Room-Temperature Polariton Lasing in All-Inorganic PerovskiteNanoplateletsRui Su,† Carole Diederichs,‡,§ Jun Wang,∥ Timothy C. H. Liew,† Jiaxin Zhao,† Sheng Liu,† Weigao Xu,†

Zhanghai Chen,∥ and Qihua Xiong*,†,‡,⊥

†Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University,Singapore 637371, Singapore‡MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore 639798, Singapore§Laboratoire Pierre Aigrain, Departement de physique de l’ENS, Ecole normale superieure, PSL Research University, Universite ParisDiderot, Sorbonne Paris Cite, Sorbonne Universites, UPMC Univ. Paris 06, CNRS, 75005 Paris, France∥State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, People’s Republic of China⊥NOVITAS, Nanoelectronics Center of Excellence, School of Electrical and Electronic Engineering, Nanyang TechnologicalUniversity, Singapore 639798, Singapore

*S Supporting Information

ABSTRACT: Polariton lasing is the coherent emission arisingfrom a macroscopic polariton condensate first proposed in1996. Over the past two decades, polariton lasing has beendemonstrated in a few inorganic and organic semiconductorsin both low and room temperatures. Polariton lasing ininorganic materials significantly relies on sophisticated epitaxialgrowth of crystalline gain medium layers sandwiched by twodistributed Bragg reflectors in which combating the built-instrain and mismatched thermal properties is nontrivial. On theother hand, organic active media usually suffer from largethreshold density and weak nonlinearity due to the Frenkel exciton nature. Further development of polariton lasing towardtechnologically significant applications demand more accessible materials, ease of device fabrication, and broadly tunableemission at room temperature. Herein, we report the experimental realization of room-temperature polariton lasing based on anepitaxy-free all-inorganic cesium lead chloride perovskite nanoplatelet microcavity. Polariton lasing is unambiguously evidencedby a superlinear power dependence, macroscopic ground-state occupation, blueshift of the ground-state emission, narrowing ofthe line width and the buildup of long-range spatial coherence. Our work suggests considerable promise of lead halide perovskitestoward large-area, low-cost, high-performance room-temperature polariton devices and coherent light sources extending from theultraviolet to near-infrared range.

KEYWORDS: Inorganic perovskite, strong coupling, exciton polariton, polariton lasing, polariton condensate

Cavity exciton polaritons are bosonic quasiparticles resultedfrom the strong coupling between excitons and confined

cavity photon modes.1,2 The half-light, half-matter nature ofexciton polaritons gives rise to their extremely light effectivemass, typically only 10−4−10−5 times the mass of an electron,which is regarded as a crucial feature for the realization ofBose−Einstein condensation (BEC) of polaritons at hightemperatures.3 BEC of polaritons is well-known to occur whenthe ground state is macroscopically occupied upon reaching acritical threshold and the distribution of occupancy follows aBose−Einstein distribution.4 Usually, influenced by the shortlifetime of polaritons, the distribution is altered by non-equilibrium effects and uncondensed excitons, resulting in lowthreshold coherent emission or the so-called polaritonlasing.5−7 Unlike conventional photonic lasing, populationinversion is no longer a prerequisite for achieving polaritonlasing, attributed to the mechanism of bosonic final-state

stimulation. This distinct feature gives rise to significant lowthreshold of polariton lasing, compared to vertical cavity surfaceemitting lasing (VCSEL) which shares precisely the same cavitystructure as polariton laser.Polariton condensation and polariton lasing in solid state

systems were first demonstrated in CdTe4 and GaAs8,9

quantum well microcavities. However, the operation ofpolariton condensation based on such semiconductors withWannier-Mott excitons, such as CdTe,4 GaAs,8,9 and morerecently InP,10 is limited at cryogenic temperatures due to thesmall exciton binding energy. On the contrary, robust excitons,as well as large oscillator strengths, promote further room-temperature realizations of polariton condensation and polar-iton lasing in ZnO11,12 and GaN.13 Nonetheless, inorganic

