Highly Anisotropic and Twofold Symmetric Superconducting Gap in Nematically Ordered FeSe_{0.93}S_{0.07}

Synthesis and Characterization of Molybdenum- and Sulfur-Doped FeSe

During the past decade, two-dimensional (2D) layered materials opened novel opportunities for the exploration of exciting new physics and devices owing to their physical and electronic properties. Among 2D materials, iron selenide has attracted much attention from several physicists as they provide a fruitful stage for developing new superconductors. Chemical doping offers a powerful approach to manipulate and optimize the electronic structure and physical properties of materials. Here, to reveal how doping affects the physical properties in FeSe, we report on complementary measurements of molybdenum- and sulfur-doped FeSe with theoretical calculations. Mo0.1Fe0.9Se0.9S0.1 was synthesized by a one-step solid-state reaction method. Crystal structure and morphology were studied using powder X-ray diffraction and scanning electron microscopy. Thermal stability and decomposition behavior in doped samples were studied by thermogravimetric analysis, and to understand the microscopic influence of doping, we performed Raman spectroscopy. First-principles calculations of the electronic structure illustrate distinct changes of electronic structures of the substituted FeSe systems, which can be responsible for their superconducting properties.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

High temperature superconductivity at FeSe/LaFeO3 interface

Enormous enhancement of superconducting pairing temperature (Tg) to 65 K in FeSe/SrTiO3 has made it a spotlight. Despite the effort of interfacial engineering, FeSe interfaced with TiOx remains the unique case in hosting high Tg, hindering a decisive understanding on the general mechanism and ways to further improving Tg. Here we constructed a new high-Tg interface, single-layer FeSe interfaced with FeOx-terminated LaFeO3. Large superconducting gap and diamagnetic response evidence that the superconducting pairing can emerge near 80 K, highest amongst all-known interfacial superconductors. Combining various techniques, we reveal interfacial charge transfer and strong interfacial electron-phonon coupling (EPC) in FeSe/LaFeO3, showing that the cooperative pairing mechanism works beyond FeSe-TiOx. Intriguingly, the stronger interfacial EPC than that in FeSe/SrTiO3 is likely induced by the stronger interfacial bonding in FeSe/LaFeO3, and can explain the higher Tg according to recent theoretical calculations, pointing out a workable route in designing new interfaces to achieve higher Tg.

Quadrupolar charge dynamics in the nonmagnetic FeSe1-x S x superconductors

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

Observation of an electronic order along [110] direction in FeSe

Multiple ordered states have been observed in unconventional superconductors. Here, we apply scanning tunneling microscopy to probe the intrinsic ordered states in FeSe, the structurally simplest iron-based superconductor. Besides the well-known nematic order along [100] direction, we observe a checkerboard charge order in the iron lattice, which we name a [110] electronic order in FeSe. The [110] electronic order is robust at 77 K, accompanied with the rather weak [100] nematic order. At 4.5 K, The [100] nematic order is enhanced, while the [110] electronic order forms domains with reduced correlation length. In addition, the collective [110] order is gaped around [−40, 40] meV at 4.5 K. The observation of this exotic electronic order may shed new light on the origin of the ordered states in FeSe.

Understanding the relation of different electronic orders in high temperature superconductors is of fundamental interest. Here, the authors observe a checkerboard charge order along [110] direction of FeSe.

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.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field μ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ_{0}H^{*}≈24  T well below μ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Topological ultranodal pair states in iron-based superconductors

Bogoliubov Fermi surfaces are contours of zero-energy excitations that are protected in the superconducting state. Here we show that multiband superconductors with dominant spin singlet, intraband pairing of spin-1/2 electrons can undergo a transition to a state with Bogoliubov Fermi surfaces if spin-orbit coupling, interband pairing and time reversal symmetry breaking are also present. These latter effects may be small, but drive the transition to the topological state for appropriate nodal structure of the intra-band pair. Such a state should display nonzero zero-bias density of states and corresponding residual Sommerfeld coefficient as for a disordered nodal superconductor, but occurring even in the pure case. We present a model appropriate for iron-based superconductors where the topological transition associated with creation of a Bogoliubov Fermi surface can be studied. The model gives results that strongly resemble experiments on FeSe_1−xS_x across the nematic transition, where this ultranodal behavior may already have been observed.

