Experimental observation of a negative grey trion in an electron-rich WSe2 monolayer

We measure the evolution of low temperature photoluminescence in a WSe2 monolayer with increasing electron concentration level. By comparing non-resonant and resonant laser excitation, we find that the formation of negative trions is facilitated by very efficient phonon emission. The most prominent line in photolumienscence spectra in the intermediate range of carrier concentrations (below cm−2) is found to be 66 meV below the bright negative trion. Its measured properties, including low oscillator strength and the temperature dependence point to an interacting bright intervalley and dark intervalley trion state as the origin of the line.


Introduction
Since the first observation of photoluminescence from mono layers (MLs) of MoS 2 , [1,2] the optical properties of mono layer transition metal dichalcogenides (TMDs) with the formula (W, Mo)(S, Se) 2 have been the subject of intense studies [3][4][5][6]. Their photoluminescence (PL) spectra con tain a number of excitonic features [7,8], as the screening of electrostatic interactions remains weak even for monolayers that are embedded in a higher dielectric constant cladding [9,10]. Strong spinorbit interactions lift the spin degeneracy of the valence and conduction bands at the K and K valleys, which are the locations of the direct bandgap [11,12]. A lack of inversion symmetry results in coupling of the valley and spin indices at these symmetry points. The optical selection rules are such that each of the two valleys can be addressed individually using circularly polarized light [13]. For WSe 2 and WS 2 monolayers, the lowest energy optical transitions are forbidden under normal light incidence; they are either spin forbidden for intravalley transitions or momentum forbidden for intervalley transitions [4]. This situation is in contrast to MoSe 2 , for which the lowest energy direct optical transition is spin conserving. The spin subbands ordering in the conduc tion band of MoS 2 is still under debate [14][15][16].
Even though the exciton ground state for WSe 2 MLs is dark [17,18], radiative recombination from free neutral (X) and charged (trions, X −/+ ) excitons is observed even at low temper atures [7,17]. In addition, in contrast to MoSe 2 MLs, typical photoluminescence spectra in WSe 2 MLs contain fea tures at energies below those of free excitons and trions. This signal has been interpreted as originating from the radiative recombination of excitons that are localized on impurities [3,[19][20][21][22] or in straininduced potential fluctuations [23,24]. More recently, phonon assisted PL of intervalley dark excitons, with electrons scattered from the K(K ) valley into lowerlying energy states in the K (K) and the Q(Q ) valleys, has success fully explained PL spectra recorded from chargeneutral WSe 2 S Supplementary material for this article is available online (Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
MLs on SiO 2 [25] and hBN [26]. Direct access to intravalley spin forbidden excitons has been gained either by mixing these states with bright excitons using external magnetic fields [27] or directly by collecting light with an electric field vector that has a component perpend icular to the ML plane [28,29].
However, several lines in PL spectra recorded from doped WSe 2 MLs do not have clearly identified origins. Various interactions of excitons with collective states for the free electron gas have been proposed to explain the PL lines at high electron concentrations [30][31][32]. Lines with intensities that scale as the square of the excitation power have been assigned to the recombination of either neutral biexcitons or fiveparticle negatively charged biexcitons [33][34][35]. Although a comprehensive theoretical analysis of possible complexes in negatively charged WSe 2 MLs has identified the spectral posi tions of complexes in the photoluminescence, some of them still need to be verified experimentally [36].
Here, we analyze subbandgap PL spectra in a negatively charged WSe 2 monolayer. We observe a qualitative change in the spectra asfree carriers are introduced by electrostatic gating. We show that the fast onset of a trion signal may be caused by double resonance in phonon scattering. The strongest spectral feature at intermediate electron doping levels is consistent with the presence of interacting bright intervalley and dark intervalley trions [37].

