Observation of universal strong orbital-dependent correlation effects in iron chalcogenides

Establishing the appropriate theoretical framework for unconventional superconductivity in the iron-based materials requires correct understanding of both the electron correlation strength and the role of Fermi surfaces. This fundamental issue becomes especially relevant with the discovery of the iron chalcogenide superconductors. Here, we use angle-resolved photoemission spectroscopy to measure three representative iron chalcogenides, FeTe0.56Se0.44, monolayer FeSe grown on SrTiO3 and K0.76Fe1.72Se2. We show that these superconductors are all strongly correlated, with an orbital-selective strong renormalization in the dxy bands despite having drastically different Fermi surface topologies. Furthermore, raising temperature brings all three compounds from a metallic state to a phase where the dxy orbital loses all spectral weight while other orbitals remain itinerant. These observations establish that iron chalcogenides display universal orbital-selective strong correlations that are insensitive to the Fermi surface topology, and are close to an orbital-selective Mott phase, hence placing strong constraints for theoretical understanding of iron-based superconductors.

S ince the discovery of high-temperature superconductivity in the iron pnictides (FePns), extensive research efforts have revealed many common properties of these materials. In the vast material base of the FePns, all parent phases are metallic, and the observed electronic structures are largely consistent with the prediction of ab initio local-density approximation (LDA) calculations 1,2 . These properties have led to theoretical understanding that the electron correlations in FePns are much weaker than in cuprate superconductors, whose parent phases are Mott insulators. Furthermore, the observation of comparable sized hole pockets at the Brillouin zone (BZ) centre and electron pockets at the BZ corner have resulted in the proposal that such a Fermi surface (FS) topology is ubiquitous and essential to superconductivity in FePns, and pairing in the FePns is mediated by antiferromagnetic fluctuations via FS nesting between the hole and electron Fermi pockets 3 . On the other hand, there have also been theoretical proposals of 'incipient Mott localization' for which the system is metallic but on the verge of localization [4][5][6] , supported by the normal state bad metal behaviour from optical conductivity measurements 7 and the large fluctuating magnetic moment comparable to the antiferromagnetic insulating copper oxides 8 . This discussion became especially relevant with the more recent discovery of iron chalcogenides (FeChs) [9][10][11] , which not only possess large local magnetic moments 12 and insulating phases 13 , but also include compounds that lack hole pockets needed for FS nesting yet have comparable superconducting transition temperatures (T C s) as FePns [14][15][16][17] .
There are currently three major classes of FeCh superconductors: FeTe 1 À x Se x , K x Fe 2 À y Se 2 , and FeSe film grown on SrTiO 3 . In the FeTe 1 À x Se x family, superconductivity is achieved with isovalent substitution of Se for Te that suppresses magnetic order in the FeTe end 18 , and becomes optimal in FeTe 0.56 Se 0.44 (FTS), where T C is 14.5 K. The K x Fe 2 À y Se 2 family has in its phase diagram insulating phases with magnetic moments as large as 3.3 m B per Fe 10,12,13 , and optimal T C is 32 K, such as achieved in K 0.76 Fe 1.72 Se 2 (KFS). FeSe film grown on SrTiO 3 is the latest addition to the FeCh family, with monolayer film (FS/STO) having a record T C possibly exceeding 65 K (refs 11,16,17). In a previous angle-resolved photoemission spectroscopy (ARPES) study 19 on KFS, we found the low-temperature state to be a metallic state with orbital-dependent renormalizationwhere the d xy orbital-dominated bands are strongly renormalized as compared with other orbitals. Raising temperature drives the material to an orbital-selective Mott phase (OSMP) in which the d xy orbital completely loses spectral weight while other orbitals remain itinerant. Subsequently, such a temperature scale was also identified by terahertz spectroscopy 20 , Hall measurements 21 and pump-probe spectroscopy 22 , where the slight temperature scale variations are due to the different definitions used. This motivates the usage of orbital selectivity to address the fundamental open question of whether it is the electron correlation strength or the nature of the FS that plays a predominant role in the microscopic physics of the FeCh materials.
