Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe

Interface-Suppressed Nematicity and Enhanced Superconducting Pairing Strength of FeSe/NdFeO3 in the Low-Doping Regime

The discovery of interfacial superconductivity in monolayer FeSe/oxides has spurred intensive research interest. Here we not only extend the FeSe/FeOx superconducting interface to FeSe/NdFeO3 but also establish robust interface-enhanced superconductivity at a very low doping level. Specifically, well-annealed FeSe/NdFeO3 exhibits a low doping level of 0.038-0.046 e-/Fe with a larger superconducting pairing gap without a nematic gap, indicating an enhancement of the enhanced superconducting pairing strength and suppression of nematicity by the FeSe/FeOx interface compared with those of thick FeSe films. These results improve our understanding of the roles of the oxide interface in the low-electron-doped regime.

Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200  K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

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.

Spontaneous orbital polarization in the nematic phase of FeSe

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. Here we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with using X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase.

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1-xSx and FeSe1-xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe_1-xS_x and FeSe_1-xTe_x which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Charge order driven by multiple-Q spin fluctuations in heavily electron-doped iron selenide superconductors

Intertwined spin and charge orders have been widely studied in high-temperature superconductors, since their fluctuations may facilitate electron pairing; however, they are rarely identified in heavily electron-doped iron selenides. Here, using scanning tunneling microscopy, we show that when the superconductivity of (Li_0.84Fe_0.16OH)Fe_1-xSe is suppressed by introducing Fe-site defects, a short-ranged checkerboard charge order emerges, propagating along the Fe-Fe directions with an approximately 2a_Fe period. It persists throughout the whole phase space tuned by Fe-site defect density, from a defect-pinned local pattern in optimally doped samples to an extended order in samples with lower T_c or non-superconducting. Intriguingly, our simulations indicate that the charge order is likely driven by multiple-Q spin density waves originating from the spin fluctuations observed by inelastic neutron scattering. Our study proves the presence of a competing order in heavily electron-doped iron selenides, and demonstrates the potential of charge order as a tool to detect spin fluctuations.

Hall Effect Anisotropy in the Paramagnetic Phase of Ho0.8Lu0.2B12 Induced by Dynamic Charge Stripes

A detailed study of charge transport in the paramagnetic phase of the cage-cluster dodecaboride Ho0.8Lu0.2B12 with an instability both of the fcc lattice (cooperative Jahn−Teller effect) and the electronic structure (dynamic charge stripes) was carried out at temperatures 1.9−300 K in magnetic fields up to 80 kOe. Four mono-domain single crystals of Ho0.8Lu0.2B12 samples with different crystal axis orientation were investigated in order to establish the singularities of Hall effect, which develop due to (i) the electronic phase separation (stripes) and (ii) formation of the disordered cage-glass state below T*~60 K. It was demonstrated that a considerable intrinsic anisotropic positive component ρanxy appears at low temperatures in addition to the ordinary negative Hall resistivity contribution in magnetic fields above 40 kOe applied along the [001] and [110] axes. A relation between anomalous components of the resistivity tensor ρanxy~ρanxx1.7 was found for H||[001] below T*~60 K, and a power law ρanxy~ρanxx0.83 for the orientation H||[110] at temperatures T < TS~15 K. It is argued that below characteristic temperature TS~15 K the anomalous odd ρanxy(T) and even ρanxx(T) parts of the resistivity tensor may be interpreted in terms of formation of long chains in the filamentary structure of fluctuating charges (stripes). We assume that these ρanxy(H||[001]) and ρanxy(H||[110]) components represent the intrinsic (Berry phase contribution) and extrinsic (skew scattering) mechanism, respectively. Apart from them, an additional ferromagnetic contribution to both isotropic and anisotropic components in the Hall signal was registered and attributed to the effect of magnetic polarization of 5d states (ferromagnetic nano-domains) in the conduction band of Ho0.8Lu0.2B12.

Unconventional localization of electrons inside of a nematic electronic phase

Among iron-based superconductors, FeSe displays an anomalous electronic nematic state, strong electronic correlations, and orbitally dependent band shifts that can influence its superconducting pairing. Here, we report detailed magnetotransport studies of thin flakes of FeSe that reveal unconventional transport, in which the hole carriers remain highly mobile, whereas the mobility of the electron carriers is low, and weakly temperature dependent, inside the nematic phase. This suggests an unusual localization of negative charge carriers that may be caused by orbital-dependent enhanced correlations, scattering of spin fluctuations, and/or a topological electronic transition. As the superconductivity is suppressed by reducing the flake thickness, it suggests that the electron pockets participate actively in pairing. By doping, electron pockets expand, enabling high-Tc superconductivity.

