Introduction

Iron-chalcogenide superconductors display a wide variety of complex electronic phases due to their multi-band nature, small Fermi-energies and large orbital-dependent electronic correlations1,2,3. These stabilise rich phase diagrams that include electronic nematic and spin-density wave phases4,5, topological surface states6 and bring the system in the proximity of a BCS-BEC transition7. The electronic nematic phase manifests as a spontaneous breaking of the rotational symmetry induced by orbital and momentum dependent band shifts8,9. Studies under small amounts of applied strain along the symmetry breaking channel lead to a divergent elastoresistivity close to the transition temperature, revealing its electronic origin10,11,12,13.

Although, nematic critical fluctuations have been suggested to enhance superconductivity14, the nematic phase is usually accompanied by a spin-density wave, making it difficult to isolate which interaction is driving the superconductivity15,16,17,18. Moreover, the finite coupling with the lattice can be detrimental on the critical nematic fluctuations and superconductivity4,19. FeSe is a unique system which harbours an extended and tunable nematic electronic phase in the absence of long range magnetic order, whilst still stablizing superconductivity at low temperatures20. Studies of the superconducting gap have suggested a s± sign-changing pairing symmetry which is consistent with a spin-fluctuation mechanism21,22,23, but competing Néel and stripe magnetic fluctuations are found in FeSe22,24. In the presence of non-magnetic disorder both superconductivity and nematicity is suppressed in Fe1−xCuxSe studies25.

The nematic order of FeSe can be effectively tuned via isoelectronic substitution of Se with S or Te, and the band structure is very sensitive to the chalcogen height above the conducting planes13,26. In addition, the Te substitution causes the chalcogen pz band to shift down towards the hole pockets of the Fe d bands and induce a band inversion at the Fermi level27, which could stabilise topological surface states6,15,28,29. The orbital dependence of the electronic correlations becomes significant for high Te concentration where the band with dxy orbital character experiences a large increase in effective mass relative to other bands with dxz/dyz orbital character1,30,31.

Single crystals inside the nematic phase of FeSe1−xTex series with low Te content have only recently become available, as the chemical vapour transport techniques have overcome the phase separation32,33. Recent studies have determined the superconducting phase diagram which harbours two superconducting regimes, one dome inside the nematic phase followed by a second dome which emerges at the nematic end point, proposed to be driven by critical nematic fluctuations34.

In this paper, we report a detailed angle-resolved photoemission spectroscopy (ARPES) study of the nematic FeSe1−xTex single crystals and determine the evolution of the low-energy features and the role of electronic correlations. Employing a detailed multi-band model, we extract the effective masses of all three hole bands which decrease with increasing Te concentration as both the nematic order and superconducting phases are suppressed. We find that the effective mass of the hole band with dxy character displays a non-monotonic variation reaching a minimum before increasing significantly with the Te substitution. Simultaneously, the dxy hole band shifts towards the Fermi level, which could open a new pairing channel for superconductivity and an enhancement in the density of states, potentially stabilising a second superconducting dome. The kz dependence of the ARPES spectra enables us to assess the contribution of the chalcogen pz band, which is instrumental in the formation of topological superconductivity. Lastly, we explore the evolution of the electron pockets with Te concentration and find that size of the pockets increase, whereas the nematic splitting slowly reduces as the nematic phase has an extended compositional range.

Results

The evolution of the hole bands

The band structure of tetragonal FeSe, which is dominated by the bands with Fe 3d orbital character at the Fermi level (EF), consists of multiple hole pockets in the centre of the Brillouin zone and electron pockets in the corners of it. Figure 1a shows the measured hole band dispersions along the A − Z − A direction for different compositions of FeSe1−xTex. To highlight weaker spectral features for some of the bands, we have calculated the corresponding curvature35, as illustrated in Fig. 1b. We clearly observe two dispersive bands with mixed dxz/yz orbital character, labelled as the α band for the outer hole band and the β band for the inner band. A third much flatter band with dominant dxy orbital character, labelled γ, has a weaker spectral weight and is seen ~ 50 meV below the Fermi level in FeSe13. As the intensity of ARPES data is proportional to the matrix elements, which are dependent on the properties of both the incident light and the excited electrons, we also use the linear vertical (LV) polarisation to isolate the β hole band, as shown in Fig. 1c36. Moreover, matrix elements suppress significantly the intensity associated with bands of dxy orbital character in both polarisations. Therefore, the γ band is mainly visible via hybridisation with the α and β bands and it can be visualised using the curvature analysis in Fig. 1b.