Methods
A WSe 2 ML was exfoliated from a bulk WSe 2 crystal onto a polydimethylsiloxane (PDMS) stamp and transferred onto a Si/SiO 2 substrate. The WSe 2 ML was then contacted to pre defined metal contacts with a fewlayerthick graphene flake that had been transferred onto the WSe 2 using another PDMS stamp. The two flakes were offset in such a way that most of the WSe 2 surface was uncovered. Another contact was made to the pdoped Si substrate, which was separated from the WSe 2 by a 308 nm thick layer of SiO 2 . The device geometry is shown schematically in figure 1.
The sample was placed in a liquidheliumcooled cold finger cryostat with electrical and optical access. The sample temperature was varied between 12 and 60 K. The carrier concentration in the ML was controlled by the application of a bias voltage, V g . The leakage current remained below 1 nA over the whole range of applied voltages, V g = −30 to 100 V. This voltage range corresponds approximately to a change of the carrier concentration from a hole concentra tion of p = 2.45 · 10 12 cm −2 to an electron concentration of n = 6.65 · 10 12 cm −2 . These values have been calculated for a parallel plate capacitor model with 308 nm thick SiO 2 layer as dielectric, on the assumption that the monolayer is depleted from free charge carriers at V g,fb = 5.0 V, a voltage at which trion emission is weakest. This situation corresponds to a value for the background hole concentration in the monolayer of p ≈ 3.5 · 10 11 cm −2 .
For PL measurements, the WSe 2 ML was excited using a continuous wave laser with a photon energy of 1.88 eV, which was focused to a spot of 1.6 µm diameter on the ML using an objective lens with a NA of 0.47. The excitation power was kept at a low level (<3 µW µm −2 ) to ensure that photogen erated carriers had a negligible effect on gateinduced carrier concentration changes. For resonant PL excitation, we used a continuous wave Ti: sapphire laser emitting at 1.75 eV, i.e. at the energy of the neutral exciton. The PL signal, which was collected using the same objective lens as that used for the excitation, was detected using a Si chargecoupled device at the output of a spectrometer.

