Angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3: strong coupling behavior and the universality of interband scattering

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Correspondence between the electronic structure and phase separation in a K-doped FeSe system

Phase separated potassium intercalated FeSe thin films have been synthesized by pulsed laser deposition. The coexistence of FeSe phase and 245 phase was investigated both by x-ray photoemission spectroscopy (XPS) and x-ray diffraction. The volume ratio of these two phases is sensitive to temperatures and amount of extra potassium dosing. The XPS and ultraviolet photoelectron spectroscopy results indicated that these two phases shows the different hybridization strength between adjacent Fe layer and Se layer. We infer that the layered electronic structure is the necessary condition of superconductivity in potassium-doped FeSe system, and the phase separation is driven by competition between quasi-2D and 3D bonding mode within FeSe layer. Similar competition may also be able to interpret the phase seperation in K _x Fe_2-y Se₂ bulk single crystal.

Correlation-Driven Topological Fermi Surface Transition in FeSe

The electronic structure and phase stability of paramagnetic FeSe is computed by using a combination of ab initio methods for calculating band structure and dynamical mean-field theory. Our results reveal a topological change (Lifshitz transition) of the Fermi surface upon a moderate expansion of the lattice. The Lifshitz transition is accompanied with a sharp increase of the local moments and results in an entire reconstruction of magnetic correlations from the in-plane magnetic wave vector, (π,π) to (π,0). We attribute this behavior to a correlation-induced shift of the van Hove singularity originating from the d(xy) and d(xz)/d(yz) bands at the M point across the Fermi level. We propose that superconductivity is strongly influenced, or even induced, by a van Hove singularity.

ARPES measurements of the superconducting gap of Fe-based superconductors and their implications to the pairing mechanism

Its direct momentum sensitivity confers to angle-resolved photoemission spectroscopy (ARPES) a unique perspective in investigating the superconducting gap of multi-band systems. In this review we discuss ARPES studies on the superconducting gap of high-temperature Fe-based superconductors. We show that while Fermi-surface-driven pairing mechanisms fail to provide a universal scheme for the Fe-based superconductors, theoretical approaches based on short-range interactions lead to a more robust and universal description of superconductivity in these materials. Our findings are also discussed in the broader context of unconventional superconductivity.

Electronic structure and superconductivity of FeSe-related superconductors

FeSe superconductors and their related systems have attracted much attention in the study of iron-based superconductors owing to their simple crystal structure and peculiar electronic and physical properties. The bulk FeSe superconductor has a superconducting transition temperature (Tc) of ~8 K and it can be dramatically enhanced to 37 K at high pressure. On the other hand, its cousin system, FeTe, possesses a unique antiferromagnetic ground state but is non-superconducting. Substitution of Se with Te in the FeSe superconductor results in an enhancement of Tc up to 14.5 K and superconductivity can persist over a large composition range in the Fe(Se,Te) system. Intercalation of the FeSe superconductor leads to the discovery of the AxFe2-ySe2 (A = K, Cs and Tl) system that exhibits a Tc higher than 30 K and a unique electronic structure of the superconducting phase. A recent report of possible high temperature superconductivity in single-layer FeSe/SrTiO3 films with a Tc above 65 K has generated much excitement in the community. This pioneering work opens a door for interface superconductivity to explore for high Tc superconductors. The distinct electronic structure and superconducting gap, layer-dependent behavior and insulator-superconductor transition of the FeSe/SrTiO3 films provide critical information in understanding the superconductivity mechanism of iron-based superconductors. In this paper, we present a brief review of the investigation of the electronic structure and superconductivity of the FeSe superconductor and related systems, with a particular focus on the FeSe films.

Spin-orbit interactions and the nematicity observed in the fe-based superconductors

High-resolution angle-resolved photoelectron spectroscopy is used to examine the electronic band structure of FeTe_{0.5}Se_{0.5} near the Brillouin zone center. A consistent separation of the α_{1} and α_{2} bands is observed with little k_{z} dependence of the α_{1} band. First-principles calculations for bulk and thin films demonstrate that the antiferromagnetic coupling between the Fe atoms and hybridization-induced spin-orbit effects lifts the degeneracy of the Fe d_{xz} and d_{yz} orbitals at the zone center leading to orbital ordering. These experimental and computational results provide a natural microscopic basis for the nematicity observed in the Fe-based superconductors.