Received: May 10, 2017Published: May 25, 2017

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© 2017 American Chemical Society 3982 DOI: 10.1021/acs.nanolett.7b01956Nano Lett. 2017, 17, 3982−3988

planar microcavities usually require sophisticated epitaxialtechniques to ensure the high quality of the microcavity aswell as the optical gain medium, in which one has to combatthe challenges of built-in strain and mismatch of thermalexpansion coefficients. In contrast, organic materials exhibitFrenkel excitons with much larger exciton binding energy andease of fabrication, providing alternative systems for achievingroom-temperature polariton emission14−16 and polaritoncondensation, for example, crystalline anthracene,17 amorphous2,7-bis[9,9-di(4-methylphenyl)-fluoren-2-yl]-9,9-di(4-methyl-phenyl) fluorine (TDAF) molecules,18 ladder-type conjugatedMeLPPP polymer,19 and enhanced green fluorescent protein.20

Nevertheless, Coulomb interaction,21 which contributesprimarily to polariton−polariton interactions, is significantlyweaker in organic materials due to the Frenkel exciton nature,leading to inefficient polariton relaxation to the ground state.22

Therefore, a much higher threshold and weaker nonlinearity areoften obtained in organic microcavities,23 compared withinorganic microcavities. In addition, there have also beentremendous and long-lasting interests in the past decade inusing hybrid organic−inorganic perovskites for polaritonemission24−28 and in investigating polariton condensation andpolariton lasing operated at room temperature in suchmaterials, as they combine the advantages of both inorganicand organic materials, such as ease of synthesis, large excitonbinding energies and excellent optical properties determined bythe inorganic component. However, up to now only the room-temperature strong coupling regime was observed24−28 withoutany successful realization of polariton condensation, which is

probably caused by the insufficient crystalline quality inducedby solution chemistry. Recently, we have shown that all-inorganic lead halide perovskites grown by an epitaxy-freevapor phase technique exhibit excellent optical gain propertieswith large exciton binding energy and oscillator strength,tunable emission band from ultraviolet to near-infrared, andbetter optical stability under high laser flux illuminationcompared with hybrid perovskites.29 Therefore, we believethat the all-inorganic perovskites are ideal alternatives for oxideand nitride inorganic materials to study the physics of BEC inan easy-access solid-state platform and to accomplish scalableand high performance polariton lasing towards electricallydriven polaritonic devices operated at room temperature.Here, the studied microcavity structure (schematically shown

in Figure 1a) consists of a 373 nm thick lead chlorideperovskite (CsPbCl3) nanoplatelet embedded in bottom andtop DBRs made of 13 and 7 HfO2/SiO2 pairs, respectively. Theperovskite nanoplatelet was grown on a muscovite micasubstrate by a chemical vapor deposition method,30,31 andtransferred to the bottom DBR by a dry transfer process. Thefull perovskite microcavity fabrication is completed followingthe sequential deposition of a top DBR by e-beam evaporation.We stress that highly crystalline CsPbCl3 platelet can also begrown on bottom DBR structures directly, suggesting thecompatibility with device fabrication (see Methods andSupplementary Section 1). No additional spacer is needed asthe thickness of the perovskite nanoplatelet can be controlledthick enough to support Fabry-Perot oscillations. Figure 1bschematically displays the angle-resolved microphotolumines-

