈ − A .Whereas the PL lines continue to red shift almost linearlywith V TG , the reflectance lines show an abrupt change inslope particularly at the lowest energies. The differencebetween the reflectance and PL lines scales linearly withthe Fermi energy (Fig. S9 in [20]). We currently cannotexplain the origin of this striking discrepancy. However,we speculate that the interactions between the dipolarexcitons in the i-region and the free carriers in the neigh-boring n- and p-doped regions, inducing a repulsive dress-ing of the excitons, could provide an explanation. Whileabsorption or reflectance measurements probe the highenergy eigenstates with a sizeable bare exciton (quasi-particle) weight, PL originates from a nonequilibriumprocess consisting of phonon-mediated relaxation of high-energy carriers and subsequent fast decay of localizedexcitons; this two-step process may be completed be-fore a screening cloud in the neighboring layers could beformed.To provide further evidence that the observed confinedstates are localized in the i-regions parallel to the edgeof the TG, we measure PL at a fixed V TG = − A ). As illustratedin the schematic shown in the inset of Fig. 4 A , we mea-sure PL at different points close to a 1 µ m wide segmentof the TG. Since this width is larger than our opticalresolution, we can separate the PL signal coming fromthe two edges of the TG. Moving from one side of theTG to the other, we observe that the discrete PL linesappear as the optical spot crosses the first edge, almostvanish when the spot is entirely on the TG, and reappearas the spot crosses the second edge. In the regions awayfrom the edge, the PL oscillator strength is mainly car-ried over to the attractive polaron branch. In the inset,we show the oscillator strength of the lower emission lineas a function of space, which shows two peaks separatedby about ∼
800 nm in good agreement with the widthof the gate when we take into account the measurementuncertainties.It is well known that emission from strongly confinedexcitons in 1D semiconductor wires is polarized along thewire axis [29–32]. To obtain confirmation of the 1D na-ture of the narrow resonances reported in Fig. 3, we mea-sure their polarization properties. Fig. 4 B - E show lin-ear polarization resolved PL measurements taken at two FIG. 4.
One-dimensional confinement. ( A ) PL measurement at V BG = 5 V and V TG = − B - E ) PL measurements as a function of linear polarization angle taken at at V BG = 5 V and V TG = − . B ) where the spot encompasses two parallel edges, and ( D ) where the optical spotis aligned on the split gate, and we expect to have two sets of orthogonally oriented wires. ( C ) and ( E ) show polar plots ofnormalized emission intensity associated with confined states for data shown in B and D respectively. The PL emission fromconfined modes exhibit a high degree of linear polarization ( ξ ∼
80 %) in the longitudinal direction of the wire. This is clearlyevidenced by the fact that whereas in B all states are y − polarized, we observe additional x − polarized confined states in D arising from the orthogonally oriented wires. The polarization axes in these two cases are illustrated by black arrows in theinsets. positions on the sample, which are illustrated in the re-spective insets: Fig. 4 B depicts PL from the 200 nm wideregion which encompasses two parallel edges. Fig. 4 D onthe other hand, shows PL obtained by aligning the opti-cal spot on the split gate which contains two sets of or-thogonal wire segments. In both measurements, the PLemission from confined exciton states exhibit a high de-gree of linear polarization ξ = ( I max − I min ) / ( I max + I min ),where I max and I min are maximum and minimum intensi-ties in the polarization scan. At V TG ∼ − ξ ≈ .
8, and a maximum value at somepositions of ξ max ≈ .