Fig. 1: Hole bands of nematic FeSe1−xTex.
figure 1

a Angle-resolved photoemission spectroscopy (ARPES) spectra measured at the Z high-symmetry point along the A − Z − A direction at 10 K using linear horizontal (LH) light polarisation. b The corresponding two-dimensional curvature of the ARPES data from a using the method in ref. 35. The solid points are the band positions extracted from Lorentzian fits to the momentum distribution curves (MDCs) (α and β bands), maximums in the energy distribution curves (EDCs) (β band) and extrema in the curvature of the EDCs (γ band). The solid lines are fits to the band positions using the low-energy model discussed in the Supplementary Note 2. c ARPES spectra for the same dispersions as in a but measured using linear vertical (LV) light polarisation. The solid points are the band positions extracted from MDC analysis, and the solid curve is a parabolic fit to the data. The solid lines in b and c corresponds to the outer hole band, α (red), the inner hole band, β (green) and the flatter dxy hole band, γ (blue). d MDCs taken at the Fermi level to determine the Fermi wavevector (kF) from a, where the errors are equal to half of the full-width half-maximum from the Lorentzian fits (dashed curves). e The extracted hole dispersions of the α and β bands for different x using LH polarisation. f The extracted β bands using LV polarisation. Different colours in d, e and f refer to the x compositions, as indicated in d.

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Next, we discuss the band dispersions of the α and β hole bands shown in Fig. 1b. To quantify precisely their position we use both momentum distribution curves (MDCs) (fitted to pairs of symmetric Lorentzian peaks in Fig. 1d) and the maximum in the energy distribution curves (EDCs) to define the top of the β band which is located mainly below EF. We observe that the α hole band clearly crosses the Fermi level (see Fig. 1d), whereas the spectral weight of the β band only emerges from x ~ 0.15 as a central peak in the MDC spectrum at EF. In tetragonal FeSe the β band forms a 3D hole pocket, however upon entering the nematic phase this pocket is pushed below the Fermi-level3,37. By suppressing the nematic phase with S substitution, the β pocket re-emerges at FeSe0.89S0.113,37 However, with Te substitution, in which the nematic phase extends over a larger compositional range towards x ~ 0.4534, the shift of this band is less pronounced. Interestingly, the γ band shifts significantly from a binding energy around 50 meV to 20 meV towards the Fermi level at both high symmetry points (see Fig. 1b and Supplementary Fig. 6) This is in contrast to findings for the FeSe1−xSx series, where the γ band is relatively unaffected by isoelectronic substitution up to x ~ 0.1838. However, these findings are in good agreement with the prediction of the density functional theory (DFT) calculations which shows that the γ band only begins to shift for value of h > 1.45 Å (see Supplementary Fig. 3).

Figure 1e, f shows that the extracted band dispersions for the α and β hole bands become narrower, suggesting a decrease in the effective masses with increasing Te concentration. The extracted values of the Fermi wavevector, kF, suggest that the size of the α hole pocket hardly varies with increasing Te concentration, consistent with studies at higher x values39 (see Fig. 1d and Supplementary Fig. 6).

The nematic order parameter, φnem is usually estimated from the energy splitting between the α and β hole bands, given by \({\Delta }_{h}=\scriptstyle\sqrt{{\varphi }_{nem}^{2}+{\lambda }_{1}^{2}}\) 40,41. As the spin-orbit coupling (SOC) parameter, λ1 ~ 23.5 meV for FeSe at high temperatures inside the tetragonal phase13,20,42, and at low temperatures Δh increase towards 37.5 meV, the value of φnem was estimated as ~ 29 meV for FeSe20,42. With S isoelectronic substitution φnem decreases and at low temperatures the β hole band crosses the Fermi level and forms the 3D pocket at Z point3,37,38. In contrast, the Δh splitting for FeSe1−xTex remains around 38(3) meV due to two competing effects: one caused by the reduction in the nematic order parameter with increasing x and the second caused by the enhanced SOC splitting (DFT calculations predict a variation from 82 meV for FeSe to 177 meV for FeTe at the Z point, as shown in Supplementary Fig. 1).

