Observation of a Hidden Hole-Like Band Approaching the Fermi Level in K-Doped Iron Selenide Superconductor

One of the ultimate goals of the study of iron-based superconductors is to identify the common feature that produces the high critical temperature (Tc). In the early days, based on a weak-coupling viewpoint, the nesting between hole- and electron-like Fermi surfaces (FSs) leading to the so-called $s\pm$ state was considered to be one such key feature. However, this theory has faced a serious challenge ever since the discovery of alkali-metal-doped FeSe (AFS) superconductors, in which only electron-like FSs with a nodeless superconducting gap are observed. Several theories have been proposed, but a consistent understanding is yet to be achieved. Here we show experimentally that a hole-like band exists in KxFe2-ySe2, which presumably forms a hole-like Fermi surface. The present study suggests that AFS can be categorized in the same group as iron arsenides with both hole- and electron-like FSs present. This result provides a foundation for a comprehensive understanding of the superconductivity in iron-based superconductors.

Thus, the proposed models based on both the weak-and strong-coupling approaches appear to fail to explain all the experimental results for AFS. In order to resolve this issue, revisiting the electronic structure of superconducting AFS is necessary. In K x Fe 2-y Se 2 , it is known that a minority superconducting phase (~10%) and a majority insulating phase (~90%) coexist due to intrinsic phase separation. 27,28) Very recently, an increased area of the superconducting phase (~30%) has been found in a K 0.62 Fe 1.7 Se 2 single crystal obtained by a one-step method with the quenching technique. 29) Thus, there is a possibility that the ARPES measurement of K 0.62 Fe 1.7 Se 2 will detect an intrinsic electronic structure responsible for the superconductivity, which has eluded previous ARPES experiments because of the smaller superconducting region in the sample surface. In this article, we report the surprising observation of a hole-like band that probably forms the hole-like FS around the Γ point by performing ARPES on a high-quality K 0.62 Fe 1.7 Se 2 single crystal with T c = 32 K. 29,30) High-quality K 0.62 Fe 1.7 Se 2 single crystals (T c = 32 K) were grown by the one-step method with the quenching technique, 29,30) where the quenching temperature was 700 ˚C. The chemical composition ratio was determined using an energy-dispersive X-ray spectrometer (EDS). ARPES measurements were carried out at BL-9A of Hiroshima Synchrotron Radiation Center (HSRC), where the energy of the light was set to 23 eV.
The total energy resolution was set to 15 meV. Samples were cleaved and measured in situ under a vacuum better than 2 × 10 -9 Pa. Calibration of E F for the sample was achieved using a gold reference.
In order to compare the experimental band structure with the results of theoretical studies, a first-principles band calculation was also performed using the VASP package. 31,32) The lattice parameter values were those determined experimentally in Ref. 33. Here, we adopted the GGA-PBEsol exchange correlation functional. 34) The wave functions were expanded by plane waves up to a cutoff energy of 550 eV and 1000 k-point meshes were used. A ten-orbital tight-binding model was derived from the first-principles band calculation exploiting the maximally localized Wannier orbitals. 35,36) The Wannier90 code was used for generating the Wannier orbitals. 37) Some modifications were made to the original band structure for a better correspondence with the experiment; the interlayer hoppings within the d xy orbital were all multiplied by a factor of 0.5 assuming the reduction of the three-dimensionality, most likely due to correlation effects, and also the on-site energy of the d xz/yz orbitals was shifted by -0.1 eV, again a tendency that is due to correlation effects. 38) The nearest-neighbor hopping of the d xy orbitals was also modified by -0.02 eV.
First, we demonstrate the low-lying electronic structure of K 0.62 Fe 1.7 Se 2 along Γ-M.  39) we find that the ζ band has a faster hole-like dispersion than the ε band. This suggests that the ε and ζ bands are different. corresponding to Γ-X. In these data, we observed the α-δ bands. In the p-pol data along Γ-X [Figs. 2(j)-2(l)], we found another E F -approaching hole-like band that is dispersed from E-E F = -120 meV and k = -0.52 Å -1 to E-E F = -60 meV and k = -0.28 Å -1 . The top of this hole-like band does not correspond to that of the ε band, which is located at E-E F = -60 meV. In addition, the slope of this band in a certain k-region (-0.52 Å -1 < k < -0.38 Å -1 ) is similar to that of the ζ band in Fig. 2(d), and is three times larger than that of the ε band in Fig. 2(a). These results indicate that the E F -approaching hole-like band in Figs.
2(j)-2(l) is the ζ band. Note that the ε band with a narrow dispersion has almost no intensity in the polarization-dependent ARPES data along Γ-X. Around the M point, four bands can be derived from the ARPES data taken along #3 in Fig . We now find that the δ and ζ bands are connected to the hole-like and electron-like dispersions around M, respectively. Except for the ζ band, the observed bands are found to be consistent with previous ARPES studies [6][7][8][9][10][11][12][13][14][15][16] . The newly identified ζ band with a steep hole-like dispersion approaches E F and possibly crosses E F around Γ, although the near-E F dispersion of the ζ band along Γ-M and Γ-X is unclear owing to its weak intensity as can be seen in Figs. 2(d) and 2(j).
In order to elucidate the near-E F dispersion of the ζ band, we measured the ARPES spectra along several cuts [#3-#5 in Figs show a finite energy dispersion of the shoulder structure that reaches -20 meV at k = +0.26 Å -1 , suggesting that E F crosses the ζ band. As mentioned above, the ζ band loses its intensity near E F , and this is discussed later in connection with theoretical studies. Now let us compare our experimental observations with the theoretical band structure. We have obtained a ten-orbital model of KFe 2 Se 2 from first-principles calculation. 31,32,37)  Regarding the bands other than the ζ band, we found that the experimentally observed α, γ, and δ bands can be assigned to the theoretically predicted d xz electron-like, d xz inner hole-like, and d yz middle hole-like bands, respectively.
Considering the selection rule for d orbitals, 40) 12) impurity scattering, 41) or matrix element effects peculiar to the d xy orbital , especially around Γ. 42) Theoretically, the position of the hole-like ζ and electron-like α bands is strongly affected by the relation between the nearest-neighbor (t 1 ) and next-nearest-neighbor (t 2 ) hoppings within the d xy orbital. 43 The experimentally observed β and ε bands are not predicted in our band calculations, although the ε band was assigned as the d xy band and its strong renormalization was discussed in terms of the orbital-selective Mott phase (OSMP). 12) This means that the number of the observed bands [ Fig. 2(r)] is larger than that in the band calculations. The presence of surface-related bands is one possible explanation for the difference in the number of bands. Another possibility is that the intrinsic phase separation may induce different metallic phases in K x Fe 2-y Se 2 . A recent scanning micro-X-ray diffraction study has revealed the existence of an interface phase that surrounds and protects the filamentary network of the metallic phase embedded in the insulating phase. 45) Reference 45 suggests that the interface phase is likely to be the OSMP, where the d xy bands are specifically localized while the other bands are itinerant. 12) The interface phase may induce the bands that are not predicted by the band calculation.
The observation of the hidden hole-like band approaching E F suggests the presence of a hole-like FS in K x Fe 2-y Se 2 . This result indicates that AFS can be categorized in the same group as iron arsenides with both hole-and electron-like FSs present. Thus, the "common identity" of the iron-based superconductors may be the presence of hole-and electron-like FSs. In order to confirm this indication, we suggest an experimental investigation of whether the hole-like FS exists in single-layer FeSe films, which are believed to be superconducting below T c ~ 60 K. [46][47][48]        )