Visualization of the electronic phase separation in superconducting KxFe2−ySe2

Type-II iron-based superconductors (Fe-SCs), the alkali-metal-intercalated iron selenide AxFe2−ySe2 (A = K, Tl, Rb, etc.) with a superconducting transition temperature of 32 K, exhibit unique properties such as high Néel temperature, Fe-vacancies ordering, antiferromagnetically ordered insulating state in the phase diagram, and mesoscopic phase separation in the superconducting materials. In particular, the electronic and structural phase separation in these systems has attracted intensive attention since it provides a platform to unveil the insulating parent phase of type-II Fe-SCs that mimics the Mott parent phase in cuprates. In this work, we use spatial- and angle-resolved photoemission spectroscopy to study the electronic structure of superconducting KxFe2−ySe2. We observe clear electronic phase separation of KxFe2−ySe2 into metallic islands and insulating matrix, showing different K and Fe concentrations. While the metallic islands show strongly dispersive bands near the Fermi level, the insulating phase shows an energy gap up to 700 meV and a nearly flat band around 700 meV below the Fermi energy, consistent with previous experimental and theoretical results on the superconducting K1−xFe2Se2 (122 phase) and Fe-vacancy ordered K0.8Fe1.6Se2 (245 phase), respectively. Our results not only provide important insights into the mysterious composition of phase-separated superconducting and insulating phases of KxFe2−ySe2, but also present their intrinsic electronic structures, which will shed light on the comprehension of the unique physics in type-II Fe-SCs.

While the structural phase separation in AxFe2−ySe2 has been extensively studied by various spatial-resolved techniques such as scanning tunnelling microscopy (STM), scanning electron microscope (SEM), transmission electron microscope (TEM) and nanofocused X-ray diffraction (XRD) [10,[16][17][18][19], the intrinsic electronic structures of the phase-separated 122 and 245 phases are not well understood yet. Angle-resolved photoemission spectroscopy (ARPES) has revealed the abnormal FS topology, isotropic superconducting gap and orbital-selective Mott phase in AxFe2−ySe2 [11][12][13][29][30][31][32]. However, due to the lack of spatial resolution, the conventional ARPES measures the mixture of the electronic structures of different phases of AxFe2−ySe2. Direct measurements on the intrinsic electronic structures of the phase-separated 122 and 245 phases are necessary in order to understand the unique properties of AxFe2−ySe2. The realization of high spatial-resolution in ARPES by adopting micro-focused beam spot (spatial-resolved ARPES or μ-ARPES) provides an ideal tool to investigate the electronic phase separation and related fine local electronic structures of different phases in AxFe2−ySe2. Previous μ-ARPES measurements have revealed interconnected networks of the minor 122 phase on the background matrix of 245 insulating phase [21,33,34], consistent with other local structural and magnetic measurements. However, partially due to the limited energy and spatial resolutions, the subtle microstructure of the minor 122 phase was not revealed and the investigation on the detailed electronic structures of the 122 and 245 phases is still essentially lacking.
In this manuscript, we use μ-ARPES to investigate the intrinsic electronic structure of the phase-separated KxFe2−ySe2. We show that the two phases are separated into 122 phase islands of micrometer scale and an insulating matrix of 245 phase. The characteristic K 3p peak in the core-level spectra shows distinctive intensity in the 122 and 245 regions, respectively; while the Se 3d peak shows a chemical shift of about 400 meV and a change of the line shape, suggesting different chemical environment for the Se atoms in the two phases. Near the Fermi energy (EF), the measured electronic structure of the 122 phase resembles the result of conventional ARPES measurements. However, a nearly flat band at ~ 700 meV below EF in the conventional ARPES measurements is absent in our μ-ARPES measurements on the 122 phase, and appears in the insulating 245 phase. The observed band gap of the insulating 245 phase is as large as 700 meV, consistent with ab-initio calculation on the 245 phase with block-spin AFM ordering [35,36]. Our results unveil the intrinsic electronic structures of the phase-separated 122 and 245 phases, which will help to understand the puzzling superconducting transition in KxFe2−ySe2 and the parent compound of this intriguing type of superconductor. Our experiments also illustrate μ-ARPES as a powerful tool to directly investigate the electronic phaseseparation phenomena in inhomogeneous materials with both high spatial and momentum resolutions.

