Population inversion and giant bandgaprenormalization in atomically thin WS2 layersAlexey Chernikov1*†, Claudia Ruppert1†, Heather M. Hill1, Albert F. Rigosi1 and Tony F. Heinz1,2,3*

Control of the optical properties of matter on ultrashort timescales is of both fundamental interest and central importancefor applications in photonics. It is desirable to achieve pronounced changes over a broad spectral range using the leastpossible amount of material. Here, we demonstrate a dramatic change over a spectral range of hundreds of meV on thefemtosecond timescale in the optical response of atomically thin two-dimensional crystals of the transition-metaldichalcogenide WS2 following excitation by intense optical pump pulses. Our findings reveal the role of extremely strongCoulomb interactions. At the direct gap, we observe a Mott transition from excitonic states to free carriers, accompaniedby a giant bandgap renormalization of approximately 500 meV and the development of population inversion.

Many-body phenomena arising from the interaction betweencharge carriers are of central importance in condensed-matter physics. In semiconductors, Coulomb interactions

can lead to the formation of stable many-particle electronic states,such as excitons, trions, excitonic molecules and dropletons, aswell as macroscopic condensates1–5. Excitonic quasi-particlesappear as pronounced resonances in the optical response and candominate absorption and emission spectra6. These many-bodyinteractions can be strongly altered in the presence of elevatedelectron–hole densities7, providing a method of modifying thematerial’s response by optical carrier injection via ultrashort,intense laser pulses. From the fundamental point of view, thisapproach offers an excellent experimental method to probe many-body interactions under controlled conditions. For applications,these phenomena can be exploited in photonic devices rangingfrom lasers to optical switches, saturable absorbers, and modulators.In this respect, the emerging field of atomically thin two-dimen-sional materials, such as semiconducting transition-metal dichalco-genides (TMDCs)8–11, shows much promise. These materialsprovide strong light–matter coupling, with optical absorptionaround 10–20% in layers as thin as 0.6 nm12–14 and extremely effi-cient Coulomb interactions, with exciton binding energies on theorder of 0.5 eV (refs 15–19). Recent theoretical studies of mono-layer TMDCs20 predict that high carrier densities should producemassive changes in the optical response. However, despite anumber of studies addressing the dynamics of excitons21–35, the be-haviour of these systems under strong photoexcitation in theregime of a dense electron–hole plasma beyond the Mott transitionremains unexplored experimentally.

Here we access this regime by subjectingWS2 mono- and bilayersto strong photoexcitation, injecting carriers via ultrashort laserpulses with fluences up to several mJ cm–2. We show that theoptical response of atomically thin TMDC crystals changes dramati-cally across a spectral range of many hundreds of meV at highelectron–hole densities. We observe both a complete disappearanceof the main excitonic resonance and the development of a spectralfeature with negative differential absorption at lower photonenergies. The semiconductor undergoes a Mott transition from aninsulating excitonic regime to an electron–hole plasma. The

subsequent response is characterized by the absence of excitonic res-onances, population inversion, and bandgap renormalization on theorder of 500 meV. The energy scale of the observed changes is atleast one order of magnitude larger than found in conventionallow-dimensional systems, such as III–V quantum wells36–38. Weshow that the strong pump-induced restructuring of the opticalproperties of the two-dimensional TMDC materials is highly tran-sient, with picosecond lifetimes and full recovery of the opticalresponse in hundreds of picoseconds, both at cryogenic androom temperatures.

