Common electronic origin of superconductivity in (Li,Fe)OHFeSe bulk superconductor and single-layer FeSe/SrTiO3 films

Advancing Superconductivity with Interface Engineering

The development of superconducting materials has attracted significant attention not only for their improved performance, such as high transition temperature (TC), but also for the exploration of their underlying physical mechanisms. Recently, considerable efforts have been focused on interfaces of materials, a distinct category capable of inducing superconductivity at non-superconducting material interfaces or augmenting the TC at the interface between a superconducting material and a non-superconducting material. Here, two distinct types of interfaces along with their unique characteristics are reviewed: interfacial superconductivity and interface-enhanced superconductivity, with a focus on the crucial factors and potential mechanisms responsible for enhancing superconducting performance. A series of materials systems is discussed, encompassing both historical developments and recent progress from the perspectives of technical innovations and the exploration of new material classes. The overarching goal is to illuminate pathways toward achieving high TC, expanding the potential of superconducting parameters across interfaces, and propelling superconductivity research toward practical, high-temperature applications.

Phase Shift and Magnetic Anisotropy Induced Field Splitting of Impurity States in (Li_{1-x}Fe_{x})OHFeSe Superconductor

Revealing the energy and spatial characteristics of impurity-induced states in superconductors is essential for understanding their mechanism and fabricating a new quantum state by manipulating impurities. Here, by using high-resolution scanning tunneling microscopy and spectroscopy, we investigate the spatial distribution and magnetic field response of the impurity states in (Li_{1-x}Fe_{x})OHFeSe. We detect two pairs of strong in-gap states on the "dumbbell-shaped" defects. They display damped oscillations with different phase shifts and a direct phase-energy correlation. These features have long been predicted for the classical Yu-Shiba-Rusinov (YSR) state and are demonstrated here with unprecedented resolution for the first time. Moreover, upon applying magnetic field, all in-gap state peaks remarkably split into two rather than shift, and the splitting strength is field orientation dependent. Via detailed numerical model calculations, we find such an anisotropic splitting behavior can be naturally induced by a high-spin impurity coupled to an anisotropic environment, highlighting how magnetic anisotropy affects the behavior of YSR states.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

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.

Prediction ofπ-electrons mediated high-temperature superconductivity in monolayer LiC12

Prediction and synthesis of two-dimensional high transition temperature (T_C) superconductors is an area of extensive research. Based on calculations of the electronic structures and lattice dynamics, we predict that graphene-like layered monolayer LiC₁₂is aπ-electrons mediated Bardeen-Cooper-Schrieffer-type superconductor. Monolayer LiC₁₂is theoretically stable and expected to be synthesized experimentally. From the band structures and the phonon dispersion spectrum, it is found that the saddle point ofπ-bonding bands induces large density of states at the Fermi energy level. There is strongly coupled between the vibration mode in the in-plane direction of the lithium atoms and theπ-electrons of carbon atoms, which induces the high-T_Csuperconductivity in LiC₁₂. TheT_Ccan reach to 41 K under an applied 10% biaxial tensile strain based on the anisotropic Eliashberg equation. Our results show that monolayer LiC₁₂is a good candidate asπ-electrons mediated electron-phonon coupling high-T_Csuperconductor.

Lix(C5H5N)yFe2-zSe2: A Defect-Resilient Expanded-Lattice High-Temperature Superconductor