Results and discussion
K1−xFe2Se2 (122 phase) crystallizes in a 122 ThCr2Si2 structure, similar to the iron pnictide BaFe2As2 as shown in Fig. 1(a). It can be viewed as alkali intercalated alpha-FeSe [1]. The insulating 245 phase crystallizes in a similarly layered structure ( Fig. 1(b)), except that there are additional Fe vacancies every fifth Fe atoms [4]. At low temperature, the Fe vacancies are proposed to form a ( 5 × 5 ) ordering [5,19,20].
μ-ARPES, combing both spatial and momentum resolutions, promises a direct investigation of the intrinsic electronic structure of phase-separated materials as schematically demonstrated in Figs. 1(c) and 1(d). The light beam needs to be strongly focused in order to get high enough spatial resolution. Usually, a Fresnel zone plate or a Schwarzschild mirror is used to focus the beam down to less than 1 micron. In order to make the samples with larger size of the superconducting islands for better μ-ARPES observation, we used the slow furnace cooling (SFC) method to treat the samples, in this case some of the islands can grow up and have dimensions as big as a couple of micrometers [10]. The onset value of the superconducting transition temperature (Tc) is around 25 K in these SFC treated samples. In comparison with normally treated samples with Tc ~ 31 K, the degraded Tc value in our samples is most likely due to a small difference in the precise chemical composition of the superconducting 122 phase or may possibly be associated with a change in the electronic interaction of the two phases (increased size of superconducting domains and decreased amount of interface), which may have potential influences on the measured electronic structures. From our SEM and XRD measurements, the chemical composition of the superconducting area is about K0.64Fe1.78Se2, which is close to the composition of normally treated sample and the related crystal structure doesn't change [10]. By scanning in the real space, the distinctive electronic structures of different phases in KxFe2−ySe2 can be measured at selected sample positions (Fig. 1(c)). Figure 1(e)(i) shows the real-space ARPES intensity map near EF scanning across the whole sample surface, showing the basic topography of cleaved KxFe2−ySe2. The zoom-in plot in Fig. 1(e)(ii) shows dark regions with higher intensity forming networks with typical width of 0.5-1 μm, confirming the existence of electronic phase separation. The further zoom-in plot in Fig. 1(e)(iii) shows discontinuous islands, consistent with previous local structural and magnetic measurements [5,10,[19][20][21][22]. Figure 2 shows the real-space variation of the core-level photoemission spectra, which can provide important insights into the related chemical composition. The electronic phase separation can be well resolved in an energy window of at least 2.5 eV below EF, where the Fe 3d orbitals dominate the density of states (Fig. 2(a)). We select 2 points from each phase (marked in Figs. 1(e) and 2(d)(left)) to show the spatial variation of the core-level spectra. As shown in Fig. 2(b) and zoom-in plots in Fig. 2(c), the identical spectra from different locations of the same phase suggest an intrinsic phase separation instead of randomly inhomogeneous variation of the chemical composition. From the spectra near EF shown in Fig. 2(c)(i), we observe much higher density of states of the Fe 3d orbitals on the dark islands, while a large energy gap exists in the major bright background. Therefore, we attribute the dark islands to the conductive 122 phase and the bright background to the insulating 245 phase with Fe vacancies [21,33,34]. Although the observed metallic islands show discontinuous pattern on the cleaved surface of bulk KxFe2−ySe2, we should note that these separated islands are interconnected in real space accounting for the bulk superconductivity of the sample [34].
In addition to the difference of the photoemission intensity near EF, we also observe differences near the characteristic K 3p and Se 3d peaks, as shown in Figs. 2(c)(ii) and 2(c)(iii). Near the Se 3d peaks, the 122 phase shows a main peak near 54.7 eV and a shoulder near 55.5 eV, while the 245 phase shows double peaks located near 54.3 and 55.3 eV. The difference in the line shape of Se 3d peaks is attributed to a chemical shift due to the different chemical environments in the two phases (Figs. 1(a) and 1(b)). We emphasize that the overall intensities of Se 3d peaks in the two phases are quite similar, suggesting a nearly uniform distribution of Se atoms in the 122 and 245 phases. Near the K 3p peak, in contrast, a clear difference of the peak intensity is observed, suggesting a lower K concentration in the 122 phase than in the 245 phase. Such photoemission results are in good agreement with the SEM experiments on the same samples [10]. For Fe 3p core level (~ 52.7 eV), possibly due to the poor photoemission cross-section under the photon energy used here (hν = 74 eV), we do not observe significant contribution from Fe 3p orbitals in the core-level spectra. The  Fig. 1(e)(iii). (c) The enlarged core-level spectra near the EF (i), K 3p peak (ii), and Se 3d peak (iii). (d) The phase separation characterized by the real space photoemission intensity map at different binding energies corresponding to EF (left), K 3p peak (middle) and Se 3d peak (right). The sample points #1-#4 indicate the positions where the spectra in (b) are collected. spatial mapping of the photoemission intensity near EF, K 3p, and Se 3d peaks are summarized in Fig. 2(d), which reflects the electronic phase separation at characteristic binding energies.
In Fig. 3, we present a close examination of the band dispersion near EF of both 122 and 245 phases. In the 122 phase, we observe hole-like band dispersion together with a weak electron pocket near EF at the Γ point and an electron-like band dispersion at the M point (Figs. 3(a) and 3(b)), consistent with previous studies [33,34]. Figure 3(c) schematically plots the major band dispersions of the 122 phase, which is in good consistence with previous ARPES measurements [11][12][13][29][30][31].
As an important fact in understanding the pairing symmetry of superconducting in Fe-SCs, we confirm the absence of the hole pocket in the FS of the intrinsic 122 phase [11][12][13]. In the insulating 245 phase, on the other hand, we observe an energy gap as large as 700 meV (Figs. 3(d) and 3(e)) and a weakly dispersive band near 700 meV below EF with strong spectral weight, as schematically shown in Fig. 3(f). Figure 3(g) compares the energy distribution curves (EDCs) at different momentum positions collected on different phases, showing the drastically distinctive line shapes. Clearly, the band dispersion of the 122 phase cannot be reproduced by a simple rigid shift of the band structure of the insulating 245 phase, indicating the fundamentally different electronic structures of the two phases.
In Fig. 4, we compare the electronic structures of the 122 phase studied with μ-ARPES and conventional ARPES (the same setup with μ-ARPES except that the beam is defocused). The measured band structures are similar to each other near EF (Figs. 4(a) and 4(b)). However, a broad and nearly disperseless band only appears in the result measured with defocused beam that covers both 122 and 245 phases, which can be nicely reproduced by artificially summing up the results measured on the 122 and 245 phases with μ-ARPES (Figs. 4(b) and 4(c)), as further proved by the EDCs near Γ and M points in Fig. 4(d). Our measurement suggests that the measurement of the electronic structure of the 122 phase using conventional ARPES is not strongly affected by the insulating background.
With high-quality μ-ARPES data, we have visualized the intrinsic electronic structures of phase-separated 122 and 245 phases of KxFe2−ySe2. The electronic states in the 122 and 245  phases are well separated in energy space, which guarantees that the conventional high-resolution ARPES reveals the correct band structure of superconducting KxFe2−ySe2 near EF, confirming the absence of the hole pockets around the Γ point in the FS. However, the EDC line shape is greatly changed by the mixture of the signals from 122 and 245 phases (Fig. 4(d)). Therefore, it is important to measure the intrinsic electronic structure of the 122 phase using μ-ARPES. The dispersions at high binding energies (> 500 meV), which are likewise important for accurately understanding the intrinsic electronic structure of superconducting 122 phase, are strongly contaminated by the electronic structure of the insulating 245 phase and can only be measured by μ-ARPES. On the other hand, it is worth to emphasize that the measured electronic structure of the insulating 245 phase, including the energy gap of ~ 700 meV and the nearly disperseless band, shows good consistence with ab-initio calculation on the 245 phase with block-spin AFM ordering [35,36] and optical measurement [37], which is important for understanding the parental phase of type-II Fe-SCs. Finally, the self-aggregation of the 122 and 245 phases with drastically different electronic structures at low temperature suggests subtle interplay between the two phases. For example, with the increased size of the superconducting island, the Tc value decreases [10], which may be due to the decreased amount of interface. Other effects, such as the balance between the chemical potentials, the proximity effect, and the strain effect should be taken into account as well in understanding the unique electronic properties of KxFe2−ySe2.