Reconstruction of band structure induced by electronic nematicity in an FeSe superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on an FeSe superconductor (T_{c}∼8  K), which exhibits a tetragonal-to-orthorhombic structural transition at T_{s}∼90  K. At low temperature, we found splitting of the energy bands as large as 50 meV at the M point in the Brillouin zone, likely caused by the formation of electronically driven nematic states. This band splitting persists up to T∼110  K, slightly above T_{s}, suggesting that the structural transition is triggered by the electronic nematicity. We have also revealed that at low temperature the band splitting gives rise to a van Hove singularity within 5 meV of the Fermi energy. The present result strongly suggests that this unusual electronic state is responsible for the unconventional superconductivity in FeSe.

Anisotropy of magnetic properties of Fe(1+y)Te

The magnetic properties of Fe(1+y)Te single crystals (y ≃ 0.1 ÷ 0.18) were studied at temperatures 4.2 ÷ 300 K. At an ambient pressure, with decreasing temperature a drastic drop in χ(T) was confirmed at T ≃ 60 ÷ 65 K, which appears to be closely related to the antiferromagnetic (AFM) ordering. It is found that the magnitudes of the anisotropy of magnetic susceptibility Δχ in the AFM phase are close in the studied samples, whereas the sign of the anisotropy apparently depends on the small variations of the excess iron y in Fe(1+y)Te samples. The performed DFT calculations of the electronic structure and magnetic properties for the stoichiometric FeTe compound indicate the presence of frustrated AFM ground states. There are very close energies and magnetic moments for the double stripe configurations, with the AFM axes oriented either on the basal plane or along the [0 0 1] direction. Presumably, both these configurations can be realized in Fe(1+y)Te single crystals, depending on the variations of the excess iron. This can provide different signs of magnetic anisotropy in the AFM phase, presently observed in the Fe(1+y)Te samples. For these types of AFM configuration, the calculations for the FeTe values of Δχ are consistent with our experimental data.

Characteristic two-dimensional Fermi surface topology of high-Tc iron-based superconductors

Unconventional Cooper pairing originating from spin or orbital fluctuations has been proposed for iron-based superconductors. Such pairing may be enhanced by quasi-nesting of two-dimensional electron and hole-like Fermi surfaces (FS), which is considered an important ingredient for superconductivity at high critical temperatures (high-Tc). However, the dimensionality of the FS varies for hole and electron-doped systems, so the precise importance of this feature for high-Tc materials remains unclear. Here we demonstrate a phase of electron-doped CaFe2As2 (La and P co-doped CaFe2As2) with Tc = 45 K, which is the highest Tc found for the AEFe2As2 bulk superconductors (122-type; AE = Alkaline Earth), possesses only cylindrical hole- and electron-like FSs. This result indicates that FS topology consisting only of two-dimensional sheets is characteristic of both hole- and electron-doped 122-type high-Tc superconductors.

Superconductivity in an electron band just above the Fermi level: possible route to BCS-BEC superconductivity

Conventional superconductivity follows Bardeen-Cooper-Schrieffer(BCS) theory of electrons-pairing in momentum-space, while superfluidity is the Bose-Einstein condensation(BEC) of atoms paired in real-space. These properties of solid metals and ultra-cold gases, respectively, are connected by the BCS-BEC crossover. Here we investigate the band dispersions in FeTe(0.6)Se(0.4)(Tc = 14.5 K ~ 1.2 meV) in an accessible range below and above the Fermi level(EF) using ultra-high resolution laser angle-resolved photoemission spectroscopy. We uncover an electron band lying just 0.7 meV (~8 K) above EF at the Γ-point, which shows a sharp superconducting coherence peak with gap formation below Tc. The estimated superconducting gap Δ and Fermi energy [Symbol: see text]F indicate composite superconductivity in an iron-based superconductor, consisting of strong-coupling BEC in the electron band and weak-coupling BCS-like superconductivity in the hole band. The study identifies the possible route to BCS-BEC superconductivity.