The magnetotransport behavior inside the nematic phase of bulk FeSe reveals unusual multiband effects that cannot be reconciled with a simple two-band approximation proposed by surface-sensitive spectroscopic probes. In order to understand the role played by the multiband electronic structure and the degree of two-dimensionality, we have investigated the electronic properties of exfoliated flakes of FeSe by reducing their thickness. Based on magnetotransport and Hall resistivity measurements, we assess the mobility spectrum that suggests an unusual asymmetry between the mobilities of the electrons and holes, with the electron carriers becoming localized inside the nematic phase. Quantum oscillations in magnetic fields up to 38 T indicate the presence of a hole-like quasiparticle with a lighter effective mass and a quantum scattering time three times shorter, as compared with bulk FeSe. The observed localization of negative charge carriers by reducing dimensionality can be driven by orbitally dependent correlation effects, enhanced interband spin fluctuations, or a Lifshitz-like transition, which affect mainly the electron bands. The electronic localization leads to a fragile two-dimensional superconductivity in thin flakes of FeSe, in contrast to the two-dimensional high-Tc induced with electron doping via dosing or using a suitable interface.

Spin fluctuations in the 112-type iron-based superconductor Ca0.82La0.18Fe0.96Ni0.04As2

We report time-of-flight inelastic neutron scattering (INS) investigations on the spin fluctuation spectrum in the 112-type iron-based superconductor (FeSC) Ca_0.82La_0.18Fe_0.96Ni_0.04As₂(CaLa-112). In comparison to the 122-type FeSCs with a centrosymmetric tetragonal lattice structure (space groupI4/mmm) at room temperature and an in-plane stripe-type antiferromagnetic (AF) order at low temperature, the 112 system has a noncentrosymmetric structure (space groupP21) with additional zigzag arsenic chains between Ca/La layers and a magnetic ground state with similar wavevectorQAFbut different orientations of ordered moments in the parent compounds. Our INS study clearly reveals that the in-plane dispersions and the bandwidth of spin excitations in the superconducting CaLa-112 closely resemble to those in 122 systems. While the total fluctuating moments⟨m2⟩≈4.6±0.2μB2/Fe are larger than 122 system, the dynamic correlation lengths are similar (ξ ≈ 10 Å). These results suggest that superconductivity in iron arsenides may have a common magnetic origin under similar magnetic exchange couplings with a dual nature from local moments and itinerant electrons, despite their different magnetic patterns and lattice symmetries.

Suppression of Superconductivity and Nematic Order in Fe1-ySe1-xSx (0 ≤ x ≤ 1; y ≤ 0.1) Crystals by Anion Height Disorder

Connections between crystal chemistry and critical temperature T_c have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry, and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that T_c correlates with the average anion height above the Fe plane, i.e., with the geometry of the FeAs₄ or FeCh₄ (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe_1-ySe_1-xS_x (0 ≤ x ≤ 1; y ≤ 0.1), we find that in alloyed crystals T_c is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in T_c(x) and tetragonal-to-orthorhombic (nematic) transition T_s(x) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)₄ tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of T_c and T_s suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with FeSe/S building blocks.

Quasiparticle dynamics and phonon softening in FeSe0.9S0.1 superconductors

The quasiparticle and longitudinal acoustic (LA) coherent phonon dynamics of the FeSe_0.9S_0.1 single crystal were investigated by femtosecond transient optical spectroscopy. The FeSe_0.9S_0.1 single crystal undergoes metal-superconductor transition at T_c = 9.5 K and structural phase transition at T_s = 72 K. To investigate the correlation between the quasiparticle/LA coherent phonon dynamics and the antiferromagnetic spin/nematic fluctuation, we measured the transient differential reflectivity ΔR(t)/R₀ in time series (R is the reflectivity) between 4-130 K. The ΔR(t)/R₀ time series showed a negative sign below T_s = 72 K, while its sign reversed from negative to positive above T_s. The ΔR(t)/R₀ time series was contributed by a combination of two exponential decays and an oscillation term. The slow decay attributed to electron-phonon and phonon-phonon coupling showed a negative amplitude below T_s and a positive amplitude above T_s. A fast decay with positive amplitude appeared at T ≥ 55 K was induced by the electron-phonon coupling of the high-temperature orthorhombic phase FeSe_0.9S_0.1. The oscillation contributed by the LA coherent phonon emerged below T_s but was not observed above T_s, indicating that it was impacted by the nematic fluctuation of FeSe_0.9S_0.1.