In this work, we study systematically the optimal superconducting members of the three FeCh families, FTS, KFS and FS/STO, using ARPES. We show that, in the low-temperature state, in contrast to the FePns, all of the FeChs are in a strongly correlated regime where strong orbital-selective renormalization is observed on the d xy bands, despite having drastically different FS topologies. In addition, by increasing temperature, all of the FeChs crossover into a phase where the d xy orbital completely loses spectral weight while other orbitals remain metallic. These observations showcase the universally strong orbital-selective electron correlations in the FeChs, and that the superconductivity in the FeChs, which is insensitive to FS topology, occurs in proximity to an orbital-selective Mott phase, placing strong constraints on the theoretical understanding of the iron-based superconductors.

Results
Orbital-selective band renormalization at low temperatures. The generic electronic structure of iron-based superconductors (FeSCs) consists of three hole bands at the BZ centre, G, and two electron bands at the BZ corner, M. The hole bands are predominantly of d xz , d yz and d xy orbital characters, while the electron bands are d xz and d xy along G-M. The relative positions of these bands with respect to each other as well as to the Fermi level (E F ) could vary with differences in lattice parameters and doping level. Hence, the FS topology among different FeSCs could be qualitatively different, as shown in Fig. 1a-d, where the Fermi pockets at the BZ centre vary from being hole-like to non-existent to electron like. The measured band structure along the G-M high-symmetry direction for the three compounds are shown in Fig. 1e-g, in comparison to that for the optimally Co-doped BaFe 2 As 2 (BFCA) (Fig. 1h), an FePn as a reference. For FTS (Fig. 1i), one of the hole bands crosses E F , and both electron bands cross E F at M, resulting in roughly compensated hole pocket at G and electron pockets at M (Fig. 1a), consistent with isovalent substitution for this compound. For both FS/STO (Fig. 1j) and KFS (Fig. 1k) in contrast, only the electron bands cross E F while the hole band tops are well below E F , with an additional small electron pocket at G in KFS. Thus, there is heavy electron doping in both compounds as reflected in a FS topology consisting only of electron pockets (Fig. 1b,c). Comparing the band structure of the three FeChs to the FePns, we notice a significant difference near the M point-there is an apparent gap between the bottom of the electron bands and the top of the hole band in all three FeChs, in sharp contrast to BFCA (Fig. 1l), in which the d xz electron band bottom is degenerate with the d yz hole band top.
Generally in FeSC, this degeneracy between the d xz electron band bottom and d yz hole band top at the zone corner is protected by the C 4 rotational symmetry, as seen in BFCA (Fig. 1l) and corresponding LDA calculations (Fig. 2a). This degeneracy is only lifted with the breaking of C 4 symmetry, as in the orthorhombic phase of underdoped BFCA 23 , NaFeAs 24,25 , bulk FeSe 26-29 and multilayer FeSe film 30,31 , where a splitting between the corresponding d xz bands and d yz bands occurs, in addition to a doubling of the bands from twinning effects due to the orthorhombic distortion. However, no static C 4 symmetry breaking has been reported for any of the FeChs studied here, nor are twinning effects observed here that is expected from a broken symmetry due to orthorhombic distortion. Rather, this apparent gap can be explained by a strong orbital-dependent band renormalization and band hybridization. As the schematic shown in Fig. 2, the LDA-calculated d xy electron band bottom is deeper than that of the d xz band. If the d xy orbital is strongly renormalized compared with the other orbitals, the d xy electron band bottom, that is, the corresponding d xy hole band top, would rise above that of the d xz electron band (Fig. 2b). The heavily renormalized d xy hole band then crosses the d xz electron band and the two bands hybridize such that a gap appears at the M point without lifting the d xz /d yz degeneracy protected by C 4 symmetry (Fig. 2c). Evidence for two nearly degenerate electron bands can be seen in the high-resolution spectra acquired on FS/STO (Fig. 3a). As an aside, we note that in the unrenormalized case (Fig. 2a), a hybridization gap between the d xy electron band and d yz hole band is not observed. This is because when considering the hopping via the chalcogen atoms along this high-symmetry direction (x), both d xy and d xz are odd while d yz is even. Hence d xy does not mix with d yz to produce a hybridization gap 32 .