Two-dimensional iron chalcogenide intercalates display a remarkable correlation of the interlayer spacing with enhancement of the superconducting critical temperature (T_c). In this work, synchrotron X-ray absorption (XAS; at the Fe and Se K-edges) and emission (XES; at the Fe Κβ) spectroscopies allow one to discuss how the important rise of T_c (∼44 K) in the molecule-intercalated Li_x(C₅H₅N)_yFe_2-zSe₂ relates to the electronic and local structural changes felt by the inorganic host upon doping (x). XES shows that widely separated layers of edge-sharing FeSe₄ tetrahedra carry low-spin moieties, with a local Fe magnetic moment slightly reduced compared to the parent β-Fe_2-zSe₂. Pre-edge XAS expresses the progressively reduced mixing of metal 3d-4p states upon lithiation. Doping-mediated local lattice modifications, probed by conventional T_c optimization measures (cf. the anion height and FeSe₄ tetrahedra regularity), become less relevant when layers are spaced far away. On the basis of extended X-ray absorption fine structure, such distortions are compensated by a softer Fe network that relates to Fe-site vacancies, alleviating electron-lattice correlations and superconductivity. Density functional theory (DFT) guided modification of the isolated Fe_2-zSe₂ (z, vacant sites) planes, resembling the host layers, identify that Fe-site deficiency occurs at low energy cost, giving rise to stretched Fe sheets, in accordance with experiments. The robust high-T_c in Li_x(C₅H₅N)_yFe_2-zSe₂, arises from the interplay of electron-donating spacers and the iron selenide layer's tolerance to defect chemistry, a tool to favorably tune its Fermi surface properties.

Band Structure of Organic-Ion-Intercalated (EMIM)xFeSe Superconductor

The band structure and the Fermi surface of the recently discovered superconductor (EMIM)xFeSe are studied within the density functional theory in the generalized gradient approximation. We show that the bands near the Fermi level are formed primarily by Fe-d orbitals. Although there is no direct contribution of EMIM orbitals to the near-Fermi level states, the presence of organic cations leads to a shift of the chemical potential. It results in the appearance of small electron pockets in the quasi-two-dimensional Fermi surface of (EMIM)xFeSe.

Research Progress of FeSe-based Superconductors Containing Ammonia/Organic Molecules Intercalation

As an important part of Fe-based superconductors, FeSe-based superconductors have become a hot field in condensed matter physics. The exploration and preparation of such superconducting materials form the basis of studying their physical properties. With the help of various alkali/alkaline-earth/rare-earth metals, different kinds of ammonia/organic molecules have been intercalated into the FeSe layer to form a large number of FeSe-based superconductors with diverse structures and different layer spacing. Metal cations can effectively provide carriers to the superconducting FeSe layer, thus significantly increasing the superconducting transition temperature. The orientation of organic molecules often plays an important role in structural modification and can be used to fine-tune superconductivity. This review introduces the crystal structures and superconducting properties of several typical FeSe-based superconductors containing ammonia/organic molecules intercalation discovered in recent years, and the effects of FeSe layer spacing and superconducting transition temperature are briefly summarized.

Polarized neutron scattering studies of magnetic excitations in iron-selenide superconductor Li0.8Fe0.2ODFeSe (Tc41 K)

We report polarized neutron scattering measurements of the low energy spin fluctuations of the iron-selenide superconductor Li_0.8Fe_0.2ODFeSe below and above its superconducting transition temperatureT_c= 41 K. Our experiments confirmed that the resonance mode near 21 meV is magnetic. Moreover, the spin excitations are essentially isotropic in spin space at 5 ⩽E⩽ 29 meV in the superconducting and normal states. Our results suggest that the resonance mode in iron-based superconductors becomes isotropic when the influence of spin-orbit coupling and magnetic/nematic order is minimized, similar to those observed in cuprate superconductors.

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.

NaOH-Intercalated Iron Chalcogenides (Na1-xOH)Fe1-yX (X = Se, S): Ion-Exchange Synthesis and Physical Properties