Intercalated Iron Chalcogenides: Phase Separation Phenomena and Superconducting Properties

Organic molecule-intercalated layered iron-based monochalcogenides are presently the subject of intense research studies due to the linkage of their fascinating magnetic and superconducting properties to the chemical nature of guests present in the structure. Iron chalcogenides have the ability to host various organic species (i.e., solvates of alkali metals and the selected Lewis bases or long-chain alkylammonium cations) between the weakly bound inorganic layers, which opens up the possibility for fine tuning the magnetic and electrical properties of the intercalated phases by controlling both the doping level and the type/shape and orientation of the organic molecules. In recent years, significant progress has been made in the field of intercalation chemistry, expanding the gallery of intercalated superconductors with new hybrid inorganic–organic phases characterized by transition temperatures to a superconducting state as high as 46 K. A typical synthetic approach involves the low-temperature intercalation of layered precursors in the presence of liquid amines, and other methods, such as electrochemical intercalation, intercalant or ion exchange, and direct solvothermal growths from anhydrous amine-based media, are also being developed. Large organic guests, while entering a layered structure on intercalation, push off the inorganic slabs and modify the geometry of their internal building blocks (edge-sharing iron chalcogenide tetrahedrons) through chemical pressure. The chemical nature and orientation of organic molecules between the inorganic layers play an important role in structural modification and may serve as a tool for the alteration of the superconducting properties. A variety of donor species well-matched with the selected alkali metals enables the adjustment of electron doping in a host structure offering a broad range of new materials with tunable electric and magnetic properties. In this review, the main aspects of intercalation chemistry are discussed, involving the influence of the chemical and electrochemical nature of intercalating species on the crystal structure and critical issues related to the superconducting properties of the hybrid inorganic–organic phases. Mutual relations between the host and organic guests lead to a specific ordering of molecular species between the host layers, and their effect on the electronic structure of the host will be also argued. A brief description of a critical assessment of the association of the most effective chemical and electrochemical methods, which lead to the preparation of nanosized/microsized powders and single crystals of molecularly intercalated phases, with the ease of preparation of phase pure materials, crystal sizes, and the morphology of final products is given together with a discussion of the stability of the intercalated materials connected with the volatility of organic solvents and a possible degradation of host materials.

Mössbauer spectroscopy study of nematicity in Ba(Fe0.962Cu0.038)2As2single crystal: enhanced orbital effect

The origin of the nematic order remains unclear due to the strong coupling between orbital, spin and lattice degrees of freedom in iron-based superconductors. Although the driving force of hole-doped BeFe₂As₂is still controversial, the nematic fluctuation of electron-doped compounds is generally believed to be spin fluctuation driven. Here, we present a comprehensive study of the nematic phase transition in Ba(Fe_0.962Cu_0.038)₂As₂single crystal by using Mössbauer spectroscopy. The electric field gradient and its in-plane asymmetry on Fe nucleus, which are directly determined by the occupation of individualt_2gorbital, are sensitive to the local nematicity of Fe ions. The nematic phase transition happens atT_nem≈ 73.8 K in the compound while the band splitting betweend_xz/d_yzorbitals begins far aboveT_nemand reaches 18.8 meV at 30 K. The temperature evolution of the hyperfine parameters proves the existence of electron-phonon interaction and non-Fermi-liquid behaviour nearT_nem. However, the spin-lattice relaxation signal is only evident belowT_nem. These observations show that the role of orbital degrees of freedom is more active in driving nematicity than in Co- or Ni-doped BaFe₂As₂compounds, and can be attributed to enhanced electronic localization caused by Cu doping.

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.

Evolution of the Nematic Susceptibility in LaFe_{1-x}Co_{x}AsO

We report a systematic elastoresistivity study on LaFe_{1-x}Co_{x}AsO single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss-like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of LaFe_{1-x}Co_{x}AsO.