This interpretation is further supported by the observed strong renormalization of the d xy hole band near G, which is significantly more renormalized than the d xz /d yz hole bands, clearly seen in all three compounds ( Fig. 1i-k). For FTS, the d xy hole band is strongly renormalized by a factor of B16 compared with LDA calculations, while d xz and d yz bands are only renormalized by factors of B4. Moreover, in the FeTe 1 À x Se x family, it has been found that the d xy band renormalization factor strongly increases towards the FeTe end compared with that of d xz /d yz , further revealing the strong orbital dependence in the itinerant to localized crossover in this system 33 . For KFS, the d xy hole band is renormalized by a factor of B10 compared with the factor of B3 for d xz /d yz bands 19 . This is even more apparent in FS/STO, where enhanced d xy orbital matrix elements in the second BZ shows the nearly flat d xy hole band extending towards the bottom of the shallow electron bands at M with a noticeable hybridization gap (Fig. 3b). In contrast, in BFCA, the renormalization factor for d xy hole band is comparable to that of the d xz /d yz hole bands (2B3) (ref. 2), as can be seen in the band slopes in the second derivative plot (Fig. 1l). In summary, all three FeCh systems show much stronger renormalization in the d xy orbital compared with the d xz / d yz orbitals in the low-temperature state, in contrast to the FePns. Here we would like to note that while ARPES is a surfacesensitive probe, the universal orbital-selective renormalization among the FeChs despite their different structure and surface terminations indicate that these properties must represent the bulk, rather than a result of extrinsic variation of surface properties.
Temperature dependence. Next, by raising temperature sufficiently high, we notice that in all three FeCh systems, the d xy orbital-dominated bands lose spectral weight completely (Fig. 4), as reported previously for KFS 19 . This can be seen first in the disappearance of the shallow d xy hole band near the G point. In the low-temperature state of FTS, the d xy hole band crosses the d yz hole band near G, and a small hybridization gap appears as can be seen in the discontinuous intensity pattern of the strong d yz hole band (Fig. 4a). At high temperature, this discontinuity disappears as only the d xz and d yz hole bands remain (Fig. 4d). In KFS, the nearly flat d xy hole band in the low-temperature state is entirely above the d xz /d yz hole band tops (Fig. 4c), and clearly disappears  NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8777 ARTICLE at high temperatures (Fig. 4f). The second evidence for the disappearance of d xy orbital at high temperatures is the vanishing of the apparent gap between the electron band bottom and the d yz hole band top at M. As shown in the schematic (Fig. 4g,h), when the d xy band disappears, its hybridization gap with the d xz electron band naturally vanishes, recovering the deeper non-hybridized d xz electron band whose bottom is degenerate with the d yz hole band top as expected. This is clearly seen in the high-temperature data in all three systems (Fig. 4d-f). Here we note that while KFS is known to have phase separation issues with the existence of superconducting regions and insulating regions 19 , FTS and FS/ STO, on the other hand, do not have such complication. Hence the universal behaviour of vanishing d xy spectral weight with raised temperature observed here reflects an intrinsic effect rather than a result of intricate phase separation in KFS.
To examine this temperature dependence more carefully, we have quantitatively analysed the spectral weight of each FeCh system. For FTS, we track the d xy hole band slightly away from the G point where it is well separated from the d yz hole band (Fig. 5a). From the energy distribution curve at this momentum, we fit Gaussian peaks for both d xy hole band near E F and d yz hole band at higher energies, along with a Shirley background (Fig. 5d), and track the integrated spectral weight of the d xy and d yz peaks as a function of temperature. Comparing these two orbitals, we see that the d xy spectral weight drops to zero B110 K, in contrast to a very weak decrease of the d yz spectral weight. This is very similar to the situation in FS/STO and KFS, where we track the spectral weight of the d xy orbital at the d xy electron band bottom at M. For KFS, the fitted peak area precipitously drops B100 K, and approaches zero above 180 K (Fig. 5i). For FS/ STO, the d xy spectral weight approaches zero above 150 K while that of the d yz orbital remains finite (Fig. 5h), demonstrating the orbital dependence of this temperature evolution.
Theoretical calculations. For all three FeCh superconductors studied, two observations are universal: (i) strong orbital-dependent renormalization at low temperatures and (ii) disappearance of d xy spectral weight with raised temperatures. Theoretically, these behaviours can be understood in proximity to an OSMP, as predicted by both a slave-spin mean-field method 34 and dynamical mean-field theory method 35 taking into account sufficiently strong intra-orbital Coulomb repulsion U and Hund's coupling J. These works show that the FeChs are close to an OSMP in which the d xy orbital is completely Mott localized while the other orbitals remain itinerant, and that a temperature scale could be identified where the d xy orbital loses coherence and spectral weight, together with its hybridization to the other orbitals.