Conclusion
In conclusion, we have clearly revealed the electronic phase separation in type-II Fe-SC KxFe2−ySe2 by means of spatialresolved ARPES. Firstly, our μ-ARPES measurements unveil the intrinsic electronic structure of the superconducting 122 phase, which compellingly confirms the unusual FS topology of superconducting KxFe2−ySe2. Secondly, we provide important insights into the composition of the phase separated 122 and 245 phases. Thirdly, we directly visualize the electronic structure and band gap of the insulating 245 phase, which is important for further improvements in constructing theoretical models for phase-separated KxFe2−ySe2. Our results thus shed light on the understanding of the unique electronic properties of KxFe2−ySe2 and we emphasize that the interplay between the 122 and 245 phases may play an important role in the superconductivity of KxFe2−ySe2.

Materials
KxFe2−ySe2 single crystals were prepared by self-flux method. K pieces and FeSe powders were used as precursors. They were mixed in an atomic ratio of K:(FeSe) = 0.8:2, and then the mixture was loaded into an alumina crucible and sealed in a quartz tube under vacuum. The mixture was subsequently heated up to 1,030 °C and held for 3 h. The sample was cooled down to 800 °C at a rate of 4 °C/h, and then it was cooled to room temperature by switching off the power of the furnace. All the weighing, mixing, grinding and pressing procedures were finished in a glove box under argon atmosphere with the oxygen and moisture below 0.1 p.p.m.
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