Introduction

1T-TiSe2 is a strong candidate for realizing an excitonic BEC1,2,3,4,5. It is a typical transition-metal chalcogenide material, whose crystal structure is formed by a stacking of TiSe2 layers6,7. Band calculations and angle-resolved photoemission spectroscopy (ARPES) studies confirmed that 1T-TiSe2 is a small gap semiconductor with an indirect band gap around 80 meV8,9,10. The valence bands (VB) of 1T-TiSe2 are located at the Brillouin zone center (\(\bar{\Gamma }\)), while the conduction bands (CB) are located at the Brillouin zone boundary (\(\bar{{\rm{M}}}\)). Below ~205 K, 1T-TiSe2 enters a 2 × 2 × 2 charge density wave (CDW) state6,11, which cannot be explained by simple Fermi surface nesting. The CDW vector in 1T-TiSe2 matches the momentum of the indirect band gap which connects the VB band at \(\bar{\Gamma }\) and the CB band bottom at \(\bar{{\rm{M}}}\). Therefore, it has been proposed that 1T-TiSe2 is a strong candidate for excitonic insulating material12,13,14. In this scenario, the CDW of 1T-TiSe2 is driven by the excitonic pairing across the indirect band gap, and the CDW transition occurs in synchrony with the BEC of excitons. Besides the exciton-driven scenario, the CDW formation in 1T-TiSe2 has also been explained as a Jahn–Teller effect15,16,17,18, where the energies of Se-4p and Ti-3d bands redistribute in the CDW state due to the change of the bond length and angle of the Ti–Se bonds. Moreover, the importance of electron–phonon coupling has also been raised recently as a primary driving force of CDW in 1T-TiSe219,20,21,22,23.

While the CDW mechanism of 1T-TiSe2 remains controversial, the transport property of 1T-TiSe2 is also abnormal6,11. Unlike other typical CDW materials where the resistivity of materials increases monotonically under the CDW transition due to the opening of the CDW gap at the Fermi energy (EF), the resistivity of 1T-TiSe2 first increases below ~205 K and then decreases rapidly at 165 K. The origin of such nonmonotonic behavior is under debate. Some explained it as a reconstruction of the Fermi surface24. Other mechanisms, such as the thermal population of the carriers25 and the renormalization of quasiparticle effective mass26 have been proposed.

To understand the exotic CDW and transport properties of 1T-TiSe2, knowing the reconstruction of electronic structure across the CDW transition, more specifically, the temperature dependence of both VB and CB, is crucial. However, angle-resolved photoemission spectroscopy (ARPES) only measures the occupied electronic states, which means that, for 1T-TiSe2, a semiconductor where EF is in the band gap, only the VB can be detected9,10,12,13,14,27. For the CB, most ARPES studies observed only the residual spectral weight that extended below EF from the tail of the CB band bottom9. It is still unclear how the CB evolves across the CDW transition in 1T-TiSe2. Here, we succeeded in measuring the detailed temperature dependence of CB in 1T-TiSe2 via ARPES and alkali-metal deposition. The alkali-metal adatoms on the sample surface dope electrons into the system. The CB is pushed down below EF and thereby can be directly observed by ARPES. We found that the CB interacts with the VB in the CDW state, resulting in an increase in the band gap between CB and VB. Such a hybridization gap is strongly related to the strength of CDW order. When the CDW order is suppressed by increasing either temperature or carrier doping, the hybridization gap between CB and VB diminishes. The results support the existence of excitonic pairing between CB and VB in the CDW state of 1T-TiSe2. More importantly, we found that the ARPES spectrum of 1T-TiSe2 exhibits an incoherent-to-coherent crossover at ~165 K. The system could be defined as a coherent metal below 165 K with well-defined quasi-particles, whose lifetime increases rapidly when lowing temperature. Our finding provides experimental evidence that explains the exotic transport properties of 1T-TiSe2. It also suggests the possible establishment of excitonic BEC in this intriguing material.