96. This high degree of linear po-larization is comparable to what was previously reportedin other 1D systems, such as semiconductor nanowires[29], carbon nanotubes [31], and 1D moir´e excitons [32].Whereas in Fig. 4 B , the PL lines are polarized only along y − , we observe additional sets of x − polarized lines inFig. 4 D , which arise from the 1D exciton wires in the gapregion that are oriented along x . In Fig. 4 C and E , the0 ◦ angle of the polar plots is set to the primary polariza-tion axis, which aligns with the wire axis in y -axis withinour experimental uncertainties of ± ◦ . By analyzing thepolarization properties of exciton and polaron resonancesfrom regions I and II, we confirm that the high degree ofpolarization is unique to the confined states, whereas allother resonances exhibit low polarization degree ( (cid:46) . (cid:96) ∼ x and y polarization components.In summary, by exploiting the ultra-strong exci-ton binding energy in monolayer MoSe and repulsiveexciton-charge interactions, we succeeded in demonstrat-ing strong confinement of excitons on length scales muchsmaller than the size of the gate electrodes. For futuredevices, our method may provide several crucial advan-tages over alternative approaches that use material mod-ulation: (i) deterministic positioning of tailor-made po-tentials can be achieved by suitable design of electrodes;(ii) electrical tunability of exciton resonance energy mayallow to overcome disorder to create multiple identicalemitters; (iii) the quantum confinement is achieved whileleaving the semiconductor pristine; and (iv) quantumconfinement of in-plane direct excitons, as opposed tolayer-indirect excitons, allows stronger coupling to light.We envision several exciting extensions of our work.First and foremost, strong confinement of excitons witha permanent dipole moment perpendicular to the wireaxis is expected to strongly enhance exciton-exciton in-teractions [35–37] while allowing for hybridization with amicrocavity-mode [38, 39]; consequently, we expect a 1Dwire strongly coupled to a cavity mode to emerge as abuilding block of a strongly interacting photonic system[40]. Even in the absence of cavity-coupling, strong inter-actions could enable the realization of an excitonic Tonks-Girardeau gas with photon correlations providing signa-tures of fermionization [41]. Furthermore, our methodcan be straightforwardly applied to achieve lower dimen-sional quantum confined structures such as quantum dotsor quantum rings using proper design of electrodes. Acknowledgements
We thank A. Srivastava, T.Chervy, I. Schwartz, R. Schmidt and N. Lassaline for insightful discussions.
Funding:
This work has beensupported by Swiss National Science Foundation undergrant 200021-178909/1. K.W. and T.T. acknowledgesupport from the Elemental Strategy Initiative con-ducted by MEXT, Japan, A3 Foresight by JSPS andCREST (grant number JPMJCR15F3) and JST. P.A.M.acknowledges funding from the European Union’sHorizon 2020 program under Marie Sklodowska-Curiegrant MSCA-IF-OptoTransport (843842). D.T. andD.J.N. acknowledge support by the Swiss NationalScience Foundation under grant 200021-165559.
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The experiments outlined in the main text are per-formed on a van der Waals heterostructure consisting of aMoSe monolayer, which is fully encapsulated by hexago-nal boron nitride (h-BN) and contacted by Pd electrodesembedded in the top h-BN spacer layer [42, 43]. Theheterostructure is placed on a gold bottom gate, whichallows to globally tune the carrier density in the device.In addition, we pattern a split top gate electrode to lo-cally control the charge density.We begin our device fabrication process by mechani-cally exfoliating MoSe and h-BN flakes from bulk crys-tals (HQ Graphene MoSe and NIMS h-BN) onto 285nm SiO substrates using wafer dicing tape (Ultron).The flake thicknesses are identified using optical contrastmeasurements and/or atomic force microscopy. For thisdevice, we selected h-BN flakes which are ∼
30 nm thick.Embedded
Via –contacts are formed by etching holes inthe h-BN spacer by means of electron beam lithographyand reactive ion etching (Oxford Plasmalab 80Plus). Theetching conditions are the following: CHF :O substrate using a stan-dard dry polymer transfer method (also used for stack-ing, see following paragraph). Next, the pre-defined holesare filled with metal by performing a second lithogra-phy step and (electron-beam) evaporation of 20 nm ofPd and 30 nm of Au. The multilayer stack is then cre-ated by picking up the top h-BN layer with embedded Via –contacts and laminating it onto a monolayer MoSe ,and a bottom h-BN flake using the aforementioned drytransfer process.For the dry transfer of flakes, we use a glass slide ontowhich a hemispherical polydimethylsiloxane (PDMS)stamp is attached. This stamp is covered with a thinlayer of polycarbonate (PC) allowing the sequential pick-up of the flakes. All stacking steps are thereby performedin an inert Ar atmosphere inside a glovebox and at a tem-perature of 120 ◦ C. The finished stack is deposited ontothe gold bottom gate by increasing the temperature upto 150 ◦ C, which allows the PC to delaminate from thePDMS and to be released on the substrate. By furtherheating to 170 ◦ C, the PC is torn at the edges. The PCis dissolved by immersing the substrate in chloroform.The bottom gate on the Si/SiO substrate is formedby lithographically defining a square of 20 µ m size andelectron-beam evaporating 3 nm of Ti and 10 nm of Au.Subsequently, we pattern a split top gate electrodewhich is 200 nm wide and includes a 100 nm gap, allow-ing the formation of a gate-defined constriction. For thiswe utilize electron-beam lithography and evaporate 3 nmof Ti and 10 nm of Au. This renders the top gate opti-cally transparent and therefore allows to probe the op- FIG. S1. Experimental Setup tical properties of the monolayer underneath. Finally,the embedded
Via –contacts in the top h-BN spacer layeralong with top gate are electrically contacted with ex-tended metal electrodes prepared using another lithogra-phy step and subsequent evaporation of 5 nm of Ti and85 nm of Au.