The discovery of the (Li_1-xFe_xOH)FeSe superconductor has aroused significant interest in metal hydroxide-intercalated iron chalcogenides. However, all efforts made to intercalate NaOH between FeSe and FeS layers have failed so far. Here we report two NaOH-intercalated iron chalcogenides (Na_1-xOH)Fe_1-yX (X = Se, S) that were synthesized by a low-temperature hydrothermal ion-exchange method. Their crystal structures were solved through single-crystal X-ray diffraction and refined against powder X-ray and neutron diffraction data. Different from the (Li_1-xFe_xOH)FeX superconductors that crystallize in a tetragonal space group P4/nmm with Z = 2, (Na_1-xOH)Fe_1-yX belong to an orthorhombic space group Cmma with Z = 4. The structural solution also reveals that there are vacancies in both Na and Fe sites and there are not iron ions in the (Na_1-xOH) layer. This is probably why both Fe(II) and Fe(III) species exist in the title compounds, as detected by X-ray photoelectron spectroscopy. Based on magnetization and electrical resistivity measurements, the two compounds were found to be paramagnetic semiconductors. The absence of superconductivity should be closely related to the iron vacancies in the Fe_1-yX layer. Theoretical calculations suggest that inducing superconductivity in (Na_1-xOH)Fe_1-ySe is promising due to the similarity of the electronic structures between stoichiometric (NaOH)FeSe and the (Li_1-xFe_xOH)FeSe superconductor.

Spectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/SrTiO3 films

Single-layer FeSe films grown on the SrTiO₃ substrate (FeSe/STO) have attracted much attention because of their possible record-high superconducting critical temperature (T_c) and distinct electronic structures. However, it has been under debate on how high its T_c can really reach due to the inconsistency of the results from different measurements. Here we report spectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/STO films. By preparing high-quality single-layer FeSe/STO films, we observe strong superconductivity-induced Bogoliubov back-bending bands that extend to rather high binding energy ~ 100 meV by high-resolution angle-resolved photoemission measurements. They provide a new definitive benchmark of superconductivity pairing that is directly observed up to 83 K. Moreover, we find that the pairing state can be further divided into two temperature regions. These results indicate that either T_c as high as 83 K is achievable, or there is a pseudogap formation from superconductivity fluctuation in single-layer FeSe/STO films.

How high the superconducting transition temperature can reach in single layer FeSe/SrTiO₃ films has been under debate. Here, the authors use Bogoliubov back-bending bands as a benchmark and demonstrate that superconductivity pairing can be realized up to 83 K in this system.

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

Observation of Distinct Spatial Distributions of the Zero and Nonzero Energy Vortex Modes in (Li_{0.84}Fe_{0.16})OHFeSe

The energy and spatial distributions of vortex bound state in superconductors carry important information about superconducting pairing and the electronic structure. Although discrete vortex states, and sometimes a zero energy mode, had been observed in several iron-based superconductors, their spatial properties are rarely explored. In this study, we used low-temperature scanning tunneling microscopy to measure the vortex state of (Li,Fe)OHFeSe with high spatial resolution. We found that the nonzero energy states display clear spatial oscillations with a period corresponding to bulk Fermi wavelength; while in contrast, the zero energy mode does not show such oscillation, which suggests its distinct electronic origin. Furthermore, the oscillations of positive and negative energy states near E_{F} are found to be clearly out of phase. Based on a two-band model calculation, we show that our observation is more consistent with an s_{++} wave pairing in the bulk of (Li, Fe)OHFeSe, and superconducting topological states on the surface.

Raman Study of Cooper Pairing Instabilities in (Li_{1-x}Fe_{x})OHFeSe

We studied the electronic Raman spectra of (Li_{1-x}Fe_{x})OHFeSe as a function of light polarization and temperature. In the B_{1g} spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T_{c}. The nearly resolution-limited peak at 110  cm^{-1} (13.6 meV) is identified as a collective mode. The peak at 190  cm^{-1} (23.6 meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band structure of (Li_{1-x}Fe_{x})OHFeSe, the most plausible explanations include conventional spin-fluctuation pairing between the electron bands and the incipient hole band and pairing between the hybridized electron bands. The absence of gap features in A_{1g} and B_{2g} symmetry favors the second case. Thus, in spite of various differences between the pnictides and chalcogenides, this Letter demonstrates the proximity of pairing states and the importance of band structure effects in the Fe-based compounds.

Preformed Cooper Pairs in Layered FeSe-Based Superconductors

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60  K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.

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.

