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Detecting photoelectrons from spontaneously formed excitons

Excitons, quasiparticles of electrons and holes bound by Coulombic attraction, are created transiently by light and play an important role in optoelectronics, photovoltaics and photosynthesis. While they are also predicted to form spontaneously in a small gap semiconductor or a semimetal, leading to a Bose-Einstein condensate at low temperature, their material realization has been elusive without any direct evidence. Here we detect the direct photoemission signal from spontaneously formed excitons in a debated excitonic insulator candidate Ta2NiSe5. Our symmetry-selective angle-resolved photoemission spectroscopy reveals a characteristic excitonic feature above the transition temperature, which provides detailed properties of excitons such as anisotropic Bohr radius. The present result evidences so called preformed excitons and guarantees the excitonic insulator nature of Ta2NiSe5 at low temperature. Direct photoemission can be an important tool to characterize steady-state excitons.

The concept of quasiparticles constitutes an essential building blocks of our understanding of solids, which allows us to unravel complex manybody interactions. An exciton, a bound state of an electron and a hole, is a popular quasiparticle in semiconductors, which is formed transiently as excited by light within the bandgap. This quasiparticle excitation not only let us understand the fundamental optical responses of semiconductors and photosynthesis 1 , but also leads to various device applications 2 , including photodetectors 3-6 , photovoltaic solar cells [7][8][9] , light emitters and excitonic lasers [10][11][12][13] . One can further make a macroscopically coherent condensate, that is, a Bose-Einstein condensate (BEC), of excitons using double layers containing electrons and holes separately in artificial structures with strong fields such as semiconductor quantum wells 14 , graphene 15 , and transition metal dichalcogenides 16,17 . The BEC of excitons may bring the above optoelectronic devices into an unprecedented coherent regime and is recognized to be important also in photosynthesis 1 .
In stark contrast, there have been growing but debated experimental evidences 18-32 of excitons formed spontaneously without any external excitation or artificial structures to constitute an insulating ground state with a finite number of steady-state excitons [33][34][35] . Such an excitonic insulator (EI) is one fundamental manybody insulating state of solids, which was theoretically proposed as early as 1960's for a small gap semiconductor or a semimetal [33][34][35] . However, the accumulated evidences for the predicted properties of EI, such as diverging electronic susceptibility 32 , anomalous optical transitions 36 , quenching of plasmonic modes 18 , and renormalized valence band dispersions 21 , have been obscured by the coexisting structure phase transitions 37 and the direct experimental identification of spontaneously formed excitons has been missing.
photoemission spectroscopy (ARPES) to investigate the formation and the symmetry of the quasiparticles in a major EI candidate Ta2NiSe5 (TNS) across its anomalous phase transition. Our experimental results below the transition temperature (Tc = 327 K) confirm the hybridization between the valence and the conduction band orbitals near the Fermi level. The origin of this interband hybridization has been debated with excitonic or structural origins. In contrast, the band structure above Tc shows no clear sign of such band hybridization, ruling out a substantial structural effect, but the band gap persists. Moreover, we identify the emergence of a characteristic photoelectron signal, which can only be explained by the direct photoemission from excitons 38 . This is the first direct signature of the spontaneously formed excitons, the so-called 'preformed excitons' preceding the emergence of BEC at a lower temperature [39][40][41][42][43][44] . The present results, therefore, guarantee an excitonic insulator transition in Ta2NiSe5 at low temperature without any ambiguity related with the structural transition occurring at Tc 39,44 . That is, this is in line with a recent theoretical proposal of a BEC-type EI transition for a semimetallic TNS 39 and indicates the existence of a novel manybody quantum state of preformed excitons at high temperature. Based on our ARPES result and a recent theory 38 , the effective radius of excitons is extracted to be very small and anisotropic; ~7.5 Å and ~3.0 Å along parallel and perpendicular to Ta and Ni chains, respectively (Fig. 1a). This is attributed to the novel manybody interaction between excitons and phonons 36,45,46 . The present work opens up a new way to characterize spontaneously formed excitons with direct photoemission probes and to exploit coherent excitons at room temperature and preformed excitons at high temperature. Figure 1b shows the overview of the band structure of TNS, revealed by our ARPES measurements along the Γ " -" and Γ " -" directions (x and y-directions in Fig. 1a, respectively) over multiple Brillouin zones. The valence band near the Fermi level is characterized by a hole-like band centered at Γ " with strongly anisotropic dispersions along the Γ " -" and Γ " -" directions -a much stronger dispersion along the Ta/Ni atomic chains. As is well known, the band structure below Tc is insulating with the valence band top located at about 0.16 eV (Fig. 1b). A distinct flattening of this valence band top, deviating significantly from a normal parabolic dispersion, is observed as shown in Fig. 2 in more detail. Together with the existence of the band gap, the band renormalization indicates a hybridization of the conduction and valence bands.