Our samples were mechanically exfoliated on quartz substratesand their optical response was investigated by spectrally resolvedultrafast pump–probe spectroscopy (see Methods for details). Thematerials were excited by 250 fs laser pulses centred at a photonenergy of 2.4 eV, corresponding to the resonance of the split-offvalence band (B-exciton) and the onset of the ionization continuumof the lowest direct transition (A-exciton) in WS2 (refs 14,17,39).In the following we use the reflectance contrast spectra (RC)as the experimental observable. This quantity is the relativereflectance of the sample with respect to the quartz substrate:RC = (Rsample − Rsubstrate)/Rsubstrate. For the ultrathin layers investi-gated here with moderate reflectance contrast signals arising fromthe samples on a transparent substrate, the reflectance contrast isessentially determined by the imaginary part of the dielectric func-tion, that is, by the sample absorption40,41 (see SupplementarySection 4 for a direct comparison of reflectance and transmissionspectra). A reflectance contrast of unity on fused silica correspondsto an increase in the optical reflectance of the sample by 0.035, asobtained from the refractive index of the substrate of 1.46. In caseof the studied TMDC layers, this corresponds to an effectiveoptical absorption of ∼0.12 for the supported samples on fusedsilica (see ref. 14 for details).

The response of a WS2 layer after strong pump excitation ispresented in Fig. 1a. Here, reflectance contrast spectra of a WS2bilayer are plotted with and without pump excitation pulses. Anapplied pump fluence of 840 μJ cm−2 or 2.2 × 1015 photons cm−2

was used. Taking the light absorption during the pump pulse tobe that in the linear regime14, we estimate an electron–holedensity per WS2 layer approaching 1.1 × 1014 cm−2. Possible

1Departments of Physics and Electrical Engineering, Columbia University, 538 West 120th Street, New York, New York 10027, USA. 2Department ofApplied Physics, Stanford University, Stanford, California 94305, USA. 3SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California94025, USA. †These authors contributed equally to this work. *e-mail: aac2183@columbia.edu; tony.heinz@stanford.edu

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nonlinear absorption of the pump pulse is discussed inSupplementary Section 5. In the absence of pump excitation, thespectrum is dominated by the A exciton resonance, lying slightlybelow 2 eV in energy and corresponding to the direct transition atthe K and K′-points of the Brillouin zone. The exciton state is, infact, associated with the charged (trion) species. This reflects thepresence of both unintentional doping and photoinduced dopingof the samples at a density of ∼1 × 1013 electrons cm−2 (seeSupplementary Section 1 for additional details). The underlying,featureless spectral background is attributed to the low-energy tailof the strong high-energy optical transitions, which have beenwidely observed in this type of material13,14,42,43 and are centredabove the pump photon energy.

After pump excitation, we find that the absorption feature associ-ated with the exciton resonance completely disappears (Fig. 1a).Instead of a peak in the absorption, we observe the emergence ofa broad dip in the spectrum, several hundreds of meV below theinitial excitonic transition, with an onset at ∼1.65 eV and amaximum around 1.7 eV. A detailed view of the relevant spectralregion is shown in the inset of Fig. 1a. The corresponding differen-tial reflectance contrast spectrum ΔRC, defined as the differencebetween the spectra with and without pump excitation, is presentedin Fig. 1b. It exhibits a strong negative signal at the exciton transitionaround 2 eV from the complete bleaching of the resonance anda weaker negative signature corresponding to the dip in theoriginal spectrum. The relative magnitude of the latter negativeresponse is about 10% of the peak absorption of the originalexcitonic transition.

To understand the origin of the drastic changes observed in theoptical response, we turn to the predictions of the well-developedmany-body theory for quasi-two-dimensional semiconductors7, atheory that has been extensively applied to conventional direct-and indirect-gap quantum-well systems36–38,44. A schematic rep-resentation of the optical absorption adapted from ref. 7 is presentedin Fig. 2a for both low and high densities of electron–hole pairs. Thelow-density case corresponds to the linear response of the materialand is characterized by the exciton ground-state resonance (X) and

the onset of the ionization continuum, that is, of the quasi-particlebandgap Egap. Here, the horizontal axis is shown in units of theexciton binding energy (EB,0) relative to the bandgap energy.The high-density case describes the semiconductor after strong,non-resonant photoexcitation and corresponds to the conditionsin our experiment. In this regime, the Coulomb interactionbetween charge carriers is strongly screened due to the highdensity of carriers. The screening of the attractive interactionbetween the opposite charges reduces the exciton binding energyto zero: the semiconductor undergoes a so-called Mott transitionfrom the insulating excitonic regime to a dense electron–holeplasma, as illustrated in Fig. 2c. The exciton is no longer a boundstate and the exciton resonance disappears. (The peak-like contri-bution from the Coulomb enhancement in the plasma continuum7