Figure 1. Microcavity structure and emission. (a) Schematic of the perovskite microcavity, which consists of a CsPbCl3 crystalline nanoplateletembedded in a planar microcavity formed by a bottom and a top HfO2/SiO2 DBR. (b) Schematic of the angle-resolved microphotoluminescencesetup with Fourier optics. Two lenses are shown as f1 and f2. (c) Microscopy image of a rectangular-shaped perovskite microcavity after fabrication.Scale bar, 12 μm. (d) Fluorescence microscopy image of as-fabricated perovskite microcavity, showing strong and uniform blue emission along theedges. Scale bar, 12 μm. (e) Room-temperature photoluminescence and absorption spectra of the CsPbCl3 perovskite nanoplatelet. Orange trace, theabsorption spectrum of the CsPbCl3 perovskite nanoplatelet on mica substrate, showing a strong excitonic peak at ∼3.045 eV. Blue trace, thephotoluminescence emission spectrum of the CsPbCl3 perovskite nanoplatelet on mica substrate, showing an emission at ∼2.99 eV with a full-widthat half-maximum (fwhm) of 80 meV. Red trace, the ground-state emission with Gaussian fitting (black dash line) of the CsPbCl3 nanoplateletembedded into the microcavity, showing an emission at ∼2.90 eV with a fwhm of ∼9.7 meV.

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cence Fourier imaging setup. Figure 1c shows a typicalrectangular-shaped CsPbCl3 nanoplatelet with a width of 12μm after cavity fabrication, along with the correspondingfluorescence image shown in Figure 1d. Figure 1e depicts theroom-temperature photoluminescence and absorption spectraof the CsPbCl3 perovskite nanoplatelet on mica substrate. Theabsorption exhibits a strong, narrow inhomogeneouslybroadened excitonic absorption peak at ∼3.045 eV, whichstrongly suggests the large exciton binding energy at roomtemperature. Previous experimental and theoretical studies haveindeed shown that excitons in CsPbCl3 perovskite possess alarge binding energy of about 72 meV,29,32 even larger than inGaN and ZnO.33 The photoluminescence emission of CsPbCl3perovskite is centered at ∼2.99 eV with a fwhm of 80 meV.While after being embedded into a microcavity, the ground-state emission of CsPbCl3 perovskite microcavity shifts to ∼2.9eV with the fwhm narrowing to 9.7 meV, corresponding to aquality factor of Q ∼ 300.We investigated the polaritonic behaviors of the CsPbCl3

perovskite microcavity by angle-resolved reflectivity andphotoluminescence measurements (equivalently as a functionof the in-plane wavevector k∥) at room temperature (T = 300K). Figure 2a,b show the k-space mappings of angle-resolved

reflectivity and photoluminescence spectrum, respectively. Thedispersion obtained in photoluminescence mapping agrees wellwith that of reflectivity measurements, except for small energydifferences due to slightly different locations of the excitationspots. Particularly, we did not observe any uncoupled excitonpeak located at ∼3.045 eV. The upper polariton dispersion canhardly be identified in both reflectivity and photoluminescencemappings, which is a broadly met situation in microcavities withlarge Rabi splitting energy,33 due to absorption in the electron−hole continuum, thermal relaxation, and the high reflectivity ofthe top DBR (Supplementary Section 2). However, the lowerpolariton dispersion features in both reflectivity and photo-luminescence mappings demonstrate unambiguously the strongexciton-photon coupling regime: (i) the dispersion curvaturetends to be smaller and smaller at large angles; (ii) an inflectionpoint is distinguished near angle ∼±50°, resulting from theonset of anticrossing between the perovskite exciton and theFabry−Perot cavity mode in the strong coupling regime. It isnoted that another parabolic-like dispersion in reflectivitymapping is attributed to the bare microcavity without anyembedded perovskite (Supplementary Section 3), owing to thesmaller size of the CsPbCl3 perovskite nanoplatelet comparedto the white light beam diameter. The dashed white lines in

Figure 2. Angle-resolved reflectivity and photoluminescence of CsPbCl3 perovskite microcavity. (a) Angle-resolved reflectivity spectrum measuredusing a white light lamp. The dashed white lines show the theoretical fitting dispersion of the upper (UP) and lower (LP) polariton dispersions. Thesolid white lines display the dispersions of uncoupled CsPbCl3 perovskite exciton (X) and cavity photon mode (C) obtained from a coupledharmonic oscillator model fitting. The parabolic-like dispersion is caused by the bare microcavity without any embedded perovskite, as a result of thesmaller sample size compared with the white light beam diameter. (b) Angle-resolved photoluminescence spectrum of perovskite microcavity. Thedetuning Δ, obtained from a coupled harmonic oscillator model fitting to the measured dispersion (dashed white lines), is indicated on the figure.Note the slight energy differences between reflectivity and photoluminescence spectra due to slightly different spot positions.