Reversible Superconductor-Insulator Transition in (Li, Fe)OHFeSe Flakes Visualized by Gate-Tunable Scanning Tunneling Spectroscopy

Electric field control of charge carrier density provides a key in situ technology to continuously tune the ground states and map out the phase diagram of correlated electron systems in one device. This technique is highly expected to be combined with the modern state-of-the art spectroscopic probes, such as angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy (STM/S), to efficiently address these states and the underlying physics. However, it is extremely difficult and not successful so far, mainly because the fabrication process of such devices makes them prohibitive for surface probes. Here, by using a solid Li-ion conductor (SIC) as gate dielectric, we have successfully developed gate-tunable STM/S and visualized the superconductor-insulator transition (SIT) in a thin flake of single crystal (Li, Fe)OHFeSe at the nanoscale. The gate-controlled Li-ion injection first enhances the superconductivity and then drives the flake into an inhomogeneous insulating state, where superconductivity is totally suppressed. This process can be reversed by applying an opposite gate voltage. Importantly, the atomically resolved images allow us to identify the critical role that the injected Li ions play in the tuning process. Our results not only provide clear evidence of the microscopic mechanism of the tunable superconductivity and SIT in the SIC-based (Li, Fe)OHFeSe devices, but also establish SIC-gating STM as a powerful tool for investigating the complicated phase diagram of correlated electron system spectroscopically in a single sample with the field-effect approach.

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.

Diamagnetic Response of Potassium-Adsorbed Multilayer FeSe Film

Intrigued by the discovery of high-temperature superconductivity in a single unit-cell layer of FeSe film on SrTiO_{3}, researchers recently found large superconductinglike energy gaps in K-adsorbed multilayer FeSe films by angle-resolved photoemission and scanning tunneling spectroscopy. However, the existence and nature of the high-temperature superconductivity inferred by the spectroscopic studies has not been investigated by measurements of zero resistance or the Meissner effect due to the fragility of K atoms in air. Using a self-developed multifunctional scanning tunneling microscope, we succeed in observing the diamagnetic response of K-adsorbed multilayer FeSe films, and thus find a dome-shaped relation between the critical temperature (T_{c}) and K coverage. Intriguingly, T_{c} exhibits an approximately linear dependence on the superfluid density in the whole K adsorbed region. Moreover, the quadratic low-temperature variation in the London penetration depth indicates a sign-reversal order parameter. These results provide compelling information towards further understanding of the high-temperature superconductivity in FeSe-derived superconductors.

Highly-Tunable Crystal Structure and Physical Properties in FeSe-Based Superconductors

Here, crystal structure, electronic structure, chemical substitution, pressure-dependent superconductivity, and thickness-dependent properties in FeSe-based superconductors are systemically reviewed. First, the superconductivity versus chemical substitution is reviewed, where the doping at Fe or Se sites induces different effects on the superconducting critical temperature (Tc). Meanwhile, the application of high pressure is extremely effective in enhancing Tc and simultaneously induces magnetism. Second, the intercalated-FeSe superconductors exhibit higher Tc from 30 to 46 K. Such an enhancement is mainly caused by the charge transfer from the intercalated organic and inorganic layer. Finally, the highest Tc emerging in single-unit-cell FeSe on the SrTiO3 substrate is discussed, where electron-phonon coupling between FeSe and the substrate could enhance Tc to as high as 65 K or 100 K. The step-wise increment of Tc indicates that the synergic effect of carrier doping and electron-phonon coupling plays a critical role in tuning the electronic structure and superconductivity in FeSe-based superconductors.

Synergetic Behavior in 2D Layered Material/Complex Oxide Heterostructures

The marriage between a 2D layered material (2DLM) and a complex transition metal oxide (TMO) results in a variety of physical and chemical phenomena that cannot be achieved in either material alone. Interesting recent discoveries in systems such as graphene/SrTiO₃ , graphene/LaAlO₃ /SrTiO₃ , graphene/ferroelectric oxide, MoS₂ /SrTiO₃ , and FeSe/SrTiO₃ heterostructures include voltage scaling in field-effect transistors, charge state coupling across an interface, quantum conductance probing of the electrochemical activity, novel memory functions based on charge traps, and greatly enhanced superconductivity. In this context, various properties and functionalities appearing in numerous different 2DLM/TMO heterostructure systems are reviewed. The results imply that the multidimensional heterostructure approach based on the disparate material systems leads to an entirely new platform for the study of condensed matter physics and materials science. The heterostructures are also highly relevant technologically as each constituent material is a promising candidate for next-generation optoelectronic devices.