also becomes negligible at these high densities.) The reduction of therepulsive Coulomb interaction between the charges of the same signresults in a decrease in the quasi-particle energy. This produces abandgap renormalization, shifting the bandgap even below theenergy of the initial exciton peak. A more detailed discussion ofthe renormalization effect can be found in Supplementary Section6. In addition, filling of the conduction and valence band stateswith electrons and holes leads to a shift of the quasi-Fermi levelsfar into the respective bands. This contributes to the bleaching ofthe exciton resonance via Pauli blocking and, more importantly,leads to inversion of the carrier population near the band edge.The latter manifests itself in the emergence of a spectral regionwith a negative optical absorption, starting at the renormalizedbandgap energy and extending to a point defined by the effectivechemical potential, where the absorption crosses zero and becomespositive. In the absence of any additional absorption or scatteringchannels this will allow the material to show optical gain, that is, toamplify radiation instead of absorbing it.

These two hallmarks of the high-density case—the disappear-ance of the exciton resonance and the simultaneous developmentof a broad dip in the spectrum at lower photon energies—matchour experimental observations. Potential contributions from thebleaching of the optically bright defect states and indirect gap

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Figure 1 | Photoinduced optical response of WS2 bilayers. a, Reflectance contrast spectra, shown without pump excitation (RC,0) and 0.4 ps after excitation(RC) by a pump pulse with an applied fluence of 840 μJ cm−2. The sample temperature was T = 70 K. The solid red line is a guide to the eye, obtained bysmoothing the original data (light red). The low-energy part of the spectra is presented in the inset. b, Corresponding differential reflectance contrast spectraΔRC = RC – RC,0. The region around 2 eV is scaled by a factor of 0.3. c, Reflectance contrast spectra at different time delays after excitation, vertically offsetfor clarity (n.p. denotes the spectrum without pump excitation). d, Differential reflectance contrast as function of time delay and photon energy in a false-colour plot. e, The ΔRC transient, spectrally integrated between 1.68 eV and 1.72 eV, as shown by the arrow and dotted rectangle in d. The instrumentresponse is indicated by the grey area.

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Γ-to-K transition in the bilayer system are excluded due to theoverall strength of the measured response (see SupplementarySection 2 for a detailed discussion). For a direct comparison, thedata from Fig. 1a are presented in Fig. 2b after subtraction of alinear background. This allows us to extract the position of therenormalized bandgap from the onset of the negative signal. Wefind a renormalized bandgap energy of 1.65 eV, which lies 300 meVbelow the energy of the exciton. Furthermore, the spectral widthof this feature of 100 meV indicates the range of population inver-sion in the electron and hole bands.

We can compare this result with expectations based on thedensity of carriers generated by the pump pulse. Because we areprobing a WS2 bilayer here, we need, however, to consider therole of additional valleys, both in the conduction (Λ) and valence(Γ) bands that lie below the band edges at the K point. To thatend, we applied a simple model of two-dimensional parabolicbands at the band extrema, with the masses (me = 0.3 (K),0.56 (Λ);mh = 0.26 (K), 1.21 (Γ)) and band offsets (ΔEΛ–K = 80 meV,ΔEΓ–K = 240 meV) taken from band-structure calculations45.Within this model, we obtain quasi-chemical potentials for theelectrons and holes of 270 meV (relative to Λ) and 375 meV (rela-tive to Γ), respectively, assuming a carrier density per layer of1.1 × 1014 cm−2 and a range of possible carrier temperatures up to1,000 K. These values for the chemical potentials correspond topopulation inversion at the K-point extending into the bands by∼140 meV, consistent with our experimental findings. This treat-ment only provides a rough estimate of the behaviour, becausemany-body effects and deviations of the band dispersions fromthe assumed parabolic shape are expected. Furthermore, directlyafter excitation, non-thermal carrier distributions may be presentin the system. Nonetheless, this simple analysis shows that thehigh density of photoexcited carriers is alone sufficient to producepopulation inversion in the K-valley of WS2 bilayers under quasi-equilibrium conditions. In addition, a rough estimate of the Mottdensity in our system based on the exciton Bohr radius a0 on the

order of 1 nm (refs 17,43) yields a value of a−20 = 1 × 1014 cm−2. Asthis model is typically considered to overestimate the actual Mottdensity6, the excitation conditions in our experiment are fully con-sistent with the observed transition from an excitonic regime to anelectron–hole plasma.

