Main

In solid state systems, spontaneous anti-Stokes emission describes the scattering of low-energy incident photons to higher energy by absorbing energy quanta of lattice oscillations (optical phonons), while Stokes emission refers to the conjugate process of adding phonons to the lattice. The efficiency of these processes can be enhanced by a large optical transition strength in the light–matter interaction, or by realizing doubly resonant conditions, meaning both incident and emitted photons are in resonance with electronic transitions whose energy spacing matches an optical phonon. In semiconductors, doubly resonant Stokes scattering has been observed by applying stress10, electrical11, or magnetic fields12 to tune the band-to-band transitions towards a double resonance, where the excitonic effect realizes an enhancement of the optical transition dipole. However, spontaneous anti-Stokes emission with excitonic double resonance has not been observed. Realizing such a selective enhancement of spontaneous anti-Stokes over Stokes processes implies the appealing possibility of optically cooling semiconductors.

Monolayer semiconductors offer a platform with both strong photon–exciton and phonon–exciton interaction effects13,14. The strong Coulomb binding15,16,17,18,19,20,21 leads to large optical transition dipoles of excitons, about one order of magnitude stronger than those in GaAs quantum wells. In particular, monolayer semiconductors possess charged exciton binding energies of the order of tens of meV, which all lie nearly resonant with corresponding optical phonon energies. For instance, in monolayer WSe2, the negatively charged exciton (X−) has a binding energy of 30 meV matching the A1′ optical phonon5,6,7,8, that is, X− plus a phonon is nearly energy degenerate with the neutral exciton (Xo), resulting in a unique excitonic doubly resonant condition10. We thus expect that, in addition to electrostatic tunability5 and exotic valley physics22,23,24, monolayer WSe2 with its large excitonic oscillator strength may offer opportunities to investigate many-body interactions between X−, Xo and phonons, including X−–phonon bound states and efficient excitonic anti-Stokes processes with the potential for laser cooling at the monolayer limit.

Here, we report the observation of spontaneous anti-Stokes scattering from the negatively charged exciton to the neutral exciton, enhanced by doubly resonant excitation in monolayer WSe2, which is simultaneously valley selective and electrically tunable (see Fig. 1a for a device image). We employ low-energy excitation spectroscopy and monitor emission at >5 meV above the excitation energy, referred to hereafter as reverse photoluminescence (PL). After photo-excitation, the resulting luminescence is directed through an adjustable 4f spectral filter, which allows the detection of either standard PL (above exciton resonance excitation) or reverse PL, and permits a quantitative comparison between the two (Fig. 1b). The black data of Fig. 1c show the standard PL spectrum near intrinsic doping levels with 1.96 eV excitation. The spectrum consists of Xo and X− peaks5.

Figure 1: Upconversion of negatively charged exciton to neutral exciton luminescence.
figure 1

a, Optical micrograph of a device with 5 μm scale bar. b, Schematic of the 4f spectral filter used in photoluminescence measurements for above- and below-Xo excitation (see Methods). c, Superposition of photoluminescence spectra for 1.96 eV excitation (black) and 1.715 eV excitation (red), indicated by the red arrow. Inset: upconversion scheme. d, Log–log plot of reverse PL intensity as a function of power showing a linear response. Black (red) data correspond to a sample temperature of 30 K (90 K). Intensity has been normalized at 10 μW for clarity, while error bars show the standard deviation of nine points around the PL peak. The blue line is a guide to the eye with a slope of unity.

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Remarkably, when exciting 30 meV below the Xo resonance, nearly resonant with X−, we find significant exciton emission (Fig. 1c, red data). The upconverted luminescence possesses the same line shape and peak energy as Xo obtained in standard PL. Figure 1d presents a log–log plot of upconverted Xo emission versus excitation intensity at 30 K (black data) and 90 K (red data), where we normalize the intensities at 10 μW excitation to facilitate comparison. At both temperatures, we excite 30 meV below the emission peak. As the data all follow the linear relationship indicated by the blue line, we rule out the possibility of nonlinear optical generation of the observed PL upconversion, such as two-photon excitation-induced emission21,25 and exciton Auger scattering26,27. A comparison of the upconverted Xo intensity with standard PL emission under the same excitation conditions reveals a ratio of about 5%, a notable contrast given that 30 meV at 30 K represents an energy gain >10kBT.