The role of the chalcogen p z band

The position of the pz band and its interaction with the hole bands is complex and heavily dependent on the chalcogen height, h, which strongly changes with the Te concentration, x, as shown in Supplementary Figs. 1 and 2. The chalcogen pz band, which is predicted to be located above the Fermi level at the Γ point in FeSe, intercepts vertically all three hole bands along the Γ − Z direction (see \({E}_{{p}_{z}}\) in Supplementary Fig. 1). Due to symmetry reasons, the crossing between the inner hole band and the chalcogen pz band is proposed to create a band inversion, allowing topological surface states to form6,15. Based on the DFT predictions, this crossing first occurs at the Z point for h ≈ 1.4 Å, and its hybridisation with the inner hole band creates a gap (along the Z − A direction). As a consequence the pz band and the inner hole band smoothly merge and their orbital characters mix, resulting in a pseudo-inner hole band having a larger degree of pz orbital character27.

In order to assess the contribution of the pz band in experiments, we perform a quantitative analysis of the ARPES intensity of the β band in relation to the α band, I(β, α). This relative intensity is evaluated at the two high-symmetry points with different kz values (Γ and Z) giving the ratio I(β, α)Z/I(β, α)Γ (see Supplementary Note 3). We find this ratio to increase beyond x = 0.33, as shown in Fig. 1 and Supplementary Fig. 7. This variation in intensity indicates an alteration in the orbital character of the bands due to hybridisation with other bands. However, changes in intensity due to nematic effects and the contribution from the γ band should manifest equally at the Γ and Z point. Thus, the variations in the intensity ratio suggest that the matrix elements have changed for the β band due to the interaction with the pz band, which is strongly kz dependent. This is in agreement with previous studies which have highlighted the presence of the pz band at Z in x ~ 0.5527,43,44. Additionally, we observe the emergence of a central peak in the MDCs at EF for x ~ 0.15, which could also be due to the enhanced intensity of the β band at Z.

The low-energy model and effective masses

In order to quantify the evolution of the electronic correlations and band shifts of the hole bands of FeSe1−xTex as a function of Te concentration, we employed a low energy three-band model to describe the effective masses of the α, β and γ bands. This model contains essentially three parabolic dispersions in the presence of SOC and the nematic order. This approach is an extension of the model developed from refs. 40,45,46 to accommodate the third hole band, γ, as detailed in Supplementary Note 2. To constrain the parameters of the model we fixed φnem to be proportional to the nematic transition temperature, Ts, such that φnem = 29 meV for FeSe, as reported in refs. 13,42. This additional constraint was introduced to account for the fact that the nematic order parameter is difficult to estimate from the splitting between the α and β hole bands, Δh. This is caused by the lack of experimental data above the Fermi level and linewidth broadening caused by the impurity scattering and averaging over two different domains.

Figure 2 shows the extracted effective masses, m*, from the three-band model as a function of Te concentration. For the α and β hole bands, m* decreases with increasing Te substitution. This is similar to the renormalisation factor for the \({d}_{{z}^{2}}\) band, as detailed in Supplementary Note 4. In contrast, the effective mass of the γ hole band displays a non-monotonic behaviour, as it decreases inside the nematic phase (from x = 0 towards a minimum close to x ~ 0.3) and then increases to values twice as large as those seen in FeSe at x ~ 0.830,31.

Fig. 2: Effective masses and Fermi energies of the hole bands.
figure 2

The effective masses of the α band in a, the β band in b and the γ hole band in c as a function of Te concentration. The solid lines in a and b are linear fits for each data set at different high symmetry points, Γ (red circles) and Z (blue squares). Data for β are from both polarisations, with open and solid symbols corresponding to linear vertical and linear horizontal, respectively. The solid line in c is a 5th order polynomial fit to the data. Open diamond and triangles are from refs. 31 and30, respectively. The Fermi energies of each band are plotted as a function of x in d (E0,α), e (E0,β) and f (E0,γ), where data from refs. 31 and30 are added. The solid lines in d and e are linear fits, while the solid line in f is described by a phenomenological model detailed in the Discussion. The error bars in all plots are calculated from the covariance values produced within the non-linear least squares fitting function.