To obtain the magnitude of the bandgap renormalization effect,we estimated the initial energy of the bilayer quasi-particle bandgap,which lies above the observed excitonic transition by the excitonbinding energy. In bilayers the measured energy separation of theexciton ground state and the first excited state is known from exper-iment to be 100 meV (ref. 17). Assuming that the excited excitonicstates scale as they do in monolayer samples, we then obtain anexciton binding energy of ∼200 meV. Thus, from the measuredexciton emission energy of 1.95 eV in the present sample, we inferthat the quasi-particle bandgap lies around 2.15 eV. The carrier-induced shift to 1.65 eV under high excitation density then corre-sponds to a renormalization of 500 meV. This value is at leastone order of magnitude greater than that seen in conventionalquantum-well systems under conditions of high excitationdensity36–38,44. The reason for such an unusually strong many-body effect in the present case is the highly efficient Coulomb inter-action in the limit of atomically thin two-dimensional materials, asmanifested in the exciton binding energies of hundreds of meV.The magnitude of the bandgap renormalization scales with thisvalue7 (Fig. 2a). Such unusually large renormalization energieshave, in fact, been explicitly predicted in a recent theoretical studyof MoS2 monolayers20.

To examine the dynamics and the reversibility of the observedoptical response, we present the evolution of the spectra in Fig. 1cas a function of delay time after excitation (additional individualspectra in the −0.3 ps to 5 ps range are presented inSupplementary Section 7). The corresponding differential spectra(ΔRC) are plotted in Fig. 1d as a function of energy and timedelay for the first 20 ps, and the inversion dynamics are shown inFig. 1e, as obtained from the spectral integration between 1.68 eVand 1.72 eV. The data at negative time delays correspond to thelinear response of the sample without pump excitation, indicatingnegligible quasi-stationary heating. The initial bleaching of theexciton peak and inversion both develop instantaneously withinthe experimental resolution of 0.4 ps, indicating that initial relax-ation processes occur on the 100 fs timescale. The inversion signal

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Figure 3 | Evolution of the population inversion with pump fluence.a, Differential reflectance contrast spectra of a WS2 bilayer 0.4 ps afterexcitation with pump fluences between 35 μJ cm−2 and 840 μJ cm−2 atT = 70 K. The spectra are vertically offset for clarity and smoothed dataare shown as solid lines. b, The low-energy region of the differentialreflectance spectra, indicated in a by the dotted rectangle.

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Figure 2 | Optical absorption of a two-dimensional semiconductor in thepresence of high electron–hole densities. a, Schematic representation of theoptical absorption of a two-dimensional semiconductor for regimes of lowand high carrier density, adapted from the predictions of microscopicmany-body theory7. The horizontal axis is plotted in units of thezero-density exciton binding energy EB,0 relative to the bandgap energy Egap.b, WS2 bilayer data for strong optical excitation from Fig. 1a after subtractionof a linear background. c, Illustration of the transition from the low-densityexcitonic regime to a dense electron–hole plasma.

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is found to decay with a time constant of ∼1 ps and is attributed tothe decay of the electron–hole population. In addition to extrinsicnon-radiative channels from defects, both efficient Auger-type pro-cesses30,32,35 and radiative recombination of electron–hole plasmacan strongly contribute at such high carrier densities. The decreas-ing rate of the initial decay observed at lower pump densities (seeSupplementary Section 3 for details) provides additional supportfor the role of these latter two density-dependent processes.Subsequently, after several picoseconds, the exciton resonanceslowly recovers, showing spectral broadening and a redshift by∼100 meV, resulting in the positive tail in the transient reflectancecontrast data in Fig. 1e. The redshift can be attributed both tolattice heating from energy transfer to the phonon system and topossible residual effects of bandgap renormalization at lowercarrier densities20. In this regime, the position of the bandgapshifts back to lie above the exciton resonance. After ∼250 ps, theoptical response fully returns to the initial condition.