Magnetism and superconductivity in Fe1+y Te1-xSex

Neutron scattering has played a significant role in characterizing magnetic and structural correlations in Fe1+y Te1-xSexand their connections with superconductivity. Here we review several key aspects of the physics of iron chalcogenide superconductors where neutron studies played a key role. These topics include the phase diagram of Fe1+y Te1-xSex, where the doping-dependence of structural transitions can be understood from a mapping to the anisotropic random field Ising model. We then discuss orbital-selective Mott physics in the Fe chalcogenide series, where temperature-dependent magnetism in the parent material provided one of the earliest cases for orbital-selective correlation effects in a Hund's metal. Finally, we elaborate on the character of local magnetic correlations revealed by neutron scattering, its dependence on temperature and composition, and the connections to nematicity and superconductivity.

Superconductivity enhancement in FeSe/SrTiO3: a review from the perspective of electron-phonon coupling

Single-layer FeSe films grown on SrTiO3, with the highest superconducting transition temperature (TC) among all the iron-based superconductors, serves as an ideal platform for studying the microscopic mechanisms of high-TCsuperconductivity. The significant role of interfacial coupling has been widely recognized, while the precise nature of theTCenhancement remains open. In this review, we focus on the investigations of the interfacial coupling in FeSe/SrTiO3from the perspective of electron-phonon coupling (EPC). The main content will include an overview of the experimental measurements associated with different theoretical models and arguments about the EPC. Especially, besides the discussions of EPC based on the measurements of electronic states, we will emphasize the analyses based on phonon measurements. A uniform picture about the nature of the EPC and its relation to theTCenhancement in FeSe/SrTiO3has still not achieved, which should be the key for further studies aiming to the in-depth understanding of high-TCsuperconductivity and the discovery of new superconductors with even enhancedTC.

Visualization of Local Magnetic Moments Emerging from Impurities in Hund's Metal States of FeSe

Understanding the origin of the magnetism of high temperature superconductors is crucial for establishing their unconventional pairing mechanism. Recently, theory predicts that FeSe is close to a magnetic quantum critical point, and thus weak perturbations such as impurities could induce local magnetic moments. To elucidate such quantum instability, we have employed scanning tunneling microscopy and spectroscopy. In particular, we have grown FeSe film on superconducting Pb(111) using molecular beam epitaxy and investigated magnetic excitation caused by impurities in the proximity-induced superconducting gap of FeSe. Our study provides deep insight into the origin of the magnetic ordering of FeSe by showing the way local magnetic moments develop in response to impurities near the magnetic quantum critical point.

Long-range magnetic order in hydroxide-layer-doped (Li1-x-y Fe x Mn y OD)FeSe

The (Li1-x Fe x OH)FeSe superconductor has been suspected of exhibiting long-range magnetic ordering due to Fe substitution in the LiOH layer. However, no direct observation such as magnetic reflection from neutron diffraction has been reported. Here, we use a chemical design strategy to manipulate the doping level of transition metals in the LiOH layer to tune the magnetic properties of the (Li1-x-y Fe x Mn y OD)FeSe system. We find Mn doping exclusively replaces Li in the hydroxide layer resulting in enhanced magnetization in the (Li0.876Fe0.062Mn0.062OD)FeSe superconductor without significantly altering the superconducting behavior as resolved by magnetic susceptibility and electrical/thermal transport measurements. As a result, long-range magnetic ordering was observed below 12 K with neutron diffraction measurements. This work has implications for the design of magnetic superconductors for the fundamental understanding of superconductivity and magnetism in the iron chalcogenide system as well as exploitation as functional materials for next-generation devices.

Anisotropic effect of a magnetic field on the neutron spin resonance in FeSe

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (E r = 3.6 meV) of superconducting FeSe (T c = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasiparticle excitations between the hole and electron Fermi surfaces.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Correlation at two-dimensional charge-transfer FeSe interface

The charge transfer and spin coupling effects are explored at the interface of two-dimensional (2D) superconducting FeSe nanosheets and molecular photochromic potassium-7,7,8,8-tetracyanoquinodimethane (KTCNQ). Light-induced conductivity in 2D FeSe nanosheets is enhanced by the electron doping from KTCNQ by the destabilized spin-Peierls phase through their interface. Furthermore, the spin coupling at the interface of FeSe and KTCNQ shifts the dimerization transition temperature of KTCNQ. Our results suggest 2D exfoliated FeSe nanosheets as a versatile strongly correlated platform for the study of interfacial electron doping and spin coupling.