B. Experimental setup
We perform our optical experiments in a confocal mi-croscope setup, as schematically illustrated in Fig. S1.The sample is mounted on x - y - z piezo-electric stages lo-cated inside a stainless steel tube, which is immersed in aliquid helium bath cryostat. The steel tube is filled with20 mbar helium exchange gas to maintain a sample tem-perature of ∼ . µ W is maintained. The polarization resolvedPL measurements are carried out with an angle-scanning0
FIG. S2.
Simultaneous measurement of optical re-flectance and source-drain current.
The onset of source-drain current approximately coincides with the onset of blueshift of the repulsive polaron resonances. polarizer placed in the emission path.
C. Device characterization
While probing the bottom gate dependence of re-flectance, we simultaneously measure the source-drain(SD) current with an applied source-drain voltage V SD =2 V (Fig. S2). At a threshold voltage of V BG = 3 V weobserve the onset of n-type electrical current. Weak p-type conduction is also observed for V BG ≤ − conduc-tion band. Moreover, we observe a good correspondencebetween the emergence of electron and hole current withthe onset of repulsive polaron blue shift in the reflectance,both of which are phenomena which require the injectionof free charge carriers into the semiconducting mono-layer. A slight mismatch between both onsets can beattributed to the fact that a SD current probes the en-tire MoSe region between the respective contacts, whilethe reflectance spectrum is a local probe of the MoSe charging configuration. At the location of the opticalspot the local charge density could be different than theglobal average doping and thus already cause polaronformation. D. Doping properties
The doping characteristics of a device with top andbottom gates are well captured by the capacitor model, σ TMD = − C T V T G + ( C T + C B ) ∆ E F e − C B V BG , (3)where C T and C B are the gate capacitances of TG andBG respectively, ∆ E F is the change in Fermi energy inthe TMD induced by applying a voltage on the gates,and σ TMD = − e (cid:90) ∆ E F D ( E ) dE (4)is the 2D charge density on the TMD. To first or-der, we can separate the doping characteristics into tworegimes: the metallic regime and the dielectric regime.The charged regime is described by the plate capacitorapproximation where D is large and ∆ E F ≈
0, thus σ TMD = − C T V T G − C B V BG , (5)while when E F is in the gap, the TMD behaves like adielectric with σ TMD ≈
0. Therefore,∆ E F e = C T V T G + C B V BG C T + C B . (6)This can be clearly seen in Fig. 2 B in the main text,where we show the normalized reflectance as a function of V BG away from the top gate. The charge neutral regimeextends approximately from − . − . V BG > − . V BG < − . C T ≈ C B , we would expect the sizeof the charge neutral region in the dielectric approxima-tion to be ∆ V BG = 2 E g /e ≈ . V . We observe however,that the actual size of the charge neutral region is sub-stantially larger than expected, with ∆ V BG ≈ V . Weattribute the larger size of the charge neutral region tothe presence of chargeable defects in the sample, whichare homogeneously distributed in energy [44]. We caninclude the effect of such defects in the capacitor modelby assuming a constant D ( E ). Eq.(3) then reads∆ E F e ( e D ( E ) + C T + C B ) = C T V T G + C B V BG . (7)Given the size of the bandgap, E G ≈ . ε h − BN , ⊥ ≈ .
8, we can estimate a defect density of D = 8 . · cm − meV − .To understand the charging behavior of the p-i-n diode,we measure the reflectance as function of V BG and V TG atthe TG edge. As discussed in the main text, we considerthree spatial regions: (I) the electron-doped region awayfrom the TG that is affected only by the BG, (II) theregion directly underneath the TG, and (III) the narrowregion between I and II.1 FIG. S3.