We now turn to the variation of the response with pump fluence,highlighting the behaviour of the inversion signature. Differentialreflectance contrast spectra of the WS2 bilayer 0.4 ps after excitationare presented in Fig. 3a for pump fluences between 35 μJ cm−2 and840 μJ cm−2 (corresponding reflectance contrast spectra arepresented in Supplementary Section 8). For relatively low fluences,the lowest-lying transition shows the combined effect of bleachingof the exciton resonance and increased spectral broadening, attrib-uted to the effect of Coulomb scattering7. Both effects grow withincreasing fluence. In addition, the previously observed inversionfeature with its negative differential response gradually develops atlower energies, as shown in Fig. 3b in more detail. The correspond-ing threshold fluence for the development of population inversion is∼200 μJ cm−2, which is somewhat smaller than that obtained fromthe rough estimate within the band-filling model presented above.The width of the inversion signature increases and the onsetappears to shift to lower energies for higher pump fluence, bothobservations consistent with our interpretation of the increasingwidth of the inversion region and larger bandgap renormalizationat higher carrier densities.

Finally, we demonstrate that the key changes in the opticalresponse observed in the WS2 bilayer—namely, the complete disap-pearance of the exciton peak and the development of an inversionfeature—are also seen in monolayer samples. Differential reflectancecontrast spectra of a WS2 monolayer at T = 70 K are presented inFig. 4a as function of photon energy and time delay for a pumpfluence of 840 μJ cm−2. In close analogy to the bilayer data inFig. 1d, the monolayer exhibits a spectrally broad negative differen-tial response extending more than 300 meV below the ground-statetransition. The decay of this signal, as shown by the transientresponse centred at 1.8 eV and plotted in Fig. 4b, is comparable,but somewhat faster than in the bilayer. The lower overall opticalresponse and the resulting lower signal-to-noise ratio in the mono-layer sample preclude a precise determination of the photon energyfor the signal’s onset. Still, inspection of the data reveals that theinversion feature in the monolayer is present at lower photon ener-gies relative to the increased bandgap energy (around 2.4 eV)17 andthat the inversion feature has a broader spectral width compared tothe bilayer. These characteristics are fully consistent with enhancedCoulomb interaction strength in the monolayer, as well as with thematerial’s direct-gap character. The corresponding spectral traces,presented in Fig. 4c as a function of delay time (differentialspectra are shown in Supplementary Section 9), illustrate the emer-gence of the exciton resonance with a redshift of ∼100 meV and thesubsequent full recovery of the linear response after 250 ps, closelymimicking the behaviour of the bilayer (cf. Fig. 1c). Moreover, thecomplete transient bleaching of the exciton transition followed bythe strong redshift and recovery are also observed in room-tempera-ture data. As an example, monolayer spectra are presented in Fig. 4dfor a pump fluence as high as 3,400 μJ cm−2 (obtained with a slightlysmaller pump spot of 3 μm diameter). The latter result demonstratesthat even under ambient conditions, monolayer TMDC samples canexhibit dramatic ultrafast changes in their optical response whenstrongly pumped.

In summary, we have shown that atomically thin TMDCs exhibita complete restructuring of their band-edge optical response afterintense photoexcitation through a Mott transition. The exciton

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Figure 4 | Photoinduced optical response of WS2 monolayers. a, Differential reflectance contrast of the WS2 monolayer as a function of time delay andenergy in a false-colour plot after excitation with a pump fluence of 840 μJ cm−2 at T = 70 K. b, ΔRC transient, spectrally integrated between 1.75 eV and1.85 eV, with the area denoted in a by the arrow and dotted rectangle. c, Corresponding reflectance contrast spectra at different time delays after pumpexcitation, vertically offset for clarity (n.p. denotes the spectrum without pump excitation). d, Same as c, for T = 290 K and a pump fluence of 3,400 μJ cm−2.