Figure 3. Power-dependent angle-resolved photoluminescence spectra. (a) Angle-resolved photoluminescence spectrum measured at 0.75 Pth.Polaritons show a broad emission distribution at all angles. (b) Angle-resolved photoluminescence spectrum measured at 1.0 Pth. The ground statenear k∥ = 0 exhibits a much stronger emission than other angles, indicating the onset of polariton lasing. (c) Angle-resolved photoluminescencespectrum measured at 1.3 Pth. The ground state near k∥ = 0 is massively occupied, experiencing a sharp increase of intensity along with a blueshift ofpeak energy.

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Figure 2a,b follow the theoretical fitting dispersion of the upperand lower polariton dispersions based on the coupled harmonicoscillator model.3 The solid white lines display the dispersionsof the uncoupled CsPbCl3 perovskite exciton (Eex = 3.045 eV)and cavity photon modes obtained from the fitting. From thefitting of the data, we extract a Rabi splitting energy of 2Ω =265 meV and a negative exciton−photon detuning of Δ = −25meV, which corresponds to an exciton fraction of 0.45 at thelower polariton branch minimum. Additionally, we alsoinvestigated the polariton dispersion of a thinner (360 nm)perovskite nanoplatelet microcavity (Supplementary Section 4).Compared with the 373 nm thick perovskite microcavity, itexhibits a flatter dispersion with a positive detuning of + 70meV due to the increased exciton fraction of 0.63, whichstrongly suggests that our system operates in strong couplingregime.To reach the emission in the nonlinear regime, the system

was pumped by off-resonant excitation centered at 375 nm witha pulse duration of 100 fs and a spot size of 25 μm. Figure 3a−cdisplay the contour maps of the angle-resolved photo-luminescence at pumping fluence corresponding to a factor0.75, 1.0, and 1.3 of the threshold fluence (Pth = 12 μJ/cm2),respectively. At the low pump fluence of 0.75 Pth, the lowerpolariton dispersion exhibits a broad emission distribution at allangles. Upon reaching the threshold fluence, the polaritondispersion near k∥ = 0 exhibits a much stronger emission alongwith a sharp increase of intensity, indicating the onset of

polariton condensation. Under even higher pump fluence of 1.3Pth, the ground state near the minimum of lower polaritondispersion (ELP(k∥ = 0) = 2.90 eV) becomes massivelyoccupied, in stark contrast to the conventional photonic lasingwhich should massively occupy the minimum of the cavitymode dispersion (EC(k∥ = 0) = 3.02 eV). The enhancedmacroscopic ground-state occupation at the minimum of thepolariton dispersion is one of the main features for polaritoncondensation and subsequent polariton lasing.Figure 4a shows the ground-state emission spectra in

logarithmic scale, measured at normal incidence (k∥ = 0)under different pump fluences. With the increase of pumpfluence, the ground-state emission witnesses a dramatic increaseof intensity, along with a narrowing of the fwhm and acontinuous blueshift in emission energy, suggesting a transitionfrom a linear regime to nonlinear regime. To investigate thistransition quantitatively, we plot the emission intensity at k∥ = 0as a function of pump fluence in a log−log scale (red trace inFigure 4b). A sharp increase, by 3 orders of magnitude, of theground-state emission intensity is observed in the output−inputcharacteristics above a threshold of Pth = 12 μJ/cm2.Remarkably, despite the low Q of our microcavity, thisthreshold is at least five times lower than previous reports atroom-temperature in epitaxy-free microcavities.17−19 Mean-while, the fwhm of the ground-state emission (blue trace inFigure 4b) first exhibits a slight broadening below threshold,due to polariton−exciton interaction,34 then, it dramatically