A flat band at the chemical potential of a Fe1.03Te0.94S0.06 superconductor observed by angle-resolved photoemission spectroscopy

The electronic structure of superconducting Fe1.03Te0.94S0.06 has been studied by angle-resolved photoemission spectroscopy (ARPES). Experimental band topography is compared to the calculations using the methods of Korringa-Kohn-Rostoker (KKR) with the coherent potential approximation (CPA) and the linearized augmented plane wave with local orbitals (LAPW+LO) method. The region of the Γ point exhibits two hole pockets and a quasiparticle peak close to the chemical potential (μ) with undetectable dispersion. This flat band with mainly d(z)(2) orbital character is most likely formed by the top of the outer hole pocket or is evidence of a third hole band. It may cover up to 3% of the Brillouin zone volume and should give rise to a Van Hove singularity. Studies performed for various photon energies indicate that at least one of the hole pockets has a two-dimensional character. The apparently nondispersing peak at μ is clearly visible for 40 eV and higher photon energies, due to an effect of the photoionization cross-section rather than band dimensionality. Orbital characters calculated by LAPW+LO for stoichiometric FeTe do not reveal the flat dz(2) band but are in agreement with the experiment for the other dispersions around Γ in Fe1.03Te0.94S0.06.

Measurement of coherent polarons in the strongly coupled antiferromagnetically ordered iron-chalcogenide Fe1.02Te using angle-resolved photoemission spectroscopy

The nature of metallicity and the level of electronic correlations in the antiferromagnetically ordered parent compounds are two important open issues for the iron-based superconductivity. We perform a temperature-dependent angle-resolved photoemission spectroscopy study of Fe(1.02)Te, the parent compound for iron chalcogenide superconductors. Deep in the antiferromagnetic state, the spectra exhibit a "peak-dip-hump" line shape associated with two clearly separate branches of dispersion, characteristics of polarons seen in manganites and lightly doped cuprates. As temperature increases towards the Néel temperature (T(N)), we observe a decreasing renormalization of the peak dispersion and a counterintuitive sharpening of the hump linewidth, suggestive of an intimate connection between the weakening electron-phonon (e-ph) coupling and antiferromagnetism. Our finding points to the highly correlated nature of the Fe(1.02)Te ground state featured by strong interactions among the charge, spin, and lattice and a good metallicity plausibly contributed by the coherent polaron motion.

Evidence for a cos(4φ) modulation of the superconducting energy gap of optimally doped FeTe(0.6)Se(0.4) single crystals using laser angle-resolved photoemission spectroscopy

We study the superconducting-gap anisotropy of the Γ-centered hole Fermi surface in optimally doped FeTe(0.6)Se(0.4) (T(c)=14.5 K), using laser-excited angle-resolved photoemission spectroscopy. We observe sharp superconducting (SC) coherence peaks at T=2.5 K. In contrast to earlier angle-resolved photoemission spectroscopy studies but consistent with thermodynamic results, the momentum dependence shows a cos(4φ) modulation of the SC-gap anisotropy. The observed SC-gap anisotropy strongly indicates that the pairing interaction is not a conventional phonon-mediated isotropic one. Instead, the results suggest the importance of second-nearest-neighbor electronic interactions between the iron sites in the framework of s(±)-wave superconductivity.

Te concentration dependent photoemission and inverse-photoemission study of FeSe1-xTex

We have characterized the electronic structure of FeSe1-x Te x for various x values using soft x-ray photoemission spectroscopy (SXPES), high-resolution photoemission spectroscopy (HRPES) and inverse photoemission spectroscopy (IPES). The SXPES valence band spectral shape shows that the 2 eV feature in FeSe, which was ascribed to the lower Hubbard band in previous theoretical studies, becomes less prominent with increasing x. HRPES exhibits systematic x dependence of the structure near the Fermi level (EF): its splitting near EF and filling of the pseudogap in FeSe. IPES shows two features, near EF and approximately 6 eV above EF; the former may be related to the Fe 3d states hybridized with chalcogenide p states, while the latter may consist of plane-wave-like and Se d components. In the incident electron energy dependence of IPES, the density of states near EF for FeSe and FeTe has the Fano lineshape characteristic of resonant behavior. These compounds exhibit different resonance profiles, which may reflect the differences in their electronic structures. By combining the PES and IPES data the on-site Coulomb energy was estimated at 3.5 eV for FeSe.