The interband hybridization itself can be more directly evidenced by revealing the orbital characteristic of the valence and conduction band edges, which are dominated by Ni 3d and Ta 5d orbitals, respectively, in the non-interacting case well above Tc 47 . This corresponds to the hightemperature orthorhombic crystal structure, where the hybridization between these two bands is forbidden by the crystal symmetry 47 . On the other hand, below Tc, the crystal structure changes to a monoclinic symmetry allowing the hybridization of Ni 3d and Ta 5d bands. The previous scanning tunneling spectroscopy study 24 indeed showed that the orbital (more accurately atomic) contributions of the valence (Ni 3d) and conduction band (Ta 5d) edges are inverted below Tc 48 .
This verifies the interband hybridization, which was interpreted as an indirect but important evidence of the EI state 21,22 . However, recent works pointed out that this hybridization itself can be explained largely by the orthorhombic-monoclinic structural transition 49 .
ARPES with linearly polarized light can be utilized to determine the mirror symmetry of wave functions for occupied bands through the dipole selection rule in photoemission. We performed ARPES measurements along the Γ " -" direction for the low-temperature phase with four different linear polarization geometries (schematically shown in Fig. 1a). The data in Fig. 2a-d show that the photoelectron intensity of the valence bands exhibits a huge difference between the 'flat-top part' centered at the Γ " point and the 'dispersive parts' away from Γ " , as summarized in Table 1. These apparent cross-sectional contrasts are independent of photon energies (50-90 eV, see Supplementary section 1) so that they are attributed to the symmetry selection rules between the light polarizations and orbital symmetries 50,51 . Based on the selection rules, the mirror parities of the valence and the conduction bands, respectively, are determined to be even (even) about YZplane and even (odd) about the XZ-plane (see Supplementary section 2 and 3). These observations are fully consistent with the hybridization of the valence and the conduction bands below Tc.
We then track the temperature dependence of the hybridization crossing the phase transition (see Supplementary section 4). Figure 3 shows the results of the polarization-dependent ARPES data above Tc at 380 K. The flattening of the valence band top and the band gap persist well above Tc (Figs. 3a,c). This is consistent with the earlier ARPES observations 23 and the resistivity measurements 45 indicating a finite band gap above Tc. However, in stark contrast to the low-temperature phase, the flat-top and the dispersive parts of the valence band exhibit the same polarization dependence; visible at XZ-polarization (Figs. 3a,c) and strongly suppressed at Ypolarization (Figs. 3b,d). This reveals unambiguously that, above Tc, the strong hybridization between the valence and the conduction band is significantly reduced for the flat-top of the valence band to retain largely the Ni 3d orbital character. This observation tells that the spontaneous orbital hybridization occurs only below Tc. Since Tc was determined by the orthorhombic-monoclinic structural transition, the present result is consistent with the picture that the interband hybridization has a structural origin; the hybridization is indeed symmetrically forbidden in the orthorhombic structure 47 . On the other hand, since the non-interacting phase of TNS is semimetallic 39 , there must be another interaction, which can explain the persistent band gap and the valence band renormalization (the flat top dispersion itself) above Tc.