Anisotropic spin fluctuations in detwinned FeSe

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

Coexistence of Ferromagnetic and Stripe-Type Antiferromagnetic Spin Fluctuations in YFe_{2}Ge_{2}

We report neutron scattering measurements of single-crystalline YFe_{2}Ge_{2} in the normal state, which has the same crystal structure as the 122 family of iron pnictide superconductors. YFe_{2}Ge_{2} does not exhibit long-range magnetic order but exhibits strong spin fluctuations. Like the iron pnictides, YFe_{2}Ge_{2} displays anisotropic stripe-type antiferromagnetic spin fluctuations at (π, 0, π). More interesting, however, is the observation of strong spin fluctuations at the in-plane ferromagnetic wave vector (0, 0, π). These ferromagnetic spin fluctuations are isotropic in the (H, K) plane, whose intensity exceeds that of stripe spin fluctuations. Both the ferromagnetic and stripe spin fluctuations remain gapless down to the lowest measured energies. Our results naturally explain the absence of magnetic order in YFe_{2}Ge_{2} and also imply that the ferromagnetic correlations may be a key ingredient for iron-based materials.

Intertwined Magnetic and Nematic Orders in Semiconducting KFe_{0.8}Ag_{1.2}Te_{2}

Superconductivity in the iron pnictides emerges from metallic parent compounds exhibiting intertwined stripe-type magnetic order and nematic order, with itinerant electrons suggested to be essential for both. Here we use x-ray and neutron scattering to show that a similar intertwined state is realized in semiconducting KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}) without itinerant electrons. We find that Fe atoms in KFe_{0.8}Ag_{1.2}Te_{2} form isolated 2×2 blocks, separated by nonmagnetic Ag atoms. Long-range magnetic order sets in below T_{N}≈35  K, with magnetic moments within the 2×2 Fe blocks ordering into the stripe-type configuration. A nematic order accompanies the magnetic transition, manifest as a structural distortion that breaks the fourfold rotational symmetry of the lattice. The nematic orders in KFe_{0.8}Ag_{1.2}Te_{2} and iron pnictide parent compounds are similar in magnitude and in how they relate to the magnetic order, indicating a common origin. Since KFe_{0.8}Ag_{1.2}Te_{2} is a semiconductor without itinerant electrons, this indicates that local-moment magnetic interactions are integral to its magnetic and nematic orders, and such interactions may play a key role in iron-based superconductivity.

Observation of dynamic charge stripes in Tm0.19Yb0.81B12 at the metal-insulator transition

Accurate low temperature charge transport measurements in combination with high-precision x-ray diffraction experiments have allowed detection of the symmetry lowering in the single domain Tm_0.19Yb_0.81B₁₂ crystals that belong to the family of dodecaborides with metal-insulator transition. Based on the fine structure analysis we discover the formation of dynamic charge stripes within the semiconducting matrix of Tm_0.19Yb_0.81B₁₂. The charge dynamics in these conducting nano-size channels is characterized by broad-band optical spectroscopy that allowed estimating the frequency (~2.4 × 10¹¹ Hz) of quantum motion of the charge carriers. It is suggested that cooperative Jahn-Teller effect in the boron sublattice is a cause of the large-amplitude rattling modes of the Tm and Yb ions responsible for the 'modulation' of the conduction band along one of the [Formula: see text] directions through the variation of 5d-2p hybridization of electron states.

Quantum Spin Liquid Intertwining Nematic and Superconducting Order in Fese

Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting superconducting order parameter to be nodeless s±d wave within each domain. Further we show that orbital dependent Kondo-like coupling can readily capture observed gap anisotropy. Our prediction calls for inelastic neutron scattering in a detwinned sample.

Resonance states near a quantum magnetic impurity in single-layer FeSe superconductors with d-wave symmetry

In this work, we investigate the local density of states (LDOS) near a magnetic impurity in single-layer FeSe superconductors. The two-orbital model with spin-orbit coupling proposed in Agterberg et al (2017 Phys. Rev. Lett. 119 267001) is used to describe the FeSe superconductor. In the strong coupling regime, two impurity resonance peaks appear with opposite resonance energies in the LDOS spectral function. For strong spin-orbit coupling, the superconducting gap in this model is d-wave symmetric with nodes, the spatial distributions of the LDOS at the two resonance energies are fourfold symmetric, which reveals typical characteristic of d-wave pairing. When the spin-orbit coupling is not strong enough to close the superconducting gap, we find that the spatial distribution of the LDOS at one of the resonance energies manifests s-wave symmetry, while the pairing potential preserves d-wave symmetry. This result is consistent with previous experimental investigations.