What is the origin of the upconversion from the X− resonance to Xo? One possibility is that an exciton–phonon replica of Xo exists near the X− resonance, since both A1′ and E′ phonons may produce replicas about 30 meV from the zero-phonon peak8. We rule out such an explanation through two experiments. First, we perform a gate-dependent study of reverse PL with excitation 30 meV below Xo (Fig. 2a). The upconverted emission at Xo reaches peak intensity at a gate voltage Vg ≍ 35 V, where electron doping leads to maximum X− state emission in conventional PL, and lies outside the doping range where Xo PL is appreciable (see Fig. 2b). In addition, the reverse PL intensity plot in Fig. 2a does not show resonant luminescence upconversion from X+ in the hole-doping regime. Were the high-energy PL simply due to upconversion of an exciton–phonon replica near X−, its behaviour would be symmetric with respect to gate voltage.

Figure 2: Gate- and polarization-dependent photoluminescence for excitation above and below the exciton.
figure 2

a,b, PL intensity plot as a function of gate and emission energy for an excitation energy of 1.713 eV (a) and 1.96 eV (b). c,d, Polarization-resolved PL spectra with an excitation energy one optical phonon (31 meV) above the neutral exciton for circular (σ+) (c) and linear (V) (d) polarized excitation. Blue arrows indicate the laser excitation position. e,f, Polarization-resolved reverse PL spectra with 1.714 eV excitation (30 meV below neutral exciton), for circularly (e) and linearly (f) polarized excitation/detection. Inset in e illustrates the valley-selective spontaneous anti-Stokes process. The solid red arrow denotes photon excitation, the blue arrow doubly resonant phonon scattering, and the dashed orange arrow spontaneous photon emission.

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Second, we examine polarization-resolved PL for excitation 31 meV above the Xo resonance—that is, resonant Stokes scattering. Figure 2c, d clearly demonstrates that the emission at Xo preserves both the circular and linear polarization of the excitation laser, showing that the involved phonon scattering preserves both the valley polarization and coherence, consistent with recent photoluminescence excitation28 (PLE) and Raman8 spectroscopy measurements. From the complete absence of linearly polarized PL near the X− resonance (Fig. 2d), we can rule out the possibility of an Xo phonon replica near X−, as it would inherit the linearly polarized emission of Xo.

Further, our polarization-resolved reverse PL also shows that the luminescence upconversion conserves valley polarization, but not valley coherence. As seen in Fig. 2e, circularly polarized excitation of X− creates co-circularly polarized Xo emission, but linearly polarized excitation yields unpolarized anti-Stokes Xo emission (Fig. 2f and Supplementary Fig. 1). This contrast between pronounced circular polarization and an absence of linear polarization in the upconverted Xo luminescence mirrors the behaviour of X− PL (ref. 5), implying the luminescence upconversion originates from X−.

In light of the fact that the 30 meV separation between Xo and X− coincides with the A1′ phonon (31 meV), we attribute the observed luminescence upconversion to an excitonic doubly resonant anti-Stokes process. The anti-Stokes scattering here involves a single phonon resonant with the separation of X− and Xo ground states, in contrast with the exciton excited-state multi-phonon Raman scattering discussed in ref. 28, which involves multiple detuned intermediate states and does not result in upconversion. We note that, although the E′ phonon also lies at 31 meV, its role would be negligible in upconversion. The polarization-resolved measurements already presented show a preservation of valley polarization for excitation both above and below Xo, consistent with the polarization properties of the A1′ phonon8. In contrast, Raman from the E′ mode is cross-polarized8 and unpolarized29 for circularly and linearly polarized excitation, respectively. Furthermore, the symmetry of the electronic states within the K valleys dictates a stronger interaction with the out-of-plane A1′ phonon than with the in-plane E′ mode14,30 (see Supplementary Methods I).

In the doubly resonant anti-Stokes process, the photon resonantly excites X−, which is converted into Xo plus an unbound electron by absorbing an A1′ phonon from the environment (Fig. 3a). Spontaneous emission from Xo then produces the upconverted luminescence. We have found that the transfer of population from X− to Xo is well described by Fermi’s golden rule (see Supplementary Methods II and III), where the conversion rate is proportional to the A1′ phonon population and can reach 0.01 ps−1 at a temperature of ≍100 K. This model explains both the polarization-resolved PL and reverse PL measurements already discussed, where the conservation of circular (that is, valley) but not linear polarization within the upconverted Xo is a straightforward consequence of inheriting the X− properties5.