In the following, we provide direct evidence of excitons formed spontaneously above Tc, which explain this extra interaction and most of the other anomalous behavior of this material. We focus on an extremely broad spectral feature at Γ " on the flat-top part of the valence band (appearing clearly only above Tc in the XZ-polarization) (see the dashed box in Fig. 3a). This feature is clearly distinguished from the dispersive parts away from Γ " , which is a usual spectroscopic feature for an Based on the discussion of the excitonic interaction in this material, we naturally check how a direct photoemission feature from excitons looks like. An excitonic feature in photoemission spectra was recently observed and characterized in detail with the pump-and-probe photoemission method as an excited state above the Fermi level and below the bottom of the conduction band 38,[53][54][55] . We adopt this analysis established for pump-excited excitons while we are dealing with a spectroscopic feature below the Fermi level for a spontaneously formed steady-state object. We have performed the peak-fitting analyses using the two-dimensional excitonic wave functions |φ(q)| 2 ~ 1/[1+(qa0) 2 /4] 4 (where q and a0 are momentum and excitonic Bohr radius, respectively) for the momentum distribution curves (MDCs) at several energies across the broad feature at Γ " (dashed lines in Fig. 4a) 38 . The results in Fig. 4b show excellent fits to all the observed MDCs across the entire binding energy range of 0.13-0.34 eV with a nearly constant excitonic Bohr radius of a0 = 6.5-7.5 Å. Based on this excitonic Bohr radius we have also performed a model calculation for the ARPES spectra arising from the excitons based on the computational method presented by Rutsagi et al. 38 (with only one major phenomenological parameter of Lorentzian energy broadening of ~0.3 eV, which will be discussed further below). The result is shown in Fig. 4c for the excitonic contribution alone and in Fig. 4d together with the valence band dispersion (see Supplementary section 5). The overall shape of high-intensity region near the valence band maximum (i.e., resembling the bright up-side-down triangle) and the three-peak structure of MDCs in the ARPES data ( Fig. 4e), can be reproduced excellently (Fig. 4f). These results convincingly indicate that we detect for the first time the direct photoemission signal from excitons formed spontaneously below the Fermi level.
The direct photoemission feature can make possible the detailed characterization of these excitons. We show in Figs. 5a and 5c the ARPES intensity plot along the Γ " − " direction and the overview of the ARPES intensity plot in the momentum space near the Fermi level, respectively.
These data reveal the giant anisotropy of the exciton photoemission feature as characterized by its much larger extent along the Γ " − " direction than along Γ " − " . The fitting analysis of MDC with an excitonic wave function, as shown in Fig. 5b, yields the excitonic Bohr radius along Γ " − " to be about 3 Å being about only half of that along the other direction (Fig. 5d). This is comparable to the distance between the Ni and the Ta chain (~2.2 Å) and signals a strong localization of excitons perpendicular to the chains. The anisotropy is natural from the quasi one-dimensional structures in the lattice and the bands. This is also likely associated with strong and anisotropic coupling of excitons to phonons, by which the excitons can self-localize due to the short-range interactions, giving rise to the strong Fano resonance and the broadening of the absorption peak 36,46,[56][57][58] .
Another interesting observation is the significant broadening of the excitonic photoemission The existence of high temperature excitons above Tc is in fact embedded as an essential ingredient of a BEC-type transition of excitons; excitons form at a much higher temperature than Tc due to its strong interactions in a material with an EI instability and condense into a macroscopic quantum state at Tc. The 'preformed'excitons above Tc are not coherent and the corresponding phase is a novel manybody quantum phase composed of spontaneously formed incoherent excitons.
The present results thus evidence for the first time the preformed excitons and an emerging phase composed of them in a solid. In turn, it tells that the present material has a huge excitonic instability beyond the thermal and the structural energy scale and unambiguously guarantees that the Ta2NiSe5 represents an EI state at a sufficiently low temperature. We stress that this particular support of the EI cannot be associated with the structural transition occurring at Tc. The existence of preformed excitons is consistent with the very recent optical spectroscopy works 32 reporting the active electronic degree of freedom above Tc. On the other hand, the preformed excitons can explain naturally the persisting gap at high temperature, which was suggested as a counterevidence of the EI nature 49 . A BEC-like EI is in contrast to the other EI candidate of 1T-TiSe2, for which a BCS-type excitonic instability is discussed 61 . This material exhibits a weak backfolding of the valence band above Tc ~ 200 K due to the effect electron-hole fluctuations 62 , which is distinct from the direct exciton photoemission feature.
We finally note that the direct photoemission feature from excitons is not clearly observed in the EI phase below Tc. That is, in the low temperature EI phase, excitons do not seem to behave as individual quasiparticles as we assume for our analysis at higher temperature. This may be natural for a BEC in a macroscopic coherence 63,64 , but no theory is available for the photoemission from a BEC of excitons at thermodynamic equilibrium at present. On the other hand, the strong interaction with the lattice (phonons) at low temperature may deviate the ground state well away from BEC as noted in a recent theoretical work 48 and the overall phase evolution follows the BEC behavior but in a heavily dressed way by the lattice degree of freedom 28 .