Results

Figure 1 illustrates how the bands fold in the CDW state of 1T-TiSe2. Here, we only consider the two-dimensional Brillouin zone for simplicity. The unit cell quadruples in the CDW states and the bands fold between the \(\bar{\Gamma }\) and \(\bar{{\rm{M}}}\) points (Fig. 1a, b). In the CDW state, the bands at \(\bar{{\rm{M}}}\)/\(\bar{\Gamma }\) consist of one original CB (c1), one folded VB from \(\bar{\Gamma }\) (V), and two folded CBs from other \(\bar{{\rm{M}}}\) points (c2/c3) (Fig. 1c, d). Note that, the dispersion of CB is highly anisotropic at the \(\bar{{\rm{M}}}\) point (Fig. 1c). The band is relatively flat along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction while steep along the \(\bar{{\rm{M}}}-\bar{{{{\rm K}}}}\) direction8,9,10,26,27. Therefore, at the \(\bar{{\rm{M}}}\)/\(\bar{\Gamma }\) point, the band bottoms of c1 and c2/c3 degenerate, while their band dispersions separate. In Fig. 1e, we further consider a gap opening between v and c1. Such gap opening pushes the c1 band bottom and the v band top away from EF while leaving the c2/c3 bands unaffected. Such band folding and band-selective gap opening were first predicted in the band calculation considered all three electron bands and multivalley effects14. Although the band folding in 1T-TiSe214,27 has been well accepted, it is still controversial which conduction bands hybridize most strongly with the v band. Here, in our toy model shown in Fig. 1, we ignored the interactions between different conduction bands and assumed that the hybridization gap opens between the c1 and v bands. We will see later that this model fits best with our doping-dependent data. We note that, all three electron bands should be symmetry equivalent in the CDW state. When rotating the momentum direction by 60 degrees, the flat electron band becomes c2 or c3. It then becomes c2 or c3 to hybridize with the v band.

Fig. 1: Crystal structure, Fermi surface, and band structure of 1T-TiSe2.
Fig. 1: Crystal structure, Fermi surface, and band structure of 1T-TiSe2.
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a Schematic of the crystal structure and the doubling of the unit cell in the CDW state of 1T-TiSe2. b Schematic of the Brillouin zone and Fermi surface of 1T-TiSe2 above and below the CDW transition temperature (Tcdw). c Schematic of the band structure of 1T-TiSe2 along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction. Inset panel illustrates the anisotropic band dispersion of the conduction band along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) and \(\bar{{\rm{M}}}-\bar{{{{\rm K}}}}\) directions. d Schematic of the band structure of 1T-TiSe2 near the \(\bar{{\rm{M}}}\)/\(\bar{\Gamma }\) point considering the band folding in the CDW state. e is the same as d, but considering a gap opening between v and c1.

We then studied the doping dependence of band structure taken around the \(\bar{{\rm{M}}}\)/\(\bar{\Gamma }\) point (Fig. 2). The doping level is illustrated using the total deposition time of alkali metal. In the pristine sample (0 s), the v band is clearly observed at ~150 meV below EF, while the tail of the CB band bottom is observed at EF as manifested by a V-shaped-like feature (Fig. 2a). Here, the pristine sample is referred to the as-grown sample of 1T-TiSe2, which is slightly self-doped due to the deviation of Ti/Se ratio from the stoichiometric ratio. With the alkali-metal deposition, both the VB and CB move to higher binding energy. In 39 s-doped samples, an electron-like band with a V-shaped band dispersion is clearly observed. With further doping, another electron-like band emerges near EF in an 88 s-doped sample, whose band dispersion is relatively flat. Considering the anisotropic band dispersion of CB, as shown in Fig. 1c, d, we attribute the V-shaped electron band to the c2/c3 bands and the flat electron band to c1, respectively. In photoemission spectroscopy, a normal band usually exhibits a continuous band dispersion and intensity distribution. However, unlike the intact V-shaped band dispersion of the c2/c3 band, the flat c1 band exhibits a discontinuous band dispersion with a suppressed photoemission intensity near its band bottom. Such characteristics are consistent with the gap opening scenario illustrated in Fig. 1e. The band hybridization occurs on the c1 and v bands, resulting in the breaking of band dispersion and the suppression of photoemission intensity observed on c1. We note that carriers pile up near the sample surface in alkali-metal deposited sample due to the band-bending effect. However, depending on how deep the penetration depth of the electronic field is, the photoemission spectra observe different behaviors. While some ARPES studies observed an electron doping effect28, some observed a separation of bulk and surface electronic state29 or an emergence of quantum well state30,31. Here, in our doping range, we did not observe any band splitting or shadow bands that could be attributed to surface bulk separation or quantum well state. Therefore, the role of alkali-metal deposition here could be viewed as a simple electron doping effect that pushes the CB below EF.