Experiments indicate an abrupt change in the pairing gap near the nematic transition in the FeSe_1−xS_x iron-based superconductor. Here, Setty et al. propose to explain them via a novel spin-1/2 paired state with topologically protected zero-energy excitations over a finite area nodal surface.

k_{z} Selective Scattering within Quasiparticle Interference Measurements of FeSe

Quasiparticle interference (QPI) provides a wealth of information relating to the electronic structure of a material. However, it is often assumed that this information is constrained to two-dimensional electronic states. We show that this is not necessarily the case. For FeSe, a system dominated by surface defects, we show that it is actually all electronic states with negligible group velocity in the z axis that are contained within the experimental data. By using a three-dimensional tight-binding model of FeSe, fit to photoemission measurements, we directly reproduce the experimental QPI scattering dispersion, within a T-matrix formalism, by including both k_{z}=0 and k_{z}=π electronic states. This result unifies both tunnelling based and photoemission based experiments on FeSe and highlights the importance of k_{z} within surface sensitive measurements of QPI.

Evidence of cooperative effect on the enhanced superconducting transition temperature at the FeSe/SrTiO3 interface

At the interface between monolayer FeSe films and SrTiO₃ substrates the superconducting transition temperature (T_c) is unexpectedly high, triggering a surge of excitement. The mechanism for the T_c enhancement has been the central question, as it may present a new strategy for seeking out higher T_c materials. To reveal this enigmatic mechanism, by combining advances in high quality interface growth, ¹⁶O \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\leftrightarrow$$\end{document}↔¹⁸O isotope substitution, and extensive data from angle resolved photoemission spectroscopy, we provide striking evidence that the high T_c in FeSe/SrTiO₃ is the cooperative effect of the intrinsic pairing mechanism in the FeSe and interactions between the FeSe electrons and SrTiO₃ phonons. Furthermore, our results point to the promising prospect that similar cooperation between different Cooper pairing channels may be a general framework to understand and design high-temperature superconductors.

The mechanism of enhanced superconducting transition temperature (T_c) at the FeSe/SrTiO₃ interface remains enigmatic. Here, Song and Yu et al. reveal the evidence of cooperation between intrinsic pairing interaction in FeSe and interfacial electron–phonon coupling to enhance the T_c at the FeSe/SrTiO₃ interface.

Enhanced superconductivity of Ba0.5K0.5Fe2As2 under surface potassium dosing

Surface potassium dosing has been proven to be an effective method in tuning the electron doping and enhancing the superconducting transition temperatures in both iron chalcogenides and electron doped iron pnictides. However, it is not clear how surface potassium dosing affects the hole doping and superconductivity in hole doped Fe-based superconductors. Here we performed K-dosing on Ba_0.5K_0.5Fe₂As₂, a prototypical hole-doped iron pnictide compound, and explored the electronic structure by in situ angle-resolved photoemission spectroscopy measurements. Starting from the slightly over-doped Ba_0.5K_0.5Fe₂As₂, surface K-dosing effectively reduces the hole concentration towards optimal doping and enhances the superconductivity. Intriguingly, the enhancement of superconductivity does not slow down at optimal doping, and the gap further increases with K dosing even when the carrier doping effect is saturated. Meanwhile, the quasiparticle coherence of the inner hole pockets is enhanced by higher K dosing. Our results uncover a novel scattering-reduction effect of K-dosing in Ba_1-x K _x Fe₂As₂, which collaborates with the carrier doping effect and enhances superconductivity.

Superconductivity in FeSe: The Role of Nematic Order

Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between s-wave and d-wave pairing channels and the changes in the orbital spectral weight promoted by the sign-changing nematic order parameter. We show that nematicity only weakly affects T_{c}, but gives rise to cos2θ variation of the pairing gap on the hole pocket, whose magnitude and size agrees with angle resolved photoemission spectroscopy and STM data. We further show that nematicity increases the weight of the d_{xz} orbital on the hole pocket, and increases (reduces) the weight of the d_{xy} orbital on the Y (X) electron pocket.