In summary, we have utilized the symmetry-selective and temperature-dependent ARPES to identify the emergence of quasipaticles and their orbital symmetries near the Fermi level across the anomalous electronic transition in an EI candidate material of Ta2NiSe5. We identify unambiguously a characteristic photoemission feature coming directly from the excitons formed spontaneously above Tc in the absence of the structural transition and in the presence of a persisting band gap. This clearly evidences the existence of the preformed excitons and fully validate the photoemission feature reveals the compact and highly anisotropic size of excitons and strong scattering of them, which indicate the strong exciton-phonon coupling even in the precursor state of the excitonic insulator, signaling the importance of a novel higher-order manybody interaction in this material. By demonstrating the observability of steady-state excitons in ARPES, our study presents a new possibility for characterizing the excitonic properties not only in various types of excitonic insulator materials, but also for the future electronic and optoelectronic devices utilizing the presence of such steady-state quasiparticles.

Sample growth
The single crystals of TNS were grown by chemical vapor transport method with iodine as a transport agent. The TNS polycrystalline sample, pre-reacted at 900 °C for 7 days, and iodine chunk (~2 mg/cm 3 ) are loaded in a quartz ampoule, which is placed in the two-zone furnace with a temperature gradient from 960°C to 850°C for 2 weeks. The as-grown single crystals are typically 2-3 x 0.1 x 0.01 mm 3 , in a long bar shape along the b-axis, whose crystallinity and stoichiometry were confirmed by X-ray diffraction and energy-dispersive spectroscopy.

Angle-resolved photoemission spectroscopy measurements
The samples were prepared by in-situ cleaving to obtain a fresh surface parallel to the xy-plane, as shown in Fig. 1a

Density functional theory calculations
We use the experimental crystal structure of Ta2NiSe5 observed at room temperature and low

Identification of the mirror parities for the valence and conduction band orbitals
The photoemission spectra can be suppressed purely based on the symmetry considerations S1,S2 .
Here we show that the identified mirror parities for the valence band (VB) orbital and the conduction band (CB) orbital mentioned in the main text is the only combinations of the xz-and yz-mirror parities that are consistent with the band visibilities observed in our ARPES measurements.
The photoemission matrix element within the dipole approximation can be written as where ψi and ψf are the initial and final states of electron, A is the vector potential of photon, and p is the momentum operator. The three terms on the right-hand side correspond to the photoemission matrix element arising from the x, y, and z components of the vector potential of photon (i.e., parallel to the photon polarization vector). Thus, for the photoemission matrix element to vanish, all of the three components must identically vanish. Each of the three terms in equation (1), can be rewritten in real space as where i = x, y, or z. Thus, the vanishing condition for the photoemission matrix element in (2) is that at least one of the spatial integral (with respect to x, y, or z) vanishes due to parity considerations (i.e., an integrand is odd). The results of this parity consideration and whether the photoemission matrix element must vanish or not for the four possible combinations of the mirror parities for the initial state are summarized in the Tables S1-S4 below. In the following tables, the yz-and xz-parities of the initial and final states of electrons are expressed as | yz-parity, xz-parity >, where "+", "-", and "x" indicate even, odd, and no (i.e., neither even nor odd) mirror parities, respectively.
From the photoemission selections rules summarized in Table S1-S4 above, it can be seen that there is no single pair of yz-and xz-parities, consistent with the observed visibilities in ARPES at T < Tc for the flat-top part at Γ 7 and the dispersive parts away from Γ 7 in Γ 7 -X 9 direction (Fig. 2). Thus, we identify the pair of mirror parities at Γ 7 and Γ 7 -X 9 line separately. Since the flat-top part is clearly visible only for Y-and YZ-polarizations (i.e., the polarization containing Y-component), it can be deduced that the dominant orbital at Γ 7 (that of conduction band orbital) should have the |+ -> parities. For the dispersive parts away from Γ 7 (predominantly of valence band orbital), they are clearly visible in XZ-, YZ-, and X-polarizations, but not in Y-polarization. Thus, it can be deduced that the xz-parity must be even (see Table S1 and S2). The yz-parity for the valence band orbital can be deduced based on the observation that the photoemission intensity at the Γ 7 point (flat-top part) is weakly visible at XZ-polarization, but nearly vanishing in X-polarization. Since the valence band orbital contribution should be weaker than the conduction band orbital (due to band inversion), but not vanishing at Γ 7 , it can be deduced that Z-component of light should be responsible for the weak visibility of the valence band at Γ 7 in the XZ-polarization. Thus, the yzparity of the valence band orbital should be identified as even; that is, the set of parity of valence band orbital at Γ 7 should be identified as |++> (see Table S2).