Fig. 2: Doping dependence of the electronic structure of 1T-TiSe2.
Fig. 2: Doping dependence of the electronic structure of 1T-TiSe2.
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a Energy–momentum cuts taken along the \(\bar{{\rm{M}}}\)-\(\bar{\Gamma }\) direction at different doping levels. The doping level is illustrated using the total deposition time. Red and blue curves are the calculated band dispersions based on a toy model considering a rigid band shift and the band hybridization between v and c1 (see Supplementary Information Section 1 for more information). b Doping dependence of the energy distribution curves (EDCs) taken at \(\overline{{\rm{M}}}{+0.1{\text{\AA }}}^{-1}\). The red curve is the guide to the eyes of the energy shift of CB. c and d are the same as b but taken at \(\overline{{\rm{M}}}\) and \(\bar{\Gamma }\) point, respectively. The blue dashed curve is the guide to the eye of the energy shift of VB. The blue shaded peaks are the guides to the eyes of the change of photoemission intensity of the v band. e Doping dependence of the band gap calculated based on the EDC peak positions in (b–d). We calculated the carrier density by counting the Fermi surface volume (Supplementary Fig. 1). The estimated doping range is from 0.01 to 0.11 e−/u.c. The error bars are estimated based on the uncertainties of the band positions of v and c1. All data were taken at 14 K.

To characterize the hybridization gap between c1 and v, we measured the doping dependence of the CB and VB band positions. For the c1 band, we took the energy distribution curves (EDCs) at \(\bar{{\rm{M}}}{+0.1{\text{\AA }}}^{-1}\), where the band minima of c1 are located, and plotted its doping dependence in Fig. 2b. The band minima of c1 first emerge at EF and then shift to higher binding energy monotonically as expected. However, for the v band, as shown in Fig. 2c, d, the EDC peaks that represent the band top of v shift nonmonotonically. It shifts to higher binding energy in lighted doped samples (<39 s) and then shifts towards EF with further doping. The nonmonotonic shift of the v band top indicates that the band gap between c1 and v changes with electron doping. We then estimated the band gap based on the band positions of c1 and v and plotted its doping dependence in Fig. 2e. The band gap starts to drop at 50 s deposition time. In the 118 s doped sample, the hybridization gap between c1 and v is suppressed to nearly zero.

Besides the change of the band gap, the photoemission intensity transfers from the folded band to the main band. In moderately doped samples (>88 s), the main v band, as manifested by the EDC peak taken at \(\bar{\Gamma }\) (Fig. 2d), becomes pronounced, while the folded v band as manifested by the EDC peak taken at \(\bar{{\rm{M}}}\) (Fig. 2c), fades away. The photoemission intensity ratio between the folded and the main bands directly characterizes the strength of the CDW order. The observed intensity transfer from the folded band to the main band suggests that the CDW order is suppressed by the alkali-metal deposition in moderately doped samples. Our doping-dependent data are consistent with the recent APRES study on alkali-doped 1T-TiSe231. The close relation between the strength of the CDW order and band gap indicates that the band hybridization between c1 and v plays an important role in promoting the CDW state of 1T-TiSe2.

We note that while the electron doping in lightly doped samples is insufficient to suppress the CDW order, it is enough to push the CB below EF, which enables ARPES to characterize the temperature dependence of CB in detail. Figure 3 shows the temperature dependence of ARPES data taken in the lightly doped sample (~39 s). The Tcdw of our sample is around 205 K, as characterized by the transport measurement. At 245 K, which is above Tcdw, the photoemission intensity of the folded v band is observed at the \(\bar{{\rm{M}}}\) point. The existence of band folding above Tcdw could be explained as the persistence of short-range CDW above Tcdw9,13,32,33. When the sample temperature decreases across Tcdw, the band top of v shifts towards higher binding energy. At 13 K, the band top of v moves to ~−200 meV, and meanwhile, its dispersion flattens. The temperature dependence of v is consistent with previous ARPES studies9,10,12,13,14. The flattening of band dispersion and the energy shift of v indicates that there is a band hybridization between c1 and v in the CDW state of 1T-TiSe2. The hybridization gap opens near Tcdw and increases gradually as the temperature decreases.