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The renormalisation factors for each band can be estimated from the ratio of the experimental effective masses to the band masses evaluated from DFT calculations. The estimated values for FeSe are 3.5 and 1.8 for the α and β band, respectively, which is in close agreement to those previously reported47. However, for the γ band we determine a value ~21, whereas previous studies give values between 8 and 1013,47. This discrepancy lies within our use of the curvature analysis, which gives us a larger momentum range to constrain the fit and our consideration for the SOC between the γ and α bands.

Evolution of the electron pockets

Figure 4a shows the evolution of the ARPES spectra corresponding to the electron pockets centred at the A high-symmetry point for different Te substitutions. We observe significant changes between the spectra for the different compositions, as compared with FeSe, in particular at high Te concentration (x ~ 0.33) where only one large electron pocket is detected. The DFT calculations in the tetragonal phase indicate that there are two degenerate points (A1 corresponds to two bands with dxz/yz character whereas A3 is for two bands of dxy character)40 (see Supplementary Fig. 1). The energy separation between spectral features along the EDC at the A point, defined as ΔA, is therefore finite inside the tetragonal phase and found to be ~20 meV for FeSe0.82S0.183. However, as the nematic phase emerges the degeneracy of the two points are lifted (see Supplementary Fig. 10) the value of ΔA has been originally interpreted as a parameter to quantify the nematic order48,49,50, increasing towards ~50 meV13 in bulk FeSe or ~70 meV in thin films of FeSe49.

Figure 3e illustrates the estimation of ΔA for different FeSe1−xTex, from the EDC curves, as the separation between the two upper-most Lorentzian centres where the energy broadening is assumed to be linearly dependent on energy (see Supplementary Note 5). This linear energy dependence, often associated to a marginal Fermi-liquid behaviour in iron-based superconductors51, is evaluated by analysing the β hole band dispersion, as shown in Fig. 1c and Supplementary Fig. 6. Figure 3f shows that there is a direct correlation between ΔA and the structural transition Ts, similar to FeSe1−xSx3, which decreases as the nematic order is suppressed with increasing Te substitution. However, to assess the precise nematic electronic order parameter any additional splitting would need to be quantified for single domain detwinned samples under applied strain, as in the case of FeSe9,40,46,48,49,50,52.

Fig. 3: Electron Pocket of FeSe1−xTex.
figure 3

a Angle-resolved photoemission spectroscopy (ARPES) spectra taken at 10 K along the Z − A − Z direction using linear vertical light polarisation for the different compositions, x. b Momentum distribution curves at the Fermi level for each x are plotted with solid curves and the dashed plots correspond to Lorentzian fits. The diamond data points indicate the Lorentzian centres, and thus the Fermi-wavevectors, kF. c The two-dimensional curvature of the ARPES spectra in a. The different parabolic dispersions are labelled for the FeSe spectra. d The estimated band dispersion for x = 0 and x = 0.33, where the data is extracted from minima within curvature of the spectra. e The estimation of ΔA by fitting the energy distribution curve (solid black curve) (integrated within the window indicated by the yellow strip for x = 0 in a). The blue solid curve is the fit, the dashed blue curves are the individual Lorentzian curves and dashed red plot is the residuals. Star data points correspond to the position of the Lorentzian centre. f The variation of ΔA as a function of composition, x, (solid square) together with those for ΔM (solid circles) from Supplementary Fig. 11. Additional data for FeSe1−xSx (open red rhombuses) are taken from ref. 3. The variation of Ts as a function of composition is plotted on right y-axis using data from refs. 38 (orange diamond) and5 (orange triangle).

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Figure 3d shows a comparison between the different band dispersions centred at the A point, using the extremal values from the curvature plots due to their weak features. Interestingly, we find the position of the hole-like band dispersion, ζ, remains unchanged up to x ~ 0.33, as shown in Fig. 3c, where this continues even for higher Te concentrations (0.56 < x < 0.75)30. Furthermore, only one electron pocket is resolved for higher x (using the MDC curves in Fig. 3b) and the kF values increase with Te concentration. This is possibly due to the electron pockets becoming more isotropic as the nematic phase is suppressed. Additionally, the Fermi surface map of x = 0.33 (see Fig. 4d) shows that the size of the electron pockets relative to the hole pockets is larger, suggesting that the system may be slightly electron doped (the average kF values for x = 0.4 is 0.12 Å−1 for the electron pockets and 0.09 Å−1 for the hole pockets).