Detection of Bosonic Mode as a Signature of Magnetic Excitation in One-Unit-Cell FeSe on SrTiO3

A "fingerprint" of Cooper pairing mediated by collective bosonic excitation mode is the reconstruction of the quasiparticle-density-of-states (DOS) spectrum with an additional "dip-hump" structure located outside the superconducting coherence peak. Here, we report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on a SrTiO₃(001) substrate. In the quasiparticle-DOS spectrum, the bosonic excitation mode characterized by the dip-hump structure is detected outside the larger superconducting gap. Statistically, the excitation mode shows an anticorrelation with pairing strength in magnitude and yields an energy scale upper-bounded by twice the superconducting gap. The observation coincides with the characteristics of magnetic resonance in cuprates and iron-based superconductors. Furthermore, the local response of superconducting spectra to magnetically distinct Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing over the Fermi surface in 1-UC FeSe. These results clarify the magnetic nature of the bosonic excitation mode and reveal a signature of electron-magnetic-excitation coupling in 1-UC FeSe/SrTiO₃(001) besides the previously established pairing channel of electron-phonon interaction.

Particle–Hole Transformation in Strongly-Doped Iron-Based Superconductors

An exact particle–hole transformation is discovered in a local-moment model for a single layer of heavily electron-doped FeSe. The model harbors hidden magnetic order between the iron d x z and d y z orbitals at the wavenumber ( π , π ) . It potentially is tied to the magnetic resonances about the very same Néel ordering vector that have been recently discovered in intercalated FeSe. Upon electron doping, the local-moment model successfully accounts for the electron-pocket Fermi surfaces observed experimentally at the corner of the two-iron Brillouin zone in electron-doped FeSe, as well as for isotropic Cooper pairs. Application of the particle–hole transformation predicts a surface-layer iron-based superconductor at strong hole doping that exhibits high T c, and that shows hole-type Fermi-surface pockets at the center of the two-iron Brillouin zone.

Enhanced Superconducting State in FeSe/SrTiO_{3} by a Dynamic Interfacial Polaron Mechanism

The observation of substantially enhanced superconductivity of single-layer FeSe films on SrTiO_{3} has stimulated intensive research interest. At present, conclusive experimental data on the corresponding electron-boson interaction is still missing. Here we use inelastic electron scattering spectroscopy and angle resolved photoemission spectroscopy to show that the electrons in these systems are dressed by the strongly polarized lattice distortions of the SrTiO_{3}, and the indispensable nonadiabatic nature of such a coupling leads to the formation of dynamic interfacial polarons. Furthermore, the collective motion of the polarons results in a polaronic plasmon mode, which is unambiguously correlated with the surface phonons of SrTiO_{3} in the presence of the FeSe films. A microscopic model is developed showing that the interfacial polaron-polaron interaction leads to the superconductivity enhancement.

Possible Pairing Symmetry in the FeSe-Based Superconductors Determined by Quasiparticle Interference

We study the momentum-integrated quasiparticle interference (QPI) in the FeSe-based superconductors. This method was recently proposed theoretically and has been applied to determine the pairing symmetry in these materials experimentally. Our findings suggest that, if the incipient bands and the superconducting (SC) pairing on them are taken into consideration, then the experimentally measured bound states and momentum-integrated QPI can be well fitted, even if the SC order parameter does not change sign on the Fermi surfaces. Therefore, we offer an alternative explanation to the experimental data, calling for more careful identification of the pairing symmetry that is important for the pairing mechanism.

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.