Doping characteristics tracked by repulsive polaron resonances. ( A ) Normalized reflectance ∆ R/R measuredfor fixed V TG = − V BG . ( B ) ∆ R/R measured for fixed V BG = 1 . V TG . In addition to thefeatures from regions II and III, we see the repulsive polaron resonance from region I at E ≈ V TG . ( C ) Normalized reflectance taken at a fixed energy E X + Γ / , I) ≡ (p , n)). In Fig. S3 C , we track the normalized reflectance at afixed energy E = E X + Γ / A and B ), as a function of V BG and V TG , whereΓ is the 2D exciton linewidth. The two parallel zig-zaglines correspond to the blue shift of repulsive polaronbranches in region II, which indicate the onset of dopingin that region. These zig-zag lines correspond to con-stant charge density and therefore allow to identify thedifferent charging configurations in the V TG − V BG plane.In general, moving vertically at fixed V TG tunes the dop-ing in region I, whereas moving horizontally, keeping V BG fixed, tunes the doping in region II. We refer to the dop-ing configuration with the notation (II , I). For example,( p, n ) refers to p-doping in II and n-doping in I. As anexample, we follow the cut (1) in Fig. S3 C , where theregion II is always p-doped. By sweeping V BG from − C . When varying V T G , thedoping in region II clearly changes and exhibits the typi-cal polaron transitions that we would expect from a TMDthat is doped from n to i to p. However, the observedcharge neutral region for region II is notably smaller thanthe lower limit of 2 E g /e that should be observable for adefect-free sample. To explain this observation, we needto consider the optical doping mechanism.When region I is neutral, a voltage bias between TGand BG results in an electric field ( F ∝ V TG − V BG ).This in turn leads to a potential well for electrons/holesin region II. Since the Fermi energy is in the gap, it isnot energetically favourable for electrons and holes to oc-cupy the well. However, upon optical excitation, excitons can dissociate under the electric field at the edges of thewell, which traps a charge. This optical doping mecha-nism gives us a reliable way of doping the region underthe top gate. In the global charge neutrality region, thecharge density in region II depends on the in-plane elec-tric field which induces dissociation and therefore scaleslinearly with σ ∝ V BG − V TG . On the other hand, thedoping situation is different when the device is globally n or p doped. In order to reach charge neutrality, V T G nowneeds to be tuned to a voltage that removes the chargesunder the top gate, therefore the equal density line fol-lows V T G + V BG = constant. We expect the doping ofopposite charge carriers in the region II to arise from thesame optical doping mechanism described above. FIG. S4.
Quantum confinement in the n-i-p regime.
Normalized reflectance ∆
R/R as a function of V TG for fixed V BG = − − ) continuum for V TG (cid:38) V TG for fixed V BG = − B . Weobserve similar qualitative signatures of quantum con-finement, i.e. the narrow discrete lines emerging outof the repulsive polaron continuum. As expected, theselines now appear at positive V TG . However, we do ob-serve conspicuous quantitative differences between thep-i-n and n-i-p settings. We find that a prolonged neu-tral region, that is seen in Fig. 3 A , is absent in the datashown in Fig. S4. Because of this we suspect that the dis-crete resonances in the n-i-p scenario do not exhibit thesharp initial red shift as observed in the voltage range − < V TG < − A . We currently do notunderstand the origin of this discrepancy. E. Electrostatic simulation of device geometry andcomparison with experimental data
In order to obtain a quantitative understanding ofthe electrostatic environment in our device, we computethe position and voltage dependence of both the chargedensity and in-plane electric field by performing finite-element calculations with the “Semiconductor” packagein COMSOL. These quantities are determined by solvingdrift-diffusion equations coupled with Poisson’s equation.The simulated device geometry is depicted in Fig. 1 A of the main text. It consists of a semiconducting ma-terial encapsulated by 30 nm thick h-BN slabs and con-tacted by ohmic electrodes. Furthermore, we include twogates with partial overlap. The bottom gate is kept ata fixed bias of 4 . − −
10 V in our simulations.The material parameters assumed for this calculation area bandgap of 2 eV, an electron / hole effective mass of m eff = 0 . m e , and an out-of-plane dielectric constant ε ⊥ = 7 .