Fig. 4: Evolution of electronic structure and correlations in FeSe1−xTex.
figure 4

a Phase diagram of FeSe1−xTex, indicating the nematic phase transition (Ts, orange squares), the superconducting transition (Tc, blue points) and the antiferromagnetic phase transition (TN, red points). Data points are taken from refs. 5,53,30,60. b Fermi energies as a function of composition, x, for the α band (solid red squares), β band (solid and open green circles extracted from the linear horizontal (LH) and linear vertical (LV) spectra) and γ band (solid blue rhombuses). Additional points for γ band are from refs. 31 (blue triangles) and30 (diamonds). The solid red and green lines are linear fits, while the blue curve is a 5th order polynomial fit. c Effective masses as a function of composition, x, where the symbols are defined as in b. The solid red and green lines are linear fits, while the blue curve is the phenomenological fit detailed in the discussion. In b and c only Γ data are shown, where the error bars are calculated from the covariance values produced within the non-linear least squares fitting function. d Fermi surface map of the first Brillouin zone for x = 0.33 taken at 10 K using angle-resolved photoemission spectroscopy with LH polarisation. The spectra outside of the dashed box is enhanced by a factor of 2.5. e Schematic Fermi surface indicating the dominant orbital character of each potion of the bands and potential pairing channels.

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Discussion

The phase diagram of FeSe1−xTex illustrates the suppression of the nematic phase with increasing the Te concentration, x, as shown in Fig. 4a. The superconducting transition temperature, Tc, decreases inside the nematic phase towards a minimum of ~6 K around x ~ 0.3, followed by an increase towards 13 K above x ~ 0.5. This resurgent superconducting dome extends over a large range and becomes filamentary as the system approaches the bi-collinear magnetic order close to FeTe53. Figure 4c shows that the effective masses, m* of the α, β and γ hole bands decrease by increasing x, which correlates with the reduction of the renormalisation factor associated the \({d}_{{z}^{2}}\) hole band (shown in Supplementary Fig. 8). Interestingly, the reduction of the effective mass of the α hole band, which crosses the Fermi level, is accompanied by the suppression of superconductivity inside the nematic phase, suggesting this hole pocket is likely to be involved in the superconducting pairing. This is consistent with previous trends detected from quantum oscillations in FeSe1−xSx, where both the effective mass and the superconducting transition temperature, Tc, reach a maximum near x ~ 0.1, followed by a strong suppression towards FeS3,38,54, as well as for FeSe0.89S0.11 under pressure4.

The changes in the effective masses also reflect the potential role played by the chalcogen pz band. The rate of decrease of the effective mass, m*, for the α band with the Te concentration, x, is very similar for both high symmetry points. On the other hand, the effective mass for the lighter β band decreases faster at the Z point, as compared with the Γ point (Fig. 2b). When the pz band intersects the β band the orbital mixing between the two is strongest at the Z point. As the pz orbital is assumed to be less correlated than the Fe d orbitals43, it is expected that the effective mass of the β band should be further reduced at the Z point relative to the Γ point, in agreement with the observed experimental trends.

Figures 4b and 2d–f show the Fermi energies, E0, of the different bands estimated from the low-energy model as a function of x, indicating that α and β bands experience minimal variation. On the other hand, the γ band with the dxy orbital character varies significantly and shifts towards the Fermi level up to x ~ 0.4, then it plateaus in its vicinity. Experimentally, there is a degree of uncertainty whether the γ band crosses the Fermi level1,7,39 or not30,31, and this discrepancy could be due to the amount of excess Fe in these systems7. Regardless, this is the region in the phase diagram where the second superconducting dome is stabilised, suggesting that the hole band with dxy orbital character could be involved in pairing. Furthermore, the strong shift of the γ band towards the Fermi level and the accompanying enhancement of superconductivity was also seen in thin films of FeSe1−xTex/CaF255.