Fig. 3: Temperature dependence of the electronic structure of 1T-TiSe2 taken in lightly doped sample.
Fig. 3: Temperature dependence of the electronic structure of 1T-TiSe2 taken in lightly doped sample.
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The energy–momentum cuts were taken along the \(\bar{{\rm{M}}}\)-\(\bar{\Gamma }\) direction. The total deposition time of alkali-metal is around 39 s. Blue and red arrows highlight the energy shift of v and c2/c3, respectively. Black arrow highlights the emergence of clear c2/c3 band dispersion.

While the temperature dependence of v is well explained, the temperature dependence of c2/c3 is unexpected. In the band hybridization scenario shown in Fig. 1e, the c2/c3 band is unaffected by the band hybridization between c1 and v and, therefore, should be nearly temperature-independent. However, in our data, two phenomena could be clearly observed. First, the c2/c3 band bottom shifts to higher binding energy. The banded bottom of c2/c3 is close to EF at ~205 K and moves to ~−80 meV at 13 K. This indicates that there is a charge transfer between c1 and c2/c3. At high temperatures, the band bottoms of c1 and c2/c3 are degenerated, and the electrons in the system fill into both bands. In the CDW state, the hybridization between c1 and v pushes c1 upwards above EF. As a result, electrons transfer from c1 to c2/c3 resulting in an energy shift of c2/c3 observed here. Second, we observe a significant change in quasiparticle lifetime on the c2/c3 bands. At high temperatures, the photoemission spectra are so broad that the c2/c3 band dispersion is indistinguishable. When the sample temperature is cooled down below ~165 K, the V-shaped band dispersion of c2/c3 could be clearly resolved. At 13 K, the spectra of c2/c3 are characterized by a clear V-shaped band dispersion. The spectra become sharper near EF, exhibiting a Fermi liquid-like behavior with well-defined quasiparticles.

Utilizing the alkali-metal deposition, we observed the detailed reconstruction of both the v and c2/c3 bands in the CDW state of 1T-TiSe2, including the band folding, the gap opening between c1 and v, the charges transfer from c1 to c2/c3, and the change of quasi-particle lifetime on c2/c3. Figure 4 characterized the temperature scales of these phenomena. First, we show the temperature dependence of EDCs taken at the \(\bar{{\rm{M}}}\) point in Fig. 4a, b. The EDC peak position represents the energy position of the v band top (Ev). We fitted the peak position using a Gaussian function and plotted it as a function of temperature in Fig. 4c. A kink is observed at ~205 K, which is consistent with the Tcdw of our sample. This suggests that an abrupt increase of the band gap between c1 and v occurs at the Tcdw. Next, we plotted the temperature dependence of MDCs taken at EF in Fig. 4d, e. The sharpness of the MDC represents the quasiparticle lifetime. We characterize the spectra sharpness using the FWHM of the MDC peak fitted using a Lorentz function. We further fitted the slope to the left of the MDC peak using a linear function to supplement the FWHM analysis. Figure 4f shows the temperature dependencies of the FWHM and the slope of MDC peaks. Instead of showing an abnormality at Tcdw, the data show a kink at ~165 K. We applied similar analysis methods to the temperature dependence of EDCs taken at the Fermi crossing (kF) of the c2/c3 band (Fig. 4g, h). Consistent results were obtained (Fig. 4i).

Fig. 4: Characterization of the different temperature scales in 1T-TiSe2.
Fig. 4: Characterization of the different temperature scales in 1T-TiSe2.
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a Merged image and b the temperature dependence of EDCs taken at the \(\bar{{\rm{M}}}\) point. The EDCs taken at different temperatures were merged into an image to highlight the spectral changes. The dashed line illustrates the Tcdw of 1T-TiSe2. c Resistivity temperature curve and the temperature dependence of the energy position of v (Ev). The resistivity data were normalized using the resistivity taken at 300 K. d Merged image and e the temperature dependence of MDCs taken at EF. The dashed line illustrates the incoherent-to-coherent transition temperature (T*) at ~165 K. f The temperature dependence of the full-width-half-maximum (FWHM), and the slope of the left edge of the MDC peak. g Merged image and h the temperature dependence of EDCs taken at the Fermi crossing of the c2/c3 band. i The temperature dependence of the FWHM and the slope of the left edge of the EDC peak. The red lines in b, e and h highlight the two characteristic temperatures at ~205 and ~165 K. The fitting results of the MDC/EDC peaks and the slope of their left edges are illustrated using blue shaded areas and red dashed lines in (e) and (h). The error bars in c, f and i are estimated based on the uncertainties of the fitting process. All data were taken in the lightly doped sample (~39 s).