2, and an in-plane dielectric constant ε (cid:107) = 16 forthe semiconductor. For h-BN we neglect the differencebetween in- and out-of-plane dielectric constants and as-sume a value of 4 .
6. Furthermore, in order to achieveconvergence, the simulation temperature is increased to350 K and a finite thickness of 5 nm is assumed for thesemiconducting TMD layer, in accordance with the pro-cedure described in [45]. The relevant electrostatic quan-tities are then extracted as measured in the middle of thislayer. We emphasize that COMSOL’s “Semiconductor”package assumes a 3D density of states for the charges inthe system. Hence, we consider our simulations rather toprovide a ballpark estimate of the important electrostaticquantities. In this manner we obtain the spatial charge densityand in-plane electric field distribution for varying topgate voltages V TG , which are depicted in the top panelof each subplot in Fig. S5. The bottom gate extends overthe entire plotted range of the position from −
80 nm to80 nm, whereas the top gate only ranges from −
80 nm to0 nm. We can identify three distinct regimes as we vary V TG , which we identify according to the doping state inregions I, II and III. For V TG > − A and B . As we decrease V TG , we de-plete regions II and III completely and hence we are inthe i-i-n regime, which is accompanied by a large increasein magnitude of the in-plane electric field | F x | . While themaximum of the field distribution is located close to thetop gate edge, owing to the large lateral extent of theneutral region, the in-plane field persists even under theTG and exhibits a spatial asymmetry. The i-i-n regimepersists until the onset of hole-doping in region II, whichoccurs in our simulations at V TG = − D ).As hole-doping starts, only a narrow ∼ −
40 nm wideneutral region remains, located at the edge of the TGand flanked by a steep increase in charge density. Thisis the p-i-n regime. As a consequence, the in-plane fielddistribution also becomes concentrated in this narrow re-gion due to screening in the neighboring charged areas.Lowering V TG further pushes the neutral junction regionfurther away from the TG, thereby making the electricfield distribution increasingly symmetric. Ultimately, at V TG = −
10 V we obtain a sizeable in-plane electric field,which peaks at 55 V/ µ m.From these quantities we determine the total excitonicconfining potential as outlined in Eq. (1) of the main text.The dc Stark shift contribution is computed by assumingan exciton polarizability α = 6 . / V [21]. Therepulsive polaron shift is determined by empirically ex-tracting an effective exciton-electron coupling strength g (cid:39) . µ eV µ m from our experimental data. It cor-responds to the slope of a linear function fitted to thedensity-dependent blue shift of repulsive polaron in thereflectance data, shown in Fig. 3 A of the main text. Thecoupling strength g is then converted into the appropriateunits µ eV µ m by taking into account the correspondingelectron charge density.The resulting potential experienced by the exciton inits center-of-mass frame for various V TG is depicted inthe lower panel of each subplot in Fig. S5. Addition-ally, whenever appropriate, we also show the numericallycalculated discrete eigenstates associated with the con-fining potential. A potential well starts to form only at V TG = − C ). However, the 2D exci-tonic state may exhibit a small red shift. At V TG < − FIG. S5.
Magnitude of charge density | n c | , in-plane electric field F x and exciton confining potential V ( x ) as afunction of position for varying top gate voltages V TG . The bottom gate extends over the entire plotted range of theposition from −
80 nm to 80 nm. The top gate ranges from −
80 nm to 0 nm. exciton energy E X and the confinement is solely drivenby the dc Stark shift. As the gate voltage is lowered fur-ther to V TG < − D to I ), where the continuum is solely determined by thehole or electron RP energy, depending on which chargehas lower density. For example, for V TG < − E X .Having calculated the discrete motional states of theexciton in the confining potential, it is possible to com-pare the absolute zero-point energy and the energy spac- ing (cid:126) ω between the lowest and first excited state withtheir experimental counterparts, extracted from the pho-toluminescence measurement shown in Fig. 3 C . As canbe seen in Fig.S6 A the redshift of the lowest energy staterelative to the 2D free exciton energy E X follows a sim-ilar trend as predicted by the simulations. The exper-imental values however tend to be slightly larger thanthe predicted ones. In Fig.S6 B we compare the energydifference between the lowest states and notice a similarorder of magnitude for the experimental and predictedvalues. Furthermore, a flattening of the increase in en-ergy splitting is discernible in both cases. We suspectthat the differences compared to the experimental values4 FIG. S6.