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resonance, which dominates the linear spectra, disappears completely.A bandgap renormalization of 500 meV or more is observed, whichis an order of magnitude larger than that found in conventionalquantum-well systems. All changes are transient and reversible innature, so the material fully recovers its initial optical response.The observed phenomena are intimately connected with thestrong Coulomb interaction between charge carriers in theseatomically thin two-dimensional systems. Induced changes inthe optical spectra over hundreds of meV are consonant withlarge exciton binding energies in these materials that also lie inthe range of hundreds of meV. The observation of these phenomenain samples at room temperatures and under ambient conditions ishighly advantageous for potential applications of the mono- andfew-layer TMDCs in optoelectronic and photonic devices, such aslasers, optical modulators and saturable absorbers, particularly forapplications benefiting from the nanoscale dimensions ofthe material.

MethodsMethods and any associated references are available in the onlineversion of the paper.

Received 9 February 2015; accepted 19 May 2015;published online 15 June 2015

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AcknowledgementsThis work was supported by the USDepartment of Energy, Office of Science, Office of BasicEnergy Sciences, with funding at Columbia University through the Energy FrontierResearch Center under Grant DE-SC0001085 and at SLAC National AcceleratorLaboratory through the AMOS programmewithin the Chemical Sciences, Geosciences andBiosciences Division, by the Keck Foundation, and by the Air Force Office of ScientificResearch (grant no. FA9550-14-1-0268). C.R. and A.C. acknowledge partial funding fromthe Alexander von Humboldt Foundation within the Feodor Lynen Research Fellowshipprogramme. H.M.H. and A.F.R. were supported, respectively, by the NSF through anIGERT Fellowship (grant no. DGE-1069240) and by a Graduate Research Fellowship(DGE-1144155).

Author contributionsA.C. and C.R., contributing equally to this work, designed the experiment, carried out themeasurements and analysed the data. H.M.H. and A.F.R. prepared and characterized thesamples. A.C., C.R. and T.F.H. wrote the manuscript. All authors contributedto discussions.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Correspondence andrequests for materials should be addressed to A.C. and T.F.H.

Competing financial interestsThe authors declare no competing financial interests.

ARTICLES NATURE PHOTONICS DOI: 10.1038/NPHOTON.2015.104

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MethodsSample preparation. Mono- and bilayer samples of WS2 were produced bymechanical exfoliation of WS2 bulk synthetic crystal onto a fused-silica substrate.The samples were identified by optical microscopy and the number of layers wasindependently confirmed by photoluminescence spectroscopy.

Pump–probe spectroscopy. The pump laser for our measurements was a frequency-doubled, amplified fibre laser system that produced pulses of 250 fs duration at arepetition rate of 200 kHz, with a photon energy centred at 2.4 eV. For the probepulse we employed broadband supercontinuum radiation generated in a YAG crystalby pulses from the fundamental frequency of the pump laser. Both the pump andprobe pulses were focused onto the sample in a collinear geometry by a microscopeobjective, yielding respective spot sizes of 5 μm and 2 μm. The two beams were

circularly polarized, with opposite polarizations (similar results were obtained forother polarization combinations). The sample was held in a cryostat and themeasurements were performed at liquid-nitrogen and room temperatures. Thereflected probe signal was spectrally dispersed in a spectrometer and detected by acharge-coupled device array. We adopted a balanced detection scheme, with areference white-light pulse being simultaneously measured to compensate forfluctuations in the intensity of the probe beam. All data were corrected for thewavelength-dependent chirp of the white-light supercontinuum, which wasmeasured using the ultrafast response of a thin gold foil. The instrumentresponse time of 400 fs (full-width at half-maximum) was estimated from the risetime of the signal from the gold sample. We also note that the reference spectra forthe substrate were also obtained under pump excitation to account for any residualpump-induced changes of the substrate.

NATURE PHOTONICS DOI: 10.1038/NPHOTON.2015.104 ARTICLES

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