Figure 4. Characterizations of CsPbCl3 microcavity polariton lasing. (a) Ground-state emission spectra at k∥ = 0 under different pumping fluences. Asharp increase of emission intensity occurs beyond 1.0 Pth, suggesting the transition to the nonlinear regime. The emission energy is observed to beblue-shifted with the increasing pump fluence. (b) Ground-state emission intensity at k∥ = 0 and fwhm as a function of pump fluence. A line widthnarrowing occurs near the threshold of Pth = 12 μJ/cm2, along with a sharp increase of emission intensity. (c) Energy blueshift with respect to thepolariton emission energy at the lowest pump fluence as a function of pump fluence. The experimental blueshift of the ground-state emission isshown as blue dots and the red solid line indicates the theoretical calculation of the blueshift. The blueshift trend below the threshold is attributed topolariton−reservoir interaction while the trend above the threshold corresponds to polariton−polariton interaction. (d) Real spacephotoluminescence image measured above threshold from one arm of the Michelson interferometer. Dashed line, sample edges. Scale bar, 4μm. (e) Real space photoluminescence image obtained above threshold from the second arm by using a retroreflector to flip the image in acentrosymmetric way. Dashed line, sample edges. Scale bar, 4 μm. (f) Interference pattern after superposition of the images above threshold from thetwo arms of the Michelson interferometer. Clear interferences are readily identified with a distance as large as 15 μm, demonstrating the buildup of along-range coherence. Dashed line, sample edges. Scale bar, 4 μm.

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narrows from 10.3 to 3.4 meV by further increasing the pumpfluence above threshold to 1.5 Pth, indicating a sharp increase ofthe temporal coherence. Beyond 1.5 Pth, the fwhm broadensslightly again, which could be attributed to decoherenceinduced by polariton self-interactions,34 as well as differentlocalized condensate modes,4 such as in previous studies oninorganic microcavities. The threshold and line width featuresclearly suggest the occurrence of stimulated scattering into thepolariton ground state at k∥ = 0. Another crucial evidence toprove the appearance of polariton condensate is the continuousblueshift of the polariton emission energy along with theincrease of excitation density, which serves as a clear signatureof the repulsive interactions between the polaritons. We plotthe energy blueshift of the ground-state emission at k∥ = 0 as afunction of pump fluence as shown in Figure 4c. We observe amaximum blueshift of 10 meV of the polariton condensate,which is much smaller than the energy difference of 120 meVbetween the minima of the lower polariton and uncoupledcavity mode dispersions. Two distinct slopes are also observedbelow and above threshold and to gain more insight into thisbehavior we developed a model by coupling the driven-dissipative Gross-Pitaevskii equation to a rate equation for areservoir of excitons (Methods). The calculated blueshift,shown as a solid red line in Figure 4c, fits well with ourexperimental results. Below threshold, it is dominated by theinteraction between polaritons and the reservoir of excitedstates. While above the threshold, the polariton−polaritoninteraction becomes much more prominent, compared with thepolariton−reservoir interactions. The difference of interactionstrengths between these two mechanisms gives rise to these twodistinct blueshift trends.18 To unambiguously prove that lasingoccurs in strong coupling regime, we further demonstrate thetransition from strong coupling to weak coupling regime at highpumping fluence based on the perovskite microcavity with apositive detuning of Δ = +70 meV, which is more likely toreach a sufficiently high carrier density in the reservoir for theformation of an electron-hole plasma (Supplementary Section4). We observed dispersion-less emissions at a pump fluence of5 times the polariton lasing threshold, associated with acontinuous redshift which is in stark contrast to the continuousblueshift in polariton lasing regime (strong coupling regime).We attribute such dispersion-less emissions as electron-holeplasma emissions which can be regarded as a signature of thetransition from strong coupling to weak coupling regime.To further confirm the occurrence of polariton lasing