Reemergence of high-Tc superconductivity in the (Li1-xFe x )OHFe1-ySe under high pressure

In order to elucidate pressure-induced second superconducting phase (SC-II) in A _x Fe_2-ySe₂ (A = K, Rb, Cs, and Tl) having an intrinsic phase separation, we perform a detailed high-pressure magnetotransport study on the isoelectronic, phase-pure (Li_1-xFe _x )OHFe_1-ySe single crystals. Here we show that its ambient-pressure superconducting phase (SC-I) with a critical temperature T_c ≈ 40 K is suppressed gradually to below 2 K and an SC-II phase emerges above P_c ≈ 5 GPa with T_c increasing progressively to above 50 K up to 12.5 GPa. Our high-precision resistivity data uncover a sharp transition of the normal state from Fermi liquid for SC-I to non-Fermi liquid for SC-II phase. In addition, the reemergence of high-T_c SC-II is found to accompany with a concurrent enhancement of electron carrier density. Without structural transition below 10 GPa, the observed SC-II with enhanced carrier density should be ascribed to an electronic origin presumably associated with pressure-induced Fermi surface reconstruction.

Resilient Nodeless d-Wave Superconductivity in Monolayer FeSe

Monolayer FeSe exhibits the highest transition temperature among the iron based superconductors and appears to be fully gapped, seemingly consistent with s-wave superconductivity. Here, we develop a theory for the superconductivity based on coupling to fluctuations of checkerboard magnetic order (which has the same translation symmetry as the lattice). The electronic states are described by a symmetry based k·p-like theory and naturally account for the states observed by angle resolved photoemission spectroscopy. We show that a prediction of this theory is that the resultant superconducting state is a fully gapped, nodeless, d-wave state. This state, which would usually have nodes, stays nodeless because, as seen experimentally, the relevant spin-orbit coupling has an energy scale smaller than the superconducting gap.

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.

Superconductivity across Lifshitz transition and anomalous insulating state in surface K-dosed (Li0.8Fe0.2OH)FeSe

In iron-based superconductors, understanding the relation between superconductivity and electronic structure upon doping is crucial for exploring the pairing mechanism. Recently, it was found that, in iron selenide (FeSe), enhanced superconductivity (T_c of more than 40 K) can be achieved via electron doping, with the Fermi surface only comprising M-centered electron pockets. By using surface K dosing, scanning tunneling microscopy/spectroscopy, and angle-resolved photoemission spectroscopy, we studied the electronic structure and superconductivity of (Li_0.8Fe_0.2OH)FeSe in the deep electron-doped regime. We find that a Γ-centered electron band, which originally lies above the Fermi level (E_F), can be continuously tuned to cross E_F and contribute a new electron pocket at Γ. When this Lifshitz transition occurs, the superconductivity in the M-centered electron pocket is slightly suppressed, and a possible superconducting gap with a small size (up to ~5 meV) and a dome-like doping dependence is observed on the new Γ electron pocket. Upon further K dosing, the system eventually evolves into an insulating state. Our findings provide new clues to understand superconductivity versus Fermi surface topology and the correlation effect in FeSe-based superconductors.

Rapid mass production of two-dimensional metal oxides and hydroxides via the molten salts method

Because of their exotic electronic properties and abundant active sites, two-dimensional (2D) materials have potential in various fields. Pursuing a general synthesis methodology of 2D materials and advancing it from the laboratory to industry is of great importance. This type of method should be low cost, rapid and highly efficient. Here, we report the high-yield synthesis of 2D metal oxides and hydroxides via a molten salts method. We obtained a high-yield of 2D ion-intercalated metal oxides and hydroxides, such as cation-intercalated manganese oxides (Na_0.55Mn₂O₄·1.5H₂O and K_0.27MnO₂·0.54H₂O), cation-intercalated tungsten oxides (Li₂WO₄ and Na₂W₄O₁₃), and anion-intercalated metal hydroxides (Zn₅(OH)₈(NO₃)₂·2H₂O and Cu₂(OH)₃NO₃), with a large lateral size and nanometre thickness in a short time. Using 2D Na₂W₄O₁₃ as an electrode, a high performance electrochemical supercapacitor is achieved. We anticipate that our method will enable new path to the high-yield synthesis of 2D materials for applications in energy-related fields and beyond.

Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer

The origin of enhanced superconductivity over 50 K in the recently discovered FeSe monolayer films grown on SrTiO₃ (STO), as compared to 8 K in bulk FeSe, is intensely debated. As with the ferrochalcogenides A_xFe_2−ySe₂ and potassium-doped FeSe, which also have a relatively high-superconducting critical temperature (T_c), the Fermi surface (FS) of the FeSe/STO monolayer films is free of hole-like FS, suggesting that a Lifshitz transition by which these hole FSs vanish may help increasing T_c. However, the fundamental reasons explaining this increase of T_c remain unclear. Here we report a 15 K jump of T_c accompanying a second Lifshitz transition characterized by the emergence of an electron pocket at the Brillouin zone centre, which is triggered by high-electron doping following in situ deposition of potassium on FeSe/STO monolayer films. Our results suggest that the pairing interactions are orbital dependent in generating enhanced superconductivity in FeSe.

The origin of superconductivity enhancement in FeSe monolayer grown on SrTiO₃ compared to bulk FeSe is still a debated issue. Here, Shi et al. report a further 15 K jump of T_c accompanying a second Lifshitz transition triggered by electron doping in FeSe/SrTiO₃ monolayer films.

High-T_{c} Superconductivity in FeSe at High Pressure: Dominant Hole Carriers and Enhanced Spin Fluctuations

The importance of electron-hole interband interactions is widely acknowledged for iron-pnictide superconductors with high transition temperatures (T_{c}). However, the absence of hole pockets near the Fermi level of the iron-selenide (FeSe) derived high-T_{c} superconductors raises a fundamental question of whether iron pnictides and chalcogenides have different pairing mechanisms. Here, we study the properties of electronic structure in the high-T_{c} phase induced by pressure in bulk FeSe from magnetotransport measurements and first-principles calculations. With increasing pressure, the low-T_{c} superconducting phase transforms into the high-T_{c} phase, where we find the normal-state Hall resistivity changes sign from negative to positive, demonstrating dominant hole carriers in contrast to other FeSe-derived high-T_{c} systems. Moreover, the Hall coefficient is enlarged and the magnetoresistance exhibits anomalous scaling behaviors, evidencing strongly enhanced interband spin fluctuations in the high-T_{c} phase. These results in FeSe highlight similarities with high-T_{c} phases of iron pnictides, constituting a step toward a unified understanding of iron-based superconductivity.

Substrate and band bending effects on monolayer FeSe on SrTiO3(001)

Motivated by the high superconducting transition temperature (T_C) shown by monolayer FeSe on cubic perovskite SrTiO₃(001) and SrTiO₃(001)-2×1 reconstructed surfaces, in this study, we explore the atomic and electronic structures of monolayer FeSe on various SrTiO₃(001)-2×1 surface reconstructions using the CALYPSO method and first-principles calculations. Our search reveals two new Ti₂O₂ and Ti₂O reconstructed surface structures, besides the Ti₂O₃ and double TiO₂ layer reconstructed surfaces, and the two new Ti₂O₂ and Ti₂O reconstructed surface structures are more stable under Ti-rich conditions than under Ti-poor conditions. The Fermi-surface topology of an FeSe monolayer on Ti₂O₃- and Ti₂O₂-type reconstructed STO surfaces is different from that of an FeSe monolayer on a Ti₂O-type STO reconstructed surface. The established structure of monolayer FeSe on a Ti₂O-type STO(001) reconstructed surface can naturally explain the experimental observation of the electronic band structure on the monolayer FeSe superconductor and obtained electrons counting per Fe atom. Surface states in the mid-gap induced by various STO surface reconstructions will result in band bending. The surface-state-induced band bending is also responsible for the electron transfer from the STO substrate to the FeSe films.