Results and discussion
The evolution of PL the signal from a WSe 2 ML with varying charge carrier type and concentration is shown in the form of a colour map in figure 2(a). Representative spectra are shown in figure 2(b). PL of the monolayer with a low carrier concen tration is dominated by radiative recombination of excitons. It is accompanied by a band of emission at lower energies (labelled I in the figure). An example of spectrum from this doping range is shown in figure 2(b) for V g = 7 V. The inten sity and spectral shape of Iband depends on the position on the monolayer (see figure SI1 in the supplementary informa tion (stacks.iop.org/JPhysCM/31/415701/mmedia)) and is strongly suppressed in the monolayer encapsulated in hBN as shown in figure SI2 in the supplementary information. The application of a voltage, V g , to the gate rapidly changes the PL spectra. Both the exciton and the Iband emission decay with applied voltage and are replaced by new lines, which are spe cific to doping type and concentration and uniform across the monolayer (figure SI1) and between the samples (figure SI2) The exciton line, X, is gradually replaced by X − as the electron concentration increases up to about <3 · 10 12 cm −2 . The X − line is redshifted by 31 meV from X and it redshifts further with increasing electron concentration as electrostatic screening by the free electrons becomes stronger [10,39,40]. When the electron concentration exceeds n ≈ 5.0 · 10 12 cm −2 , the X − line is replaced by a much brighter line, X − , which is located 56 meV below X. It has been suggested that this line originates from the fine structure of the trion [3], the presence of double charged trion X −− [34] or an exciton interacting with shortrange intervalley plasmons [30]. Over the entire range of carrier concentrations in which the X − line is present, it is accompanied by another line at approximately 1.66 eV (labelled X − g ). No such replica is vis ible for the positive trion, X + as one can see in figure SI3 of the supplementary information. The correlation between the X − g and X − lines can be seen in the intensity ratio of the two lines as the carrier concentration and excitation power are varied (figures 2(c) and (f), respectively). The X − g line is more intense than the X − line and is the brightest line in the pho toluminescence spectra over the range of electron concentra tions between 0.5 · 10 12 cm −2 and 5.0 · 10 12 cm −2 , as can be seen in figures 2(a) and (b). A signal with this energy has been interpreted as originating from the recombination of dopant bound excitons [22,41], although the presence of a fixed but unknown carrier concentration in the experiments then ren ders such an assignment difficult.
Upon excitation with photons whose energy is at resonance with the exciton energy, as shown in figure 2(d), Raman signal lines are superimposed on the PL signal from the sample. The strongest line, which appears at the position of the X − line, does not shift in energy with carrier concentration indicating that it is dominated by unresolved A and E Raman lines [42]. This double resonance between excitation at the energy of the X line and scattered photons at the energy of the X − line indicates that one can expect efficient trion formation in this system [43]. Whereas the intensity of the X − line is dominated by the Raman signal, upon resonant excitation the X − g line becomes the brightest PL line over the entire probed carrier concentration range, further confirming the correlation between the X − and X − g lines. Although X − g is more pronounced in the PL spectra than X − , it is absent in reflectance spectra, even though the X − signal is clearly visible, as shown in figure 2(e). This result indicates that the X − g line originates from a state that has low oscillator strength. Its relatively high PL intensity must therefore result from high occupancy of this state. At the same time, the shelving of excitons in this long lived state leads to the reduction of the total PL signal compared with undoped  [38]. The Raman line is detuned from X + , which now appears very weak. The X − g line is stronger than in (a). (e) Reflectance spectra acquired from the electrondoped ML. The neutral exciton signal has decreased as the electron doping increased while the negative trion signal increased in strength. X − g is absent from the spectra. (f) Normalised integrated intensities of the X − and X − g lines determined from spectra acquired at V g = 20 V, plotted as a function of the normalised integrated intensity of the X line (acquired at different laser excitation intensities) following a power law dependence with exponent α, as shown in the figure. The intensities of the X, X − and X − g lines are normalised to unity at the lowest excitation power. case as can be seen in figure 2(c) because the long lived exci tons are more likely to recombine nonradiatively. As the temperature is increased, the thermal excitation increases the population of bright states [44,45]. The X − line becomes brighter and becomes as bright as X at 60 K (figure 3). At the same time, the X − g line becomes weaker and is very weak in the data acquired at 60 K. Stronger nonradiative recombina tion rate may additionally reduce the intensity of X − g at higher temperature.
The X − g line has the same polarization properties as the X − line [3]. Polarization resolved PL from the monolayer with a moderate electron concentration of n ≈ 8.75 · 10 11 cm −2 , at which the X − line coexists with the X line, is shown in figure 4. Only the X line shows linear dichroism, while X, X − and X − g show copolarization with the circularly polarized excitation. Linear dichroism of the X line observed in a WSe 2 ML has been interpreted as a signature of valley coherence [3] and was shown to be robust under nonresonant laser excita tion [38].
All of the observed properties of the X − g line are consistent with a picture of grey trions, which was proposed by Danovich et al [37] and is illustrated in figure 5. Upon excitation with left circularly polarized photons, intervalley trions, X The intravalley trion, X KuK d K , can be scattered into the momentumdark intervalley trion state, X The interac tions between the X K u K d K trion and the intervalley bright trion X K d K u K result in a new ground state for the system: a grey trion, X − g , which has a small but nonzero oscillator strength derived from the intervalley bright trion. As it has a small oscillator strength, X − g is absent from reflectance measurements and is more susceptible to nonradiative recombination than X − , which can explain the overall reduction in PL intensity in the negatively doped sample (figure 2(c) and at higher temper atures. The reduction of X − g intensity with temperature can also be explained by an increased probability of thermal exci tation of dark trions into bright ones.
The expected energies of photons emitted from the radia tive recombination of X − g can be estimated by considering the trion dynamics illustrated in figure 5. Following phonon scattering, the energy of the optically generated X KuK d K state is reduced to E D − , which is the energy of the intervalley dark trion X is accompa nied by upconversion of the extra electron from the K d to the K d state, which is higher in energy by ∆ CB . The energy of the emitted photon is therefore E D − − ∆ CB which should be com pared with the energy E D− + ∆ CB,T of the photon emitted by the recombining intervalley trion, where ∆ CB,T is the energy difference between the two trion configurations.
The energy difference between the X − and X − g lines in the PL spectra is therefore ∆ CB,T + ∆ CB . ∆ CB,T has recently been   measured to be 32 meV and has been used to estimate ∆ CB as being equal to 26 meV [27]. These values for ∆ CB,T and ∆ CB indi cate that the energy separation between X − g and X − of approxi mately 58 meV, which is very close to the value of 55.3 ± 0.3 meV measured at a voltage bias of 20 V (n ≈ 8.75 · 10 11 cm −2 ) as an average across the entire sample area.

Conclusions
We have shown that photoluminescence spectra obtained from a moderately ndoped WSe 2 monolayer are dominated by a negative trion related signal. Very low doping levels are suffi cient to observe negative trions, indicating that trion formation and recombination are very efficient. Trion formation may be facilitated by efficient phonon emission by the exciton. This scattering process manifests itself as a double resonance in Raman scattering spectra seen when the incident photons are resonant with the exciton states and the scattered photons with the trion states. At an intermediate electron concentration, the most intense photoluminescence is measured from the radia tive recombination of a grey trion, which is the ground state of the interacting bright intervalley and dark intervelly trions. This state is yet another multiparticle complex identified in WSe 2 monolayer alongside others, such as dopantbound excitons and negatively charged biexctions.