Comparison between PL data and predictionfrom electrostatic simulations. ( A ) Evolution of zero-point energy and ( B ) level splitting (cid:126) ω between the lowest twostates as a function of V TG . Data obtained from simulationsis depicted in blue, while experimental data points from thePL measurement are shown in red. originate from deviations in material parameters, such asthe bandgap, effective mass, exciton polarizability etc.In addition, the simulation assumes an operating condi-tion of V BG = 4 . V BG = 4 V. F. Line shape analysis of reflectance andphotoluminescence data
While a detailed analysis of the reflectance line shaperequires the use of the transfer matrix method, a morestraightforward approach is to describe the measuredreflectance signal as Im (cid:2) e iα ( E ) χ ( E ) (cid:3) , where χ ( E ) isthe MoSe monolayer optical susceptibility and α ( E ) awavelength-dependent effective phase shift [46]. The pa-rameter α ( E ) captures the effect of light interfering atdifferent material interfaces in our device heterostruc-ture (e.g. h-BN/Au). To first order we assume α to bewavelength-independent in our spectral range of interest.The reflectance spectral profile S ( E ) associated with anoptical resonance can then be modelled in the followingmanner: L ( E ) = 1 π Γ / E − E ) + Γ / L D ( E ) = E − E ( E − E ) + Γ / S ( E ) = A (cos( α ) L ( E ) + sin( α ) L D ( E )) + C (10)where L ( E ) and L D ( E ) constitute a pure Lorentzianand a dispersive Lorentzian line shape, respectively, with E being the center frequency and Γ the linewidth. Theparameter A characterizes the overall amplitude of theresonance, while C takes into account any broad back-ground signal. The result of fitting this spectral profileto the bare 2D exciton transition (corresponding to theline cut taken at V TG = − . B ) is depictedin Fig. S7 A .We attribute the origin of the discrete spectral fea-tures in our reflectance and PL measurements (Fig. 3 A and C ), to quantum confinement of excitons. As a conse-quence, when the energy splitting (cid:126) ω becomes compara-ble to the exciton linewidth, we expect to see a coherent superposition of overlapping discrete lines which are as-sociated with individual states splitting off from a broadcontinuum resonance. To justify this claim we take thespectrum at V TG = − . B ) as an example andfit it with a superposition of multiple narrow spectral pro-files (cid:80) i S ( E ; E ,i , Γ i , A i , α c ), which characterize the linesassociated with quantized motional states, and a broadresonance S ( E ; E RP , Γ RP , A RP , α RP ), that accounts forthe repulsive polaron continuum. As shown in Fig. S7 B ,a good fit of the measured data can be achieved overthe whole spectral range of interest. We emphasize thatduring this procedure the same phase factor α c is as-sumed for all lines associated with confined states. Thiscan also be seen in Fig. S7 C , which depicts the individ-ual components of the overall spectrum. The states, forwhich the transition energy is not traced in Fig. 3 D , arethereby marked in gray. Furthermore, the phase factorof the hole repulsive polaron resonance α RP is not thesame as α c . This is justified considering that the originof this resonance is rooted in a separate spatial region ofthe device, thus causing a different interference pattern.For the purpose of illustration, we also show in Fig. S7 D the resonances when the asymmetry in their line shapeis removed by setting α c = 0 ◦ while retaining the otherfit parameters.The full list of parameters obtained from the fit ofthis spectrum at V TG = − . i (cid:38) µ eV, which is almost a factor of 4 smaller than thebare 2D exciton linewidth (see Fig. S7 A ). At lower V TG ,where a stronger excitonic confinement is expected, weobserve narrowing of the linewidth down to 300 µ eV. Thisanalysis shows how after the onset of hole doping, notonly does the continuum blue shift due to the emergenceof the repulsive polaron, but concurrently a broadeningand loss of oscillator strength for the higher-lying discretestates is observed.In contrast to the reflectance measurement, the spec-tra acquired in the photoluminescence dataset shown inFig. 3 C are fit by a superposition of pure Lorentziansi.e. (cid:80) i L ( E ; E ,i , Γ i , A i ). i E (meV) Γ (meV) A (meV) α ( ◦ )1 1638.2 0.42 0.043 -25.22 1638.7 0.62 0.108 -25.23 1639.5 0.91 0.098 -25.24 1640.1 0.56 0.073 -25.25 1640.5 0.88 0.055 -25.26 1641.2 0.53 0.052 -25.27 1642.0 1.02 0.094 -25.28 1642.9 1.00 0.058 -25.2RP 1644.7 4.95 1.310 -155TABLE I. Fit parameters obtained by fitting ∆ R/R at V TG = − . B ) FIG. S7.