To confirm that the observed 165 K temperature scale reflects the intrinsic properties of 1T-TiSe2, we repeated the similar temperature-dependent experiment in the pristine samples (Supplementary Fig. 2). Although the c2/c3 bands are barely observed in the pristine samples due to the lack of electron doping, the rapid decline of quasi-particle scattering below 165 K was observed consistently. We further excluded the band shift and thermal broadening effect as the cause for the change of spectrum sharpness at 165 K (Supplementary Fig. 3). Similar EDC and MDC analysis was also done on the valence band far away from EF (Supplementary Fig. 4). Consistent results were obtained on the valence band showing the existence of two temperature scales at 205 and 165 K.

For a coherent metal, the lifetime of the quasiparticle near EF, as manifested by the spectral sharpness, increases monotonically when temperature increases. This is consistent with what we observed below 165 K in Fig. 4f, i. However, above 165 K, the temperature dependence of the EDC and MDC FWHM clearly deviates from a coherent metallic behavior. The temperature dependence of the EDC and MDC FWHM is strongly suppressed. The sharpness of the spectrum is no longer a one-to-one correspondence to the lifetime of the quasiparticle, which suggests that the system remains to be an incoherent metal above 165 K.

Discussion

Our observation of incoherent-to-coherent crossover at the 165 K in ARPES naturally explains the transport anomalies observed by other experiment techniques. The resistivity temperature curve of 1T-TiSe2 shows an infection point at 165 K6,11. Optical spectroscopy observed a significant increase in Drude's weight below 165 K34. In previous studies, the transport anomalies at 165 K have been explained as a crossover behavior due to the Fermi surface reconstruction or the change of carrier density24,25. However, the change in carrier density is normally related to the band shift or gap opening. According to our temperature-dependent data, the change of band structure starts at 205 K, which cannot explain the transport anomalies at 165 K. Instead, our data show that the transport anomalies in 1T-TiSe2 could be explained by the incoherent-to-coherent crossover observed here. Above 165 K, the system is described as an incoherent metal, as also evident by the lack of clear Fermi cut-off in the EDCs taken at high temperatures (Fig. 4b, h). Below 165 K, an incoherence-to-coherence crossover occurs, the system could be described as a coherent metal in transport, optical and spectral measurements.

Our data show that the evolution of electronic structure in 1T-TiSe2 can be divided into three different stages. In the first stage, short-range CDW forms above Tcdw, and the bands fold between \(\bar{\Gamma }\) and \(\bar{{\rm{M}}}\). In the second stage, the band hybridization between c1 and v takes place. Electrons transfer from c1 to c2/c3. As a result, the Ti-3d conduction bands can be divided into two groups with different properties. The c1 Ti-3d band interacts with the Se-4p band. The hybridization between them pushes these bands away from EF, exhibiting an insulating property. Meanwhile, the c2/c3 Ti-3d bands are filled with electrons, exhibiting a metallic property. Finally, in the third stage below 165 K, the incoherence-to-coherence crossover occurs. The quasiparticle scattering on the c2/c3 bands declines rapidly when the temperature decreases.

We then discuss the possible mechanisms of the different stages of transition in 1T-TiSe2. In the early studies of 1T-TiSe2, it was believed that the CDW transition is driven by the excitonic interactions between Ti-3d bands and Se-4p bands. However, recently, ultrafast spectroscopy experiments point out that the role of electron–phonon interaction cannot be negnelcted19,20,21,22,23. It was found that the periodic lattice distortion persists in 1T-TiSe2 even when the excitonic correlations are quenched35. Here in our studies, the carrier doping suppresses the excitonic interactions effectively due to a screening of Coulomb interactions. However, in the heavily doped sample where the excitonic interaction between c1 and v is suppressed to nearly zero, the CDW order, as manifested by the band folding, could still be resolved (Fig. 2). Furthermore, according to our studies, the exciton formation as characterized by the hybridization gap between c1 and v is boosted at Tcdw. This is consistent with the momentum-resolved electron energy loss spectroscopy experiment, which confirms the formation of exciton in 1T-TiSe2 at around 180 K36. However, the band folding or the formation of short-range CDW order persists even at 250 K, which is far above Tcdw32,33. Based on the above facts, we suggest that the formation of CDW order above Tcdw in 1T-TiSe2 cannot be solely driven by the excitonic interactions. The electron–phonon interaction may need to be considered.