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.

Odd and Even Modes of Neutron Spin Resonance in the Bilayer Iron-Based Superconductor CaKFe_{4}As_{4}

We report an inelastic neutron scattering study on the spin resonance in the bilayer iron-based superconductor CaKFe_{4}As_{4}. In contrast to its quasi-two-dimensional electron structure, three strongly L-dependent modes of spin resonance are found below T_{c}=35  K. The mode energies are below and linearly scale with the total superconducting gaps summed on the nesting hole and electron pockets, essentially in agreement with the results in cuprate and heavy fermion superconductors. This observation supports the sign-reversed Cooper pairing mechanism under multiple pairing channels and resolves the long-standing puzzles concerning the broadening and dispersive spin resonance peak in iron pnictides. More importantly, the triple resonant modes can be classified into odd and even symmetries with respect to the distance of Fe-Fe planes within the Fe-As bilayer unit. Thus, our results closely resemble those in the bilayer cuprates with nondegenerate spin excitations, suggesting that these two high-T_{c} superconducting families share a common nature.

Superconducting selenides intercalated with organic molecules: synthesis, crystal structure, electric and magnetic properties, superconducting properties, and phase separation in iron based-chalcogenides and hybrid organic-inorganic superconductors

Layered iron-based superconducting chalcogenides intercalated with molecular species are the subject of intensive studies, especially in the field of solid state chemistry and condensed matter physics, because of their intriguing chemistry and tunable electric and magnetic properties. Considerable progress in the research, revealing superconducting inorganic-organic hybrid materials with transition temperatures to superconducting state, T _c, up to 46 K, has been brought in recent years. These novel materials are synthesized by low-temperature intercalation of molecular species, such as solvates of alkali metals and nitrogen-containing donor compounds, into layered FeSe-type structure. Both the chemical nature as well as orientation of organic molecules between the layers of inorganic host, play an important role in structural modifications and may be used for fine tuning of superconducting properties. Furthermore, a variety of donor species compatible with alkali metals, as well as the possibility of doping also in the host structure (either on Fe or Se sites), makes this system quite flexible and gives a vast array of new materials with tunable electric and magnetic properties. In this review, the main aspects of intercalation chemistry are discussed with a particular attention paid to the influence of the unique nature of intercalating species on the crystal structure and physical properties of the hybrid inorganic-organic materials. To get a full picture of these materials, a comprehensive description of the most effective chemical and electrochemical methods, utilized for synthesis of intercalated species, with critical evaluation of their strong and weak points, related to feasibility of synthesis, phase purity, crystal size and morphology of final products, is included as well.

A novel metastable state magnetic phase of monolayer FeSe

We found a novel metastable magnetic phase by systematically calculating total energy of monolayer FeSe in various antiferromagnetic (AFM) orders using first-principles method. The new metastable magnetic phase named as QAFM is a magnetic state with short-range magnetic structure which can be regarded as a transitional state between checkerboard-like AFM state and collinear AFM state. Both magnetic moments with important fluctuation and charge density difference with a 2  ×  4 reconstruction of orbitals breaks C ₄ symmetry and possibly commonly corresponds to the nematic phase in recent transmission electron microscopy and neutron scattering experiment observations. Its electronic band displays a Dirac-like band structure along Γ-X in the folding Brillouin zone of the supercell. The QAFM phase of FeSe holds metallic feature with d _xz , d _yz and [Formula: see text] band crossing Fermi level even including spin-orbit coupling. Additionally, the weight of 3d orbitals varies as the applied expansion strain which may be directly correlated with the emerging nematic phase and superconducting state of strained monolayer FeSe. The finding of novel magnetic order may provide important clues to elucidate the relationship of antiferromagnetism and superconductivity for unconventional Fe-based superconductor.