To understand the significant shift towards the Fermi level of the γ band one can consider two mechanisms. Firstly, DFT predicts that the γ band moves up linearly with Te concentration, x, as the chalcogen height, h, increases and the lattice expands (see Supplementary Fig. 3). Secondly, variations of the bandwidth, due to electronic correlations, will also cause the Fermi energy to change, which can be crudely scaled as ~ 1/m*. Thus, by combining the effect of the lattice and of the electronic correlations, the changes in the position of the γ band could be described by a phenomenological model, \({E}_{\gamma }(x)={\nu }_{1}x+{\nu }_{2}/{m}_{\gamma }^{* }(x)+{\nu }_{3}\). Figure 4c shows a fit to the experimental positions of the γ band, where ν1 is the weight of the lattice effect, ν2 is the weight of the bandwidth and ν3 is an arbitrary offset (\({m}_{\gamma }^{* }(x)\) is taken as the 5th order polynomial fit from Fig. 2c). We find the fit captures the initial increase followed by a plateau for x > 0.4. For even higher x values a new hole-like pocket with \({d}_{{z}^{2}}\) orbital character was detected at the X point for x ≥ 0.8 due to the increase in electronic correlations which leads to the loss of the spectral weight of the dxy band31.

The presence of the third hole band with dxy orbital close to the Fermi level and its involvement in pairing could manifest in different ways. Firstly, the hybridisation of the α hole band with the γ band would lead to a reduction in the Fermi velocity, thus increasing the density of states and enhancing superconductivity. Secondly, the orbital mixing between these bands would open up a new pairing channel which connects to the dxy orbital character at the electron pocket with the hole pockets (see Fig. 4e). Thirdly, a new pairing channel could be achieved if E0,γ is smaller than the superconducting gap, as in this regime the γ band can play the role of an incipient band56. The superconducting pairing in FeSe is proposed to be mediated by spin fluctuations between the hole and electron pockets with dyz orbital character along \({\overrightarrow{Q}}_{xy/yz}=(\pi ,\pi )\) (Fig. 4d and e)17,23,24,57. A similar vector, \({\overrightarrow{Q}}_{xy}\), that would connect the dxy channel, and the observation of stripe magnetic fluctuations in FeSe1−xTex could suggest that the second superconducting dome may also be driven by spin fluctuations53,58,59. However, neutron scattering studies also observe the development of (π, 0) spin fluctuations which compete with superconductivity53. This competition is evident as the suppression of superconductivity, towards FeTe, is accompanied by the development of a double-stripe magnetic order with a (π, 0) wave vector60.

There is a strong contrast between the FeSe1−xTex and FeSe1−xSx series, which displays no enhancement of Tc outside the nematic phase and the dxy hole band is located 50 meV below the Fermi level3. On the other hand, quantum oscillations found a direct correlation between the evolution of the effective mass of the α band and Tc in FeSe1−xSx54, which also occurs inside the nematic phase of FeSe1−xTex. These trends change significantly in the vicinity of the nematic end point of FeSe1−xTex (x ~ 0.5), as the effective masses for the α and β hole bands remain rather constant30,31, whereas the superconductivity is enhanced (see Fig. 4a). On the other hand, both the effective mass for the γ band and Tc increase at a similar composition x. This suggests that the mechanism for superconductivity likely changes across the phase diagram of FeSe1−xTex30,61 and the hole band γ, with dxy orbital character, plays an important role.

An alternative mechanism for the enhancement of superconductivity can be related to its proximity to the nematic end point. Theoretically, nematic fluctuations should support superconductivity in both an s or d-wave pairing channel1,19, and elastoresistivity studies find a divergence of the nematic susceptibility near its end point34. However, studies of FeSe0.89S0.11 under pressure suggest the critical fluctuations could either be quenched via the coupling of the nematic order to the lattice4 or obscured within the nematic islands of a quantum Griffiths phase62. Moreover, other hallmarks of a quantum critical point in FeSe1−xTex, such as the divergence of the effective masses at the nematic end point and/or a linear dependence of resistivity in temperature are not observed5. These systems are rather bad metals, with large linewidths in the ARPES spectra, which could be caused by the large distribution of the Se and Te ions (chalcogen heights differ by 0.24 Å)63 and the stabilisation of the interstitial Fe that could act as additional scattering centres.