Below Tcdw, the formation of exciton is boosted as manifested by the rapid increase of band gap between c1 and v at 205 K. It is intriguing to note that, the charge transfer between c1 and c2/c3 evacuates the free carriers on the c1 band, which boosts the excitonic formation on the c1 and v bands. Below 165 K, we observed a significant increase in quasiparticle lifetime, indicating that the system transfers from a relatively disordered state to a more ordered state. In one scenario, the loss of spectral coherence above 165 K could be attributed to the melting of CDW order37. When the sample temperature increases above 165 K, long-range CDW order melts, and short-range CDW bubbles persist near the defects and domain boundaries. However, there is no indication of CDW melting below 205 K in X-ray diffraction (XRD) experiments11, which excludes this scenario. On the other hand, the phonon softening in CDW materials could also trigger an incoherent-to-coherent crossover. However, the high-resolution XRD results show that the phonon softening at the CDW Q is well established at Tcdw19,38, which cannot explain the 165 K temperature scale. Finally, we turn to the BEC of excitons. In this scenario, the excitons first form at a high temperature and then condense at a slightly lower temperature. The condensation of excitons may block the scattering between c2/c3 and c1, which increases the quasiparticle lifetime on the c2/c3 band. Furthermore, the excitons in 1T-TiSe2 are constructed by the Ti-3d electrons and Se-4p holes. The BEC of excitons may also lead to an increase in the structural orderliness of the Ti–Se bonds. Consistently this has been reported recently in an XRD experiment where a modulation of Se atomic layer was found at 165 K39. We note that the incoherence-to-coherence crossover observed here in ARPES is not a direct probe of the phase relation for a quantum many-body system. To confirm the possible establishment of excitonic BEC at this temperature, further experiments that measure the multi-particle correlations or phase relations are needed.

In summary, utilizing ARPES and in-situ alkali-metal deposition, we characterized the detailed doping dependence and temperature dependence of the electronic structure of 1T-TiSe2. We establish a close relationship between the strength of CDW order and the excitonic formation. When the CDW order is suppressed by increasing either temperature or carrier doping, the hybridization gap between CB and VB diminishes. More importantly, we unveiled an incoherence-to-coherence crossover at 165 K. We attributed it to the BEC of excitons that occurs beneath the CDW transition in 1T-TiSe2. Our result naturally explains the anomalies observed at 165 K in transport and optical measurements in 1T-TiSe2. It also points out an intriguing coexistence of both metallic state and excitonic insulating state in 1T-TiSe2. While the electrons on the c2/c3 band exhibit a metallic behavior, the electrons on the c1 band bond with the holes on the v band, exhibiting an insulating behavior. It is surprising that the excitonic correlation is established in 1T-TiSe2 while free electrons are present. Further experimental and theoretical studies are required to understand this exotic coexistence of electronic states with conflict properties in 1T-TiSe2.

Methods

Sample growth

High-quality single crystals of 1T-TiSe2 were synthesized using the chemical vapor transport (CVT) method. By mixing the appropriate ratio of Ti powder and Se pieces (2% excess) well, the compound was sealed in a quartz tube using iodine as a transport agent. The quartz tube was put in the two-zone furnace with a thermal gradient between 560 and 640 °C for 336 h.

Resistivity measurements

Resistivity data were measured in a physical property measurement system (PPMS, Quantum Design, Inc.) utilizing the standard four-probe method. The residual resistivity ratio (RRR) of our sample is around 3.7, which confirms the high quality of our samples.

ARPES measurements

ARPES measurements were performed at Peking University using a DA30L analyzer and a helium discharging lamp. The photon energy of a helium lamp is 21.2 eV. The overall energy resolution was ~12 meV, and the angular resolution was ~0.3°. The crystals were cleaved in-situ and measured in a vacuum with a base pressure better than 6 × 10−11 mbar. The EF for the samples was referenced to that of a gold crystal attached to the sample holder by Ag epoxy.

Alkali-metal deposition

The alkali-metal deposition was performed in situ using a SAES rubidium dispenser. The working current was set to be 5.6 A. For each deposition step, we only kept the rubidium evaporator at the working current for a few seconds to achieve a fine doping step and then took ARPES spectra. The depositing time is defined as the total time of the rubidium deposition.