Neutron Spin Resonance in the 112-Type Iron-Based Superconductor

We use inelastic neutron scattering to study the low-energy spin excitations of the 112-type iron pnictide Ca_{0.82}La_{0.18}Fe_{0.96}Ni_{0.04}As_{2} with bulk superconductivity below T_{c}=22  K. A two-dimensional spin resonance mode is found around E=11  meV, where the resonance energy is almost temperature independent and linearly scales with T_{c} along with other iron-based superconductors. Polarized neutron analysis reveals the resonance is nearly isotropic in spin space without any L modulations. Because of the unique monoclinic structure with additional zigzag arsenic chains, the As 4p orbitals contribute to a three-dimensional hole pocket around the Γ point and an extra electron pocket at the X point. Our results suggest that the energy and momentum distribution of the spin resonance does not directly respond to the k_{z} dependence of the fermiology, and the spin resonance intrinsically is a spin-1 mode from singlet-triplet excitations of the Cooper pairs in the case of weak spin-orbital coupling.

Antiferromagnetic Order in Epitaxial FeSe Films on SrTiO_{3}

Single monolayer FeSe film grown on a Nb-doped SrTiO_{3}(001) substrate shows the highest superconducting transition temperature (T_{C}∼100  K) among the iron-based superconductors (iron pnictides), while the T_{C} value of bulk FeSe is only ∼8  K. Although bulk FeSe does not show antiferromagnetic order, calculations suggest that the parent FeSe/SrTiO_{3} films are antiferromagnetic. Experimentally, because of a lack of a direct probe, the magnetic state of FeSe/SrTiO_{3} films remains mysterious. Here, we report direct evidence of antiferromagnetic order in the parent FeSe/SrTiO_{3} films by the magnetic exchange bias effect measurements. The magnetic blocking temperature is ∼140  K for a single monolayer film. The antiferromagnetic order disappears after electron doping.

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.

Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser

The interactions that lead to the emergence of superconductivity in iron-based materials remain a subject of debate. It has been suggested that electron-electron correlations enhance electron-phonon coupling in iron selenide (FeSe) and related pnictides, but direct experimental verification has been lacking. Here we show that the electron-phonon coupling strength in FeSe can be quantified by combining two time-domain experiments into a "coherent lock-in" measurement in the terahertz regime. X-ray diffraction tracks the light-induced femtosecond coherent lattice motion at a single phonon frequency, and photoemission monitors the subsequent coherent changes in the electronic band structure. Comparison with theory reveals a strong enhancement of the coupling strength in FeSe owing to correlation effects. Given that the electron-phonon coupling affects superconductivity exponentially, this enhancement highlights the importance of the cooperative interplay between electron-electron and electron-phonon interactions.

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.

Structure of spin excitations in heavily electron-doped Li0.8Fe0.2ODFeSe superconductors

Heavily electron-doped iron-selenide high-transition-temperature (high-T_c) superconductors, which have no hole Fermi pockets, but have a notably high T_c, have challenged the prevailing s_± pairing scenario originally proposed for iron pnictides containing both electron and hole pockets. The microscopic mechanism underlying the enhanced superconductivity in heavily electron-doped iron-selenide remains unclear. Here, we used neutron scattering to study the spin excitations of the heavily electron-doped iron-selenide material Li_0.8Fe_0.2ODFeSe (T_c = 41 K). Our data revealed nearly ring-shaped magnetic resonant excitations surrounding (π, π) at ∼21 meV. As the energy increased, the spin excitations assumed a diamond shape, and they dispersed outward until the energy reached ∼60 meV and then inward at higher energies. The observed energy-dependent momentum structure and twisted dispersion of spin excitations near (π, π) are analogous to those of hole-doped cuprates in several aspects, thus implying that such spin excitations are essential for the remarkably high T_c in these materials.

The microscopic mechanism underlying an enhanced superconductivity in electron-doped iron selenide superconductor remains unclear. Here, Pan et al. report the spin excitations of Li_0.8Fe_0.2ODFeSe, revealing analogous momentum structure and dispersion to hole-doped cuprates.

Antiferroquadrupolar Order and Rotational Symmetry Breaking in a Generalized Bilinear-Biquadratic Model on a Square Lattice

The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an S=1 generalized bilinear-biquadratic model with multineighbor interactions. We find a large parameter regime for a (π, 0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C_{4}-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis. We discuss the implications of our results for FeSe and related iron-based superconductors.