Two distinct superconducting pairing states divided by the nematic end point in FeSe1-x S x

Unconventional superconductivity often competes or coexists with other electronic orders. In iron-based superconductors, a central issue has been the relationship between superconductivity and electronic nematicity, spontaneous breaking of the lattice rotational symmetry. Using spectroscopic-imaging scanning tunneling microscopy, we simultaneously investigated the electronic structure and the superconducting gap in FeSe_1-x S _x , where the nematicity diminishes above the nematic end point (NEP) at x = 0.17. The nematic band structure appears as anisotropic quasiparticle-interference patterns that gradually become isotropic with increasing x without anomalies at the NEP. By contrast, the superconducting gap, which is intact in the nematic phase, discontinuously shrinks above the NEP. This implies that the presence or absence of nematicity results in two distinct pairing states, whereas the pairing interaction is insensitive to the strength of nematicity.

Abrupt change of the superconducting gap structure at the nematic critical point in FeSe1-xSx

The emergence of the nematic electronic state that breaks rotational symmetry is one of the most fascinating properties of the iron-based superconductors, and has relevance to cuprates as well. FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering, providing a significant opportunity to investigate the role of nematicity in the superconducting pairing interaction. Here, to reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specific heat of FeSe1 - x S x , in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at [Formula: see text] We find that, in the whole nematic regime ([Formula: see text]), the field dependence of two quantities consistently shows two-gap behavior; one gap is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime ([Formula: see text]), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of [Formula: see text] and [Formula: see text] orbitals are enhanced equally in the tetragonal side, whereas they develop differently in the orthorhombic side. Our observation therefore directly implies that the orbital-dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction.

Superconducting gap anisotropy sensitive to nematic domains in FeSe

The structure of the superconducting gap in unconventional superconductors holds a key to understand the momentum-dependent pairing interactions. In superconducting FeSe, there have been controversial results reporting nodal and nodeless gap structures, raising a fundamental issue of pairing mechanisms of iron-based superconductivity. Here, by utilizing polarization-dependent laser-excited angle-resolved photoemission spectroscopy, we report a detailed momentum dependence of the gap in single- and multi-domain regions of orthorhombic FeSe crystals. We confirm that the superconducting gap has a twofold in-plane anisotropy, associated with the nematicity due to orbital ordering. In twinned regions, we clearly find finite gap minima near the vertices of the major axis of the elliptical zone-centered Fermi surface, indicating a nodeless state. In contrast, the single-domain gap drops steeply to zero in a narrow angle range, evidencing for nascent nodes. Such unusual node lifting in multi-domain regions can be explained by the nematicity-induced time-reversal symmetry breaking near the twin boundaries.

The superconducting gap structure of FeSe remains a debated issue. Here, Hashimoto et al. report momentum dependence of the gap in single- and multi-domain regions of orthorhombic FeSe crystals, revealing an unusual node lifting of the gap structure in multi-domain regions.

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, T _c, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.

Discovery of orbital-selective Cooper pairing in FeSe

The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the Γ = (0, 0) and X = (π/a_Fe, 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the d _yz orbitals of the iron atoms.

Single crystal growth, transport and scanning tunneling microscopy and spectroscopy of FeSe1−xSx

“Ampoule in ampoule” design to grow single crystals of FeSe_1−xS_x.

Effect of nematic ordering on electronic structure of FeSe

Electronically driven nematic order is often considered as an essential ingredient of high-temperature superconductivity. Its elusive nature in iron-based superconductors resulted in a controversy not only as regards its origin but also as to the degree of its influence on the electronic structure even in the simplest representative material FeSe. Here we utilized angle-resolved photoemission spectroscopy and density functional theory calculations to study the influence of the nematic order on the electronic structure of FeSe and determine its exact energy and momentum scales. Our results strongly suggest that the nematicity in FeSe is electronically driven, we resolve the recent controversy and provide the necessary quantitative experimental basis for a successful theory of superconductivity in iron-based materials which takes into account both, spin-orbit interaction and electronic nematicity.