unambiguously, we checked the long-range spatial coherenceby interferometry measurements, as it is one of the importantfeatures of polariton condensation. For this purpose, the realspace emission image of the polariton condensate is sent to aMichelson interferometer in which one of the arms is replacedby a retroreflector to invert the image in a centro-symmetricalconfiguration. The use of the retroreflector enables themeasurement of the first-order spatial coherence g(1)(r, −r)based on the interference fringes contrast or in other words thephase coherence between points localized at r and −r from thecenter of the polariton condensate. Figures 4d,e display the realspace emission image of the polariton condensate and itsinverted image, respectively. First of all, we observe severalbright spots in the real space emission image, which areassociated with the localization of the polariton condensate,possibly as a result of the photonic disorder inherited from thesample transfer process during the fabrication of the perovskitemicrocavity. Similar phenomena have been widely observed in

organic and inorganic polariton condensates before.4,17

Furthermore, effects on the polariton distribution near k∥ = 0from disorder can also be identified from the lower polaritonbranch above the polariton lasing threshold of other typicalsamples on the same sample chip (Supplementary Section 5).We extended the Gross-Pitaevskii theory to account for spatialdynamics in the real space. Using the dispersion obtained fromcoupled oscillator fitting and including some disorder, thelocalization effect can be successfully reproduced (seeSupplementary Section 6). Finally, Figure 4f presents theinterference image resulting from the superposition of the twoprevious images shown in Figure 4d,e, where unambiguousinterference fringes are readily identified along a distance aslarge as 15 μm. This latter result is a clear demonstration of thebuildup of a long-range spatial coherence associated with theformation of a polariton condensate in our all-inorganicperovskite system.In conclusion, we have observed unambiguous evidences for

polariton condensation and the subsequent polariton lasing inan all-inorganic CsPbCl3 perovskite planar microcavity at roomtemperature. The successful realization of polariton lasingwithin a low Q microcavity, along with its ease of fabricationand the inorganic nature of its active medium, significantlyalleviates the stringent requirements to approach thefundamental physics of BEC. Our findings open a new platformwith compelling properties toward realization of large-area, low-cost, and high-performance polariton devices and potentiallytoward an electrically pumped BEC coherent light source atroom temperature.

Methods. Microcavity Fabrication. The bottom DBR wasfirst fabricated by an e-beam evaporator, consisting of 13 pairsof silicon dioxide (73 nm) and hafnium dioxide (54 nm)capped by silicon dioxide. It was then put as an in situ substratein a single zone tube furnace (Lindberg/Blue MTF55035C-1)to directly grow CsPbCl3 perovskite crystals on top of thebottom DBR. The detailed procedure of the growth of theperovskite is the same as described in our previous report onmica substrate.29 Thinner CsPbCl3 perovskite platelets couldalso be transferred from growth mica substrate to bottom DBRsubstrates by a dry tape transfer process, while the micasubstrate was totally removed by exfoliation using a scotch tape.The bottom DBR with CsPbCl3 perovskite platelet on top wasthen transferred into the e-beam evaporator again to completethe fabrication of a top DBR, which consists of seven pairs ofsilicon dioxide (68 nm) and hafnium dioxide (50 nm). Bothmethods (in situ growth or dry transfer) can work to producehigh quality samples for cavity polariton studies (seeSupplementary Section 1).

Optical Spectroscopy Characterization. The fluorescenceimage of the perovskite microcavity was obtained through anOlympus microscope where the microcavity is illuminated withan Olympus U-HGLGPS lamp after passing through a 355 nmbandpass filter. The absorption spectrum was measured using aPerkinElmer Lambda 950 UV−vis-IR spectrometer. Steady-state photoluminescence measurement was conducted in aconfocal spectrometer (Horiba Evolution) by using a helium−cadmium laser (325 nm) with a pump power of 10 μW. Angle-resolved photoluminescence and reflectivity spectroscopy wasmeasured in a home-built microphotoluminescence setupwithin the Fourier imaging configuration. For a continuouswave laser of 325 nm pumping and white light illumination, theangle-resolved photoluminescence and reflectivity shown inFigure 2 were measured through a high numerical aperture