Figure 3: Doubly resonant anti-Stokes and temperature-dependent PL.
figure 3

a, Schematic of the negatively charged and neutral exciton energy level diagram. The red curve is the charged exciton dispersion with its centre-of-mass momentum k−. The blue curves are the dispersions of the unbound exciton–electron pair with their centre-of-mass momentum k0 + ke, different curves correspond to different relative momenta so they form an energy continuum. By absorbing a phonon with momentum Q, the charged exciton can be converted into an unbound exciton–electron pair (dashed arrow). b,c, Temperature-dependent PL intensity plot for excitation at 1.96 eV (b) and 30 meV (c) below peak emission. d, Integrated Xo peak intensity versus temperature, extracted from three different samples, normalized to the intensity at 30 K.

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The upconversion seen here implies efficient population transfer between X− and Xo mediated by resonant phonons, where the absorption/emission of a phonon resonantly induces X− discharging/Xo charging. Correspondingly, higher lattice temperatures should increase the ratio between the upconversion and the downconversion rates of X− and Xo, and we expect a temperature increase to raise the intensity ratio between Xo and X− in standard PL. Our temperature-dependent measurements show behaviour consistent with this picture. Figure 3b, c presents temperature-dependent standard and reverse PL maps, respectively, over a temperature range of 20–250 K. In standard PL measurements, we fix the excitation energy at 1.96 eV, while for reverse PL we maintain an excitation energy 30 meV below the energy of peak Xo emission for each temperature. Across three samples we find a consistent intensity increase of both the standard and reverse Xo PL up to 100 K (Fig. 3d), a consequence of the upconversion rate increasing with the phonon population. Above 100 K, the growth halts as decreasing trion absorption and Xo radiative decay rates counteract the increasing phonon population. Detailed analysis shows the temperature-dependent behaviour of the reverse PL to be in agreement with calculations of upconversion within a phonon-induced discharging model (see discussion in Supplementary Methods V).

Careful examination of the X− spectrum further reveals a doublet structure. As shown in Fig. 4a, this X− doublet can be fit with two Gaussians, which we label as states X|2〉− (high energy) and X|1〉− (low energy), shown by the blue lines (see Supplementary Fig. 2 for an obvious doublet in boron-nitride-supported WSe2,). Through reverse PLE measurements, in which we monitor Xo emission while varying the excitation energy from 1.691 eV to 1.722 eV (red detunings of 23–55 meV from Xo), we find that the higher energy peak, X|2〉−, dominates the upconversion. Figure 4b gives the reverse PLE intensity plot as a function of excitation and luminescence energy, where the anti-Stokes luminescence reaches a maximum for an excitation energy of 1.716 eV. We extract the PLE spectrum by taking a line cut at peak Xo intensity and superpose it with the X− doublet (red squares in Fig. 4a). Clearly, the spectrum peak coincides with X|2〉−. For this particular sample, we find a low-energy tail extending over X|1〉−, although other samples reveal a PLE spectrum more localized to the X|2〉− state (Supplementary Fig. 3). This correspondence supports the attribution of the upconversion to doubly resonant excitonic anti-Stokes, since the phonon energy matches the Xo and X|2〉− energy separation, while X|1〉− lies at a detuning of 7 meV, rendering phonon scattering inefficient. We also find within the X− doublet a strong excitation wavelength and polarization dependence (see Supplementary Fig. 4). For instance, X|2〉− exhibits a larger degree of circular polarization than X|1〉− in standard PL (Fig. 4c and Supplementary Fig. 4a).

Figure 4: Negatively charged exciton fine structure and its role in anti-Stokes.
figure 4

a, Comparison of reverse PLE intensity (red) and conventional PL spectrum (black), with a bi-Gaussian fit to the charged exciton X− peak doublet (blue). Inset: Reverse PLE intensity versus laser detuning, with error bars showing the standard deviation of nine points around the PL peak. b, Reverse PLE intensity plot as a function of excitation and emission energy. c, Polarization-resolved PL spectra with σ+ polarized excitation at 1.96 eV. Black and red curves are co-circular and cross circular detection, respectively. d, Right: Top and bottom cartoons show the inter-valley and intra-valley X−. The diagonal exchange interaction present for the inter-valley X− (green double arrows) lifts the energy degeneracy with intra-valley configurations. Moreover, the inter- and intra-valley X− are coupled by the off-diagonal electron–hole exchange interaction (thick orange double arrow). These exchange effects lead to the two split dispersions of X− shown on the left, where the degree of circular polarization of photon emission (denoted by colour) decreases with momentum. Because of the steeper dispersion of the higher-energy branch, the same thermal broadening in energy corresponds to a narrower distribution in momentum (depicted by the shaded area), and hence a larger degree of polarization than the lower-energy X− branch.