Effect of Nematic Order on the Low-Energy Spin Fluctuations in Detwinned BaFe_{1.935}Ni_{0.065}As_{2}

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

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

FeSe exhibits a novel ground state in which superconductivity coexists with a nematic order in the absence of any long-range magnetic order. Here, we report on an angle-resolved photoemission study on the superconducting gap structure in the nematic state of FeSe_{0.93}S_{0.07}, without the complications caused by Fermi surface reconstruction induced by magnetic order. We find that the superconducting gap shows a pronounced twofold anisotropy around the elliptical hole pocket near Z (0, 0, π), with gap minima at the end points of its major axis, while no detectable gap is observed around Γ (0, 0, 0) and the zone corner (π, π, k_{z}). The large anisotropy and nodal gap distribution demonstrate the substantial effects of the nematicity on the superconductivity and thus put strong constraints on current theories.

Charge-induced nematicity in FeSe

The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing properties of the iron-based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains a challenge, however, because their associated susceptibilities are not easily accessible by conventional probes. Here, using FeSe as a model system, and symmetry-resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural/nematic transition temperature, [Formula: see text] 90 K. The diverging behavior of the associated nematic susceptibility foretells the presence of a Pomeranchuk instability of the Fermi surface with d-wave symmetry. The excellent scaling between the observed nematic susceptibility and elastic modulus data demonstrates that the structural distortion is driven by this d-wave Pomeranchuk transition. Our results make a strong case for charge-induced nematicity in FeSe.

Magnetic ground state of FeSe

Elucidating the nature of the magnetism of a high-temperature superconductor is crucial for establishing its pairing mechanism. The parent compounds of the cuprate and iron-pnictide superconductors exhibit Néel and stripe magnetic order, respectively. However, FeSe, the structurally simplest iron-based superconductor, shows nematic order (T_s=90 K), but not magnetic order in the parent phase, and its magnetic ground state is intensely debated. Here we report inelastic neutron-scattering experiments that reveal both stripe and Néel spin fluctuations over a wide energy range at 110 K. On entering the nematic phase, a substantial amount of spectral weight is transferred from the Néel to the stripe spin fluctuations. Moreover, the total fluctuating magnetic moment of FeSe is ∼60% larger than that in the iron pnictide BaFe₂As₂. Our results suggest that FeSe is a novel S=1 nematic quantum-disordered paramagnet interpolating between the Néel and stripe magnetic instabilities.

Different ground states of high-temperature superconductors reveal complex nature of magnetism. Here, Wang et al. report stripe and Néel spin fluctuations coexisting with non-magnetic nematic phase in FeSe, providing a viewpoint towards understanding the magnetism of cuprate and iron-based superconductors.

Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe

The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.

Spin Ferroquadrupolar Order in the Nematic Phase of FeSe

We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of the FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitatively consistent result with inelastic neutron scattering experiments on FeSe at both low and high energies. We verify that FQ can coexist with C_{4} breaking environments in the mean-field calculation, and further discuss the possibility that quantum fluctuations in FQ act as a source of nematicity.

Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the C_{2} Symmetry Breaking in the Self-Energy

To understand the nematicity in Fe-based superconductors, nontrivial k dependence of the orbital polarization [ΔE_{xz}(k), ΔE_{yz}(k)] in the nematic phase, such as the sign reversal of the orbital splitting between Γ and X, Y points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole and electron pockets are elongated along the k_{y} and k_{x} axes, respectively, consistently with experiments. In addition, an electron pocket splits into two Dirac cone Fermi pockets while increasing the orbital polarization. The orbital order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility.

Ultrafast Dynamics Evidence of High Temperature Superconductivity in Single Unit Cell FeSe on SrTiO_{3}

We report the time-resolved excited state ultrafast dynamics of single unit cell (1 UC) thick FeSe films on SrTiO_{3} (STO), with FeTe capping layers. By measuring the photoexcited quasiparticles' density and lifetime, we unambiguously identify a superconducting (SC) phase transition, with a transition temperature T_{c} of 68 (-5/+2)  K and a SC gap of Δ(0)=20.2±1.5  meV. The obtained electron-phonon coupling strength λ is as large as 0.48, demonstrating the likely crucial role of electron-phonon coupling in the high temperature superconductivity of the 1 UC FeSe on STO systems. We further find a 0.05 THz coherent acoustic phonon branch in the capping layer, which provides an additional decay channel to the gluing bosons.