Magnetic excitations in iron chalcogenide superconductors

Nuclear magnetic resonance and neutron scattering experiments in iron chalcogenide superconductors are reviewed to make a survey of the magnetic excitations in FeSe, FeSe1-x Te x and alkali-metal-doped Ax Fe2-y Se2 (A = K, Rb, Cs, etc). In FeSe, the intimate relationship between the spin fluctuations and superconductivity can be seen universally for the variations in the off-stoichiometry, the Co-substitution and applied pressure. The isovalent compound FeTe has a magnetic ordering with different wave vector from that of other Fe-based magnetic materials. The transition temperature Tc of FeSe increases with Te substitution in FeSe1-x Te x with small x, and decreases in the vicinity of the end member FeTe. The spin fluctuations are drastically modified by the Te substitution. In the vicinity of the end member FeTe, the low-energy part of the spin fluctuation is dominated by the wave vector of the ordered phase of FeTe; however, the reduction of Tc shows that it does not support superconductivity. The presence of same wave vector as that of other Fe-based superconductors in FeSe1-x Te x and the observation of the resonance mode demonstrate that FeSe1-x Te x belongs to the same group as most of other Fe-based superconductors in the entire range of x, where superconductivity is mediated by the spin fluctuations whose wave vector is the same as the nesting vector between the hole pockets and the electron pockets. On the other hand, the spin fluctuations differ for alkali-metal-doped Ax Fe2-y Se2 and FeSe or other Fe-based superconductors in their wave vector and strength in the low-energy part, most likely because of the different Fermi surfaces. The resonance mode with different wave vector suggests that Ax Fe2-y Se2 has an exceptional superconducting symmetry among Fe-based superconductors.

Unconventional anisotropic s-wave superconducting gaps of the LiFeAs iron-pnictide superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on Fe-based superconductor LiFeAs (T(c)=18 K). We reveal multiple nodeless superconducting (SC) gaps with 2Δ/k(B)T(c) ratios varying from 2.8 to 6.4, depending on the Fermi surface (FS). We also succeeded in directly observing a gap anisotropy along the FS with magnitude up to ~30%. The anisotropy is fourfold symmetric with an antiphase between the hole and electron FSs, suggesting complex anisotropic interactions for the SC pairing. The observed momentum dependence of the SC gap offers an excellent opportunity to investigate the underlying pairing mechanism.

One-Fe versus two-Fe Brillouin zone of Fe-based superconductors: creation of the electron pockets by translational symmetry breaking

We investigate the physical effects of translational symmetry breaking in Fe-based high-temperature superconductors due to alternating anion positions. In the representative parent compounds, including the newly discovered Fe-vacancy-ordered K(0.8)Fe(1.6)Se(2), an unusual change of orbital character is found across the one-Fe Brillouin zone upon unfolding the first-principles band structure and Fermi surfaces, suggesting that covering a larger one-Fe Brillouin zone is necessary in experiments. Most significantly, the electron pockets (critical to the magnetism and superconductivity) are found only created with broken symmetry, advocating strongly its full inclusion in future studies, particularly on the debated nodal structures of the superconducting order parameter.

Magnetic resonant mode in the low-energy spin-excitation spectrum of superconducting Rb2Fe4Se5 single crystals

We have studied the low-energy spin-excitation spectrum of the single-crystalline Rb(2)Fe(4)Se(5) superconductor (T(c)=32 K) by means of inelastic neutron scattering. In the superconducting state, we observe a magnetic resonant mode centered at an energy of ℏω(res)=14 meV and at the (0.5 0.25 0.5) wave vector (unfolded Fe-sublattice notation), which differs from the ones characterizing magnetic resonant modes in other iron-based superconductors. Our finding suggests that the 245-iron selenides are unconventional superconductors with a sign-changing order parameter, in which bulk superconductivity coexists with the √5×√5 magnetic superstructure. The estimated ratios of ℏω(res)/k(B)T(c)≈5.1±0.4 and ℏω(res)/2Δ≈0.7±0.1, where Δ is the superconducting gap, indicate moderate pairing strength in this compound, similar to that in optimally doped 1111 and 122 pnictides.