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From the above experimental facts, we attribute the observed doublet to X− fine structure induced by the diagonal exchange interaction between the electron and hole constituents (green double arrows in Fig. 4d). In WSe2, the negatively charged exciton has two exchange-split branches31,32, with circularly polarized emission at the dispersion minima and linearly polarized emission at large kinetic energies (Fig. 4d). The off-diagonal electron–hole exchange interaction at finite velocity (thick orange double arrow in Fig. 4d) is largely responsible for depolarization of both neutral and charged excitons5. The steeper dispersion of the upper branch causes a narrower distribution of the velocities at a given temperature, leading to less depolarization of the luminescence compared to the lower X− branch (Fig. 4d). This is consistent with our PL measurements showing larger circular polarization for X|2〉− than X|1〉−. Further, more efficient formation of X|2〉− compared to X|1〉− also contributes to its larger PL polarization32. Our measurements across 14 samples find a mean X− peak splitting of 6.9 ± 0.5 meV, with little temperature dependence (see Supplementary Fig. 5), consistent with theoretical estimations31,32,33. Such a large splitting reveals the exchange interaction in monolayer WSe2 to be an order of magnitude stronger than in GaAs systems, a direct consequence of strong Coulomb interactions within this 2D semiconductor.

We note that when the excitation laser energy is significantly higher than the Xo resonance, X|1〉− and X|2〉− can have various formation channels, including multiple phonon emission28, while the excess laser energy facilitates a dynamical equilibration between Xo, X|1〉− and X|2〉−. Thus, all three constituents appear in the PL spectrum when exciting at higher energy. If, on the other hand, the laser resonantly excites Xo, the most efficient X− formation channel is the single-phonon emission process discussed above. Here, alignment of the Xo–X|2〉− energy separation with the A1′ phonon energy favours the formation of X|2〉− instead of X|1〉−. This is consistent with the observed behaviour of both luminescence upconversion (seen in reverse PL) and downconversion (for example, standard PL under resonant Xo excitation) by single-phonon absorption and emission, respectively.

In summary, our report of luminescence upconversion from the negatively charged to neutral exciton resonances with valley selectivity and electrical control stems from the doubly resonant condition of Raman scattering, which is selectively fulfilled in anti-Stokes, but not Stokes, processes. Since the degeneracy between a Raman active optical phonon energy and the charged exciton binding energy exists in other monolayer transitional metal dichalcogenides (for example, monolayer MoSe2), the conditions for doubly resonant anti-Stokes are likewise satisfied. We remark that the observation of excitonic upconversion enhanced by doubly resonant Raman scattering could be general within these 2D semiconductors, and may imply a new cooling channel for 2D semiconductors. Our results reveal strong interactions between ground-state neutral and charged excitons mediated by resonant phonons, a new aspect of 2D exciton physics, which will impact our fundamental understanding of existing and future experiments on valley excitons in 2D semiconductors.

Methods

Monolayer WSe2 crystals are first obtained by mechanical exfoliation of bulk WSe2 crystals onto a SiO2/Si wafer and visually identified in an optical microscope, after which electrical contacts are patterned using standard lithographic techniques. To spectrally resolve individual excitonic states, we perform measurements at cryogenic temperatures (30 K), unless otherwise noted. For standard PL measurements, we use a 633 nm HeNe laser as the excitation source. For low-energy excitation, we employ the output of an ultra-narrow linewidth MSquared SolsTiS laser, with a tunable wavelength range of 690–950 nm.

Spectral filtering for the reverse PL measurements is accomplished in three stages. First, a long-pass filter eliminates the high-energy tail of the SolsTiS excitation beam. Second, a 750 nm short-pass filter on the detection side removes remnant components at wavelengths well above the Xo resonance. Third, a 4f spectral filter provides a continuously tunable short- or long-pass spectral filter (see Fig. 1b). By placing two gratings (G) at the outside conjugate focal planes of two lenses (L), the beam is focused at the central focal plane, with the spectral distribution mapped into a spatial separation. Placement of an adjustable slit (S) at the central focal plane allows tunable pass-band selection.