Here, we note that the mirror parities about XZ-and YZ-plane are not strictly good quantum numbers in the monoclinic structure (T < Tc) but the selection rules based on the orthorhombic symmetry well explain the observed ARPES polarization dependence. We believe that the monoclinic distortion is too small (less than 1°) S3 to affect considerably the photoemission cross section of wave functions.
As a further verification that the difference in the band visibilities for the "flat-top" part and the dispersive parts are unique to the linearly polarized incident lights, which selectively probes the wave functions with the compatible mirror symmetries, we have also performed the ARPES measurements with circularly polarized light. Since the photoemission selection rules based on the mirror parities does not give any general restrictions for the circular polarizations, we expect that both flat-top and the dispersive parts should be visible. Such expectations are indeed confirmed as shown in Fig. S2 shown below.

Symmetries of the valence and the conduction bands from DFT calculations
In order to support the experimental identifications of the symmetries of the valence and conduction band orbitals, we have performed the ab-initio band structure calculation for Ta2NiSe5 in the monoclinic phase using density functional theory. Figure  orbitals for Ni and Ta atoms, and it can be seen that the wave function composed of these orbitals must have the parities of (σyz, σxz) = (even, odd), consistent with our ARPES identification.
Furthermore, as shown in Figs. S3f-h, the wave function at the dispersive part of the valence band is dominantly composed of dz2, dxz, and dxy orbitals, and it can be seen that the σxz parity is even.
The results that the flat-top part exhibiting the opposite σxz parity from the dispersive part but the same parity as the conduction band is consistent with the picture of strong hybridization (inversion) between the valence and conduction bands, and is consistent with our symmetry identifications based on ARPES.
We note that while these symmetry identifications are different from the ones presented S4,S5 , the point of view that the valence and the conduction band possess different set of mirror symmetries are common to these and our studies. Our experimental and theoretical identifications, in the mutual agreement, correctly assign the mirror parities of the conduction and the valence bands.  Figure S4 below shows the ARPES intensity plots taken at the temperature of T = 280-400 K. It can be clearly seen that the intensity plots for the temperature below Tc (Figs. S4a and S4b) show the strong suppression of the intensity near top of the valence band at the Γ 7 point (due to the photoemission selection rules mentioned in the main text and Section 2 above). This is qualitatively same as the observation at T = 70 K. In contrast, the intensity plots for the temperatures above Tc (Fig. S4c-e) clearly show the appearance of the strong intensity at the Γ 7 point near the top of the valence band.

Model calculations for the photoemission signals from excitons
In order to simulate how the photoemission intensity should appear when there are finite number of exciton present in the material (preformed exciton phase), we have followed the theoretical model calculation scheme presented in Rustagi et al. S6 , designed for time-resolved photoemission after the excitons have been created by the pump pulse. The model equation is S6 : In order to perform the computations for TNS above the EI transition temperature, several assumptions have been made. First, since the exciton band is theoretically predicted to cross the valence band maximum at Tc to induce the excitonic instability S7 , the exciton band should lie close to the valence band maximum. For this reason, we have placed the exciton band so that its bottom coincides with the valence band maximum in TNS. For the exciton distribution function, since the BEC-type EI transition is characterized by condensation of zero-momentum excitons formed above Tc S8 , we only compute the photoemission signature arising from the excitons with Q = 0.
For this reason, the knowledge of the exciton band dispersion (at finite Q), which is not exactly known for TNS becomes unnecessary for the purpose of our computations. The equation (1) takes into account the effect of finite temporal width of the pulse in the Gaussian shape (the exponential factor at the end of the equation), which gives rise to the finite linewidth in the computed ARPES spectra. On the other hand, in our measurement, the pulse width (train bunch width at the synchrotron) is estimated to be ~ 20 ps and this gives rise to nearly completely negligible contribution from the temporal-width-induced broadening. On the other hand, in solids, the exciton can be scattered by phonons, impurities etc. and such process can induce the finite broadening, which will be reflected in the finite width of the actual ARPES spectra. Thus, the exponential factor at the end of equation (1)