The orbital selectivity arises from two factors 19,34 . The crystal field splitting of the tetragonal lattice makes the d xy orbital energy level higher than that of d xz /d yz . Because the threshold interaction for the Mott transition is larger for degenerate orbitals than for non-degenerate orbitals 36 , it is easier to localize the d xy electrons. The tendency towards OSMP is further enhanced when the projected bandwidth is different 37 , as is the case here with the d xy band being narrower than the d xz /d yz bands. When the material is sufficiently close to such an OSMP, the d xy mass renormalization is much stronger than that of other orbitals, as observed in the low-temperature state of the FeChs. For the system to be close to this OSMP, it must exhibit strong electron correlations, which from the two theoretical studies is shown to be a combined result of Coulomb interactions U and Hund's coupling J.
Among the three FeChs, FTS is undoped, with n ¼ 6, while FS/STO and KFS are electron doped, with n ¼ 6.12 and 6.15, as estimated from FS volume counting. Figure 6 shows our calculated transition temperatures into the OSMP versus U phase diagrams for systematic dopings from n ¼ 6-6.15. The blue shading indicates the d xy quasiparticle spectral weight, Z xy , for each doping. When Z xy drops to zero, the system enters the OSMP. This transition boundary is marked by solid blue lines in    6. Furthermore, we see that for and only for integer filling, n ¼ 6 in the calculated doping range, there exists a Mott insulator phase (marked by a red line), where all orbitals become Mott localized with sufficiently large U. With increasing electron filling, the critical U for the system entering the OSMP at a given temperature shifts to larger values, as can be seen by tracing the blue lines at both 10 and 240 K, indicating that electron doping brings the system away from the OSMP. This is consistent with the observation that the temperature at which the d xy spectral weight disappears increases from FTS (110 K) to the doped FS/STO (150 K) and KFS (180 K). Here we note that the resistivity for the FeTe 1 À x Se x family exhibits a weak hump 18 suggestive of a crossover from insulating-like to metallic-like behaviour much like the case of KFS 10 , and this crossover temperature scale shifts to lower value with decreasing x, consistent with the stronger renormalization values towards the FeTe end 33 and the understanding that the low-temperature state of FeTe end sits closer to the OSMP.

Discussion
The strong orbital-selective behaviour in the FeCh family is a manifestation of its strong electron correlations, and suggests that they may serve as a bridge between the strongly correlated cuprates as doped Mott insulators and the weaker correlated FePns that are more itinerant. The OSMP of the FeChs can only occur when the overall electron correlations are strong. In that sense, the existence of an OSMP indicates the presence of strong   ARTICLE correlations, such that the system is in proximity to a Mott transition. The latter links these materials to the cuprates, where optimal superconductivity develops not too far from a Mott insulating state. The linkage can be made more explicit by the Hund's coupling-induced suppression of the interorbital coupling in the case of the iron-based materials 19,34,38 . This is relevant to the current discussion on the pairing mechanism of FeSC in both KFS and FS/STO as the lack of hole pockets do not seem to prevent them from superconducting at temperatures comparable to or even higher than FePns, which is unexpected from a weakcoupling FS nesting picture 3 . In a recent theoretical study 39 , it has been shown that under a strong coupling approach, where the driving force for pairing comes from the close-neighbour exchange interactions, the pairing strength can be comparable in the FeChs and FePns, as they approach a Mott transition by increasing exchange interaction in the former and reducing the renormalized bandwidth in the latter. The observed universal strong correlation in the FeChs and proximity to an OSMP here supports such a scenario.

Methods
Sample growth. High-quality single crystals of K 0.76 Fe 1.72 Se 2 and FeTe 0.56 Se 0.44 were grown using the flux method 19,40 . Monolayer FeSe films were grown on SrTiO 3 using molecular beam epitaxy 17 .
ARPES measurements. ARPES measurements were carried out at beamline 5-4 of the Stanford Synchrotron Radiation Lightsource and beamline 10.0.1 of the Advanced Light Source using SCIENTA R4000 electron analyzers. The total energy resolution was set to 10 meV and the angular resolution was 0.3°. Single crystals were cleaved in situ at 10 K for each measurement. The FeSe films were transported to the beamline under vacuum and further annealed before measurements. All measurements were done in ultra high vacuum with a base pressure lower than 4 Â 10 À 11 torr.