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100× microscope objective (NA = 0.9), covering an angularrange of ±64.1°. For pulsed laser pumping, the angle-resolvedphotoluminescence shown in Figure 3 was measured through along working distance 100× microscope objective (NA = 0.75),covering an angular range of ±48.5°. The emission from themicrocavity is collected through the same objective and sent toa 550 mm focal length spectrometer (Horiba iHR550) with a600 lines/mm grating and a 256 × 1024 pixel liquid nitrogencooled charge-coupled device (CCD). The perovskite micro-cavity is pumped by off-resonant excitation centered at 375 nmwith pulse duration of 100 fs and repetition rate of 1 kHz (lightconversion optical parametric amplifier pumped by a SpectraPhysics Spitfire Ace Ti:sapphire regenerative amplifier). Theexcitation laser beam, which is slightly elliptic, was focuseddown to a ∼25 μm spot on the sample.Nonequilibrium Condensation Model. To describe the

nonequilibrium condensation in our system we apply thedriven-dissipative model of previous report,35 neglecting forsimplicity spatial dependence

ψ α ψ ψ

ψ

ℏ = + | | + + ℏ − Γ

= − Γ + | |

⎡⎣⎢

⎤⎦⎥i

tE g n

irn

nt

P r n

dd 2

( )

dd

( )

02

R R R

RR

2R

Here ψ represents the coherent polariton field, coupled to anequation for the density of higher energy excitations nR (areservoir). E0 is the energy of the bare polariton resonance; αrepresents the strength of polariton−polariton interactions; gRis the strength of interactions between polaritons and the highenergy reservoir; r is the condensation rate; Γ is the polaritondissipation rate; ΓR is the reservoir decay rate; and P is thepumping rate.The equations are readily solved analytically for the steady

state, where the condensate mean-field population |ψ|2 is

nonzero above the threshold pumping rate = ΓΓℏP

r0R . Above the

threshold, the polariton energy shift with pumping rate is givenby

α αΔ = ℏ

Γ−

Γ+

Γℏ

EP

r

g

rR R

and below the threshold, the polariton energy shift withpumping rate is given by

Δ =Γ

Eg PR

R

This allows plotting the theoretical curve in Figure 4c, taking

parameters =Γ

ℏ 10.6 meVg

rR and =αΓ 0.86 meV

rR as the

relevant fitting parameters (it is also assumed that thetheoretical pumping rate P is linearly proportional to theexperimental pump power). The slope of the energy shift withpumping rate has a discontinuity at the threshold, becausebelow and above threshold the condensate and reservoirpopulations have different growth rates with pumping rate. Inaddition, the interaction energy associated with polariton−polariton interaction and polariton−reservoir interaction isgenerally different.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.7b01956.

Additional information on sample synthesis, character-ization of room-temperature photoluminescence, DBRcavities, polariton dispersion, and theoretical calculationson condensate localization (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail address: Qihua@ntu.edu.sg.

ORCIDQihua Xiong: 0000-0002-2555-4363Author ContributionsR.S., C.D., and Q.X. conceived the idea and designed theresearch; R.S., J.W., and Z.C. performed the DBR fabrication,sample growth, and all the optical measurements; T.C.L.carried out the theoretical calculations. R.S., C.D., Z.C., andQ.X. analyzed the data; R.S., C.D., T.C.L., and Q.X. wrote themanuscript. All authors discussed and commented on themanuscript.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSQ.X. acknowledges the support from the Singapore NationalResearch Foundation through the NRF Investigatorship Award(NRF-NRFI2015-03), and the Singapore Ministry of Educationvia AcRF Tier 2 Grant (MOE2015-T2-1-047). This work wasalso supported in part by a Competitive Research Program(NRF-CRP-6-2010-2) from the Singapore National ResearchFoundation. T.L. acknowledges support from the SingaporeMinistry of Education via AcRF Tier 2 Grant (2015-T2-1-055).

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DOI: 10.1021/acs.nanolett.7b01956Nano Lett. 2017, 17, 3982−3988

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