The evolution of the band structure and the significant shifts of the dxy band via Te substitution have implications on other studies. The chalcogen height h is an important parameter that influences the changes in the band structure, magnetic ground state and superconductivity26,64. For example, h, could be shifted towards higher values with applied pressure in other iron chalcogenides, despite the shrinking of the unit cell. Theoretical studies of FeSe and NMR studies of FeSe0.88S0.12 have suggested that the hole dxy band could lead to the enhanced superconducting dome induced by pressure65,66. However, pressure also induces magnetic order and the maximum in Tc is often located at the end point of the magnetic phase in FeSe1−xSx5,67, suggesting that magnetic fluctuations are important for superconducting pairing.

Conclusion

In this study we present a comprehensive investigation of the low-temperature band structure of the nematic FeSe1−xTex series. We identify a direct correlation between the changes in the nematic transition with the spectral features in the dispersions at the corner of the Brillouin zone, in agreement with other studies on iron-chalcogenide superconductors. Additionally, the changes in the relative intensities of spectra corresponding to the inner and outer hole bands reflect the contribution of the pz band, as it is brought towards the Fermi level by increasing Te concentration.

By using a low-energy three-band model, which captures much of the underlying electronic properties, we extract the effective mass for the hole bands that show an unexpected decrease inside the nematic phase. These findings are consistent with the decrease in the renormalisation associated the higher energy \({d}_{{z}^{2}}\) bands. On the other hand, the effective mass of the third hole band with dxy orbital character has a local minimum before increasing significantly in the tetragonal region. Concomitantly, we detect the gradual shift of this, rather flat, dxy hole band towards the Fermi-level with increasing Te concentration, which could lead to an enhancement of the density of states and the opening of a new pairing channel. This effect could be responsible for the emergence of the second superconducting dome outside the nematic phase involving the hole band with dxy orbital character, in contrast to the superconducting dome inside the nematic phase. These trends occur at the same time as the chalcogen height increases, and our findings may have implications for other studies, like those under applied pressure. Moreover, at high Te concentration, the resistivity of FeSe1−xTex reflects bad metallic behaviour but superconductivity remains rather robust. Our findings suggest changes in the superconducting mechanism between that emerging from the nematic phase, with rather weak electronic correlations, and the second superconducting dome outside the nematic phase. Further theoretical studies that aim to understand the superconducting mechanisms in these systems could consider the presence of the orbitally dependent electronic correlations, the enhanced density of states induced by a nearly-flat band with dxy orbital character and potentially the significant effects caused by the local variation in the chalcogen height.

Methods

Sample characterisation

Single crystals of FeSe1−xTex were grown via the new chemical vapour transport method68 and screened via transport studies and X-ray diffraction (XRD). The nematic transition, Ts was evaluated from the temperature dependence of the longitudinal resistivity (as the extremum in the first derivative as a function of temperature) as well as from X-ray studies, and compared with a previous report5. After each ARPES experiment, we also performed Energy Dispersive X-ray (EDX) spectroscopy studies to directly measure the composition of each investigated crystal and these values are reported here.

ARPES measurements were performed at the I05 beamline at the Diamond Light Source synchrotron using a MBS A1 hemispherical analyser giving a combined energy resolution of ~3 meV69. The incident photon energy was varied between 23–100 eV to probe the kz dependence of the electronic structure and to identify the high-symmetry points. The single crystals were cleaved in-situ using a top-post and all measurements were performed at the base temperature of 10 K and under ultrahigh vacuum at 10−10 mbar. The beamspot was ~50 μm which is much larger than the nematic domains of the samples70. Therefore, all spectra are a superposition of the two orthogonal domains. Besides the reported data on new crystals of FeSe1−xTex, we compare our results to previous ARPES data on FeSe from refs. 13,20 and the tetragonal system, FeSe0.82S0.18, reported previously in refs. 3,38.

Density functional theory

To complement the experimental data, we have performed DFT band structure calculations using the Wien2k software in the GGA approximation with and without SOC71 which are presented in Supplementary Note 1. These calculations were performed in the tetragonal phase with lattice parameters taken from refs. 5,38,72, as listed in Supplementary Table 1.