X-Ray spectra and electronic correlations of FeSe(1-x)Te(x)

Critical issues concerning emerging Fe-based superconductors include the degree of electron correlation and the origin of the superconductivity. X-Ray absorption spectra (XAS) and resonant inelastic X-ray scattering spectra (RIXS) of FeSe(1-x)Te(x) (x = 0-1) single crystals were obtained to study their electronic properties that relate to electron correlation and superconductivity. The linewidth of Fe L(2,3)-edges XAS of FeSe(1-x)Te(x) is narrower than that of Fe-pnictides, revealing the difference between their hybridization effects and localization character and those of other Fe-pnictides. While no significant differences exist between the Fe L-edge XAS and RIXS of FeSe(1-x)Te(x) and those of Fe-pnictides, Se K-edge and Te K-edge XAS exhibit substantial edge shift, suggesting that the superconductivity in an Fe-Se superconductor is strongly associated with the ligand states. A comparison of the Se K-edge and Te K-edge spectra reveals that the charge transfer may occur between Se and Te. Given the Coulomb interaction and the bandwidth, the spectral results indicate that FeSe(1-x)Te(x) is unlikely to be a weakly correlated system unlike the Fe-pnictides of the "1111" and "122" families. The spectral results further demonstrate that superconductivity in this class of Fe-based compounds is strongly associated with the ligand 4p hole state.

Absence of a holelike fermi surface for the iron-based K0.8F1.7Se2 superconductor revealed by angle-resolved photoemission spectroscopy

We have performed an angle-resolved photoemission spectroscopy study of the new iron-based superconductor K(0.8)Fe(1.7)Se(2) (T(c)∼30 K). Clear band dispersion is observed with the overall bandwidth renormalized by a factor of 2.5 compared to our local density approximation calculations, indicating relatively strong correlation effects. Only an electronlike band crosses the Fermi energy, forming a nearly circular Fermi surface (FS) at M (π, 0). The holelike band at Γ sinks ∼90 meV below the Fermi energy, with an indirect band gap of 30 meV, to the bottom of the electronlike band. The observed FS topology in this superconductor favors (π, π) inter-FS scattering between the electronlike FSs at the M points, in sharp contrast to other iron-based superconductors which favor (π, 0) inter-FS scattering between holelike and electronlike FSs.

Distinct fermi surface topology and nodeless superconducting gap in a (Tl0.58Rb0.42)Fe1.72Se2 superconductor

High resolution angle-resolved photoemission measurements have been carried out to study the electronic structure and superconducting gap of the (Tl0.58Rb0.42)Fe1.72Se2 superconductor with a T(c) = 32  K. The Fermi surface topology consists of two electronlike Fermi surface sheets around the Γ point which is distinct from that in all other iron-based superconductors reported so far. The Fermi surface around the M point shows a nearly isotropic superconducting gap of ∼12  meV. The large Fermi surface near the Γ point also shows a nearly isotropic superconducting gap of ∼15  meV, while no superconducting gap opening is clearly observed for the inner tiny Fermi surface. Our observed new Fermi surface topology and its associated superconducting gap will provide key insights and constraints into the understanding of the superconductivity mechanism in iron-based superconductors.

Anisotropic structure of the order parameter in FeSe(0.45)Te(0.55) revealed by angle-resolved specific heat

The central issues for understanding iron (Fe)-based superconductors are the symmetry and structure of the superconducting gap. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes'). A unique method for addressing this issue, and one of very few methods that are bulk and angle resolved, is measuring the electronic-specific heat in a rotating magnetic field. In this study, we present the first such measurement for an Fe-based high-T(c) superconductor. We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction. Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.