Line shape analysis of reflectance data. ( A ) Spectral profile described by Eq. (10) fit to the bare 2D excitontransition at V TG = − . B ) Reflectance linecut at V TG = − . (cid:80) i S ( E ; E ,i , Γ i , A i , α c ) + S ( E ; E RP , Γ RP , A RP , α RP ). ( C ) Individual components of the fit. ( D ) Individual components afterremoving line asymmetry by setting α c and α RP to 0 ◦ . The resulting overall lineshape is shown in red. G. Polarization anisotropy
To verify that the strong polarization anisotropy wereport in the main text is indeed associated with theconfined states of the exciton, we perform polarization-resolved PL measurements also for various other opti-cal transitions observed in our device. Fig. S8 A demon-strates a reference bottom gate ( V BG ) scan conductedat a position away from the TG region. Also shown inFig. S8 B and C is a V TG scan performed on the splitgate away from the gap region. We reiterate that sincethe spot size of our excitation beam is larger than thesplit gate width (200 nm), PL emission from three dis-tinct spatial regions is measured:(I) The region away from the TG is electron-dopedand thus gives rise to a broad attractive polaronresonance (AP − I ) centered at ∼ .
615 eV, whichremains unaffected as a function of V TG .(II) The region underneath the TG leads to neutral ex-citon (X ) and attractive polaron resonances (AP − II and AP +II ), as it changes from being electron-doped,neutral and finally hole-doped when V TG is lowered.(III) The neutral intermediate region at the edge ofTG gives rise to red-shifting confined exciton lines(X ), as V TG is lowered.In Fig. S8 D - F , we show the polarization dependenceof these optical transitions by plotting the normalized PL emission as a function of linear polarization detection an-gle. 0 ◦ thereby constitutes the y -direction (also see Fig. 2and 4 of the main text). As shown in Fig. S8 F , the at-tractive polaron resonances originating from underneaththe TG (AP +II ) and away from the TG (AP − I ) have a lowdegree of linear polarization ξ = ( I max − I min ) / ( I max + I min ) (cid:46) I max and I min are the maximum andminimum intensities, respectively. These are obtained byfitting the function A · cos ( θ − θ ) + C to the normal-ized PL intensities as function of the detection angle θ .The neutral exciton originating from underneath the TG(X ) exhibits a similar behavior ( ξ ≈ E ).Furthermore, the primary polarization axis of these res-onances, given by θ , has varying orientation and doesnot align with the TG edge. As a reference, we also com-pute ξ for these optical transitions away from the TG andfind that it is in the same range (Fig. S8 D ). In stark con-trast to this behavior, the confined exciton states exhibit ξ = 96% along with a primary polarization axis orientedwithin ± ◦ along the TG edge.Due to the similarity in polarization properties of ex-citon and polaron resonances from region I and II, weconclude that the strongly polarized emission of the con-fined excitonic states has its origin in the 1D confinementrather than a screening by the metallic TG, the effectof which cannot be distinguished from a typical strain-induced polarization dependence. If the geometry of themetallic TG had an impact on the polarization proper-ties of the emission, also other optical transitions wouldexhibit an enhanced linear emission.6 FIG. S8.
Linear polarization anisotropy of different optical resonances. ( A ) PL bottom gate ( V BG ) scan conductedon bare MoSe away from top gate region. ( B ), ( C ) PL top gate ( V TG ) scan performed on the split gate away from the gapregion. ( D )-( F ) Polarization dependence of optical transitions in regions I, II and III, which are represented in purple, magentaand orange, respectively. The exciton, hole-side attractive polaron and electron-side attractive polaron is marked with a circle,cross and dash, respectively.FIG. S9. Discrepancy between reflectance and PL.