The upper critical field and its anisotropy in (Li1-x Fe x )OHFe1-y Se

The temperature dependence of the upper critical field (H _c2) in a (Li_1-x Fe _x )OHFe_1-y Se single crystal ([Formula: see text] K) has been determined by means of magnetotransport measurements down to 1.4 K both for inter-plane ([Formula: see text], [Formula: see text]) and in-plane ([Formula: see text], [Formula: see text]) field directions in static magnetic fields up to 14 T and pulsed magnetic fields up to 70 T. [Formula: see text] exhibits a quasilinear increase with decreasing temperature below the superconducting transition and can be described well by an effective two-band model with unbalanced diffusivity, while [Formula: see text] shows a flattening below 35 K and follows the Werthamer-Helfand-Hohenberg (WHH) model incorporating orbital pair-breaking and spin-paramagnetic effects, yielding zero-temperature critical fields of [Formula: see text] T and [Formula: see text] T. The anisotropy of the upper critical fields, [Formula: see text] monotonically decreases with decreasing temperature from about 7 near T _c to 1.5 at 0 K. This reduced anisotropy, observed in most Fe-based superconductors, is caused by the Pauli limitation of [Formula: see text].

Nanoscale assembly of superconducting vortices with scanning tunnelling microscope tip

Vortices play a crucial role in determining the properties of superconductors as well as their applications. Therefore, characterization and manipulation of vortices, especially at the single-vortex level, is of great importance. Among many techniques to study single vortices, scanning tunnelling microscopy (STM) stands out as a powerful tool, due to its ability to detect the local electronic states and high spatial resolution. However, local control of superconductivity as well as the manipulation of individual vortices with the STM tip is still lacking. Here we report a new function of the STM, namely to control the local pinning in a superconductor through the heating effect. Such effect allows us to quench the superconducting state at nanoscale, and leads to the growth of vortex clusters whose size can be controlled by the bias voltage. We also demonstrate the use of an STM tip to assemble single-quantum vortices into desired nanoscale configurations.

Superconductivity in FeSe Thin Films Driven by the Interplay between Nematic Fluctuations and Spin-Orbit Coupling

The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both s-wave and d-wave symmetries are equally favored, and T_{c} is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry breaking at the film interface lifts this harmful degeneracy and selects the s-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated Li_{1-x}(OH)_{x}FeSe.

High T_{c} via Spin Fluctuations from Incipient Bands: Application to Monolayers and Intercalates of FeSe

We investigate superconductivity in a two-band system with an electronlike and a holelike band, where one of the bands is away from the Fermi level (or "incipient"). We argue that the incipient band contributes significantly to spin-fluctuation pairing in the strong coupling limit where the system is close to a magnetic instability and can lead to a large T_{c}. In this case, T_{c} is limited by a competition between the frequency range of the coupling (set by an isolated paramagnon) and the coupling strength itself, such that a domelike T_{c} dependence on the incipient band position is obtained. The coupling of electrons to phonons is found to further enhance T_{c}. The results are discussed in the context of experiments on monolayers and intercalates of 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.

What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study

Monolayer FeSe films grown on SrTiO₃ (STO) substrate show superconducting gap-opening temperatures (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}}$$\end{document}Tc) which are almost an order of magnitude higher than those of the bulk FeSe and are highest among all known Fe-based superconductors. Angle-resolved photoemission spectroscopy observed “replica bands” suggesting the importance of the interaction between FeSe electrons and STO phonons. These facts rejuvenated the quest for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc enhancement mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here, we perform the first numerically-exact sign-problem-free quantum Monte Carlo simulations to iron-based superconductors. We (1) study the electronic pairing mechanism intrinsic to heavily electron doped FeSe films, and (2) examine the effects of electron–phonon interaction between FeSe and STO as well as nematic fluctuations on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc. Armed with these results, we return to the question “what makes the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc of monolayer FeSe on SrTiO₃ so high?” in the conclusion and discussions.

Superconductivity below 20 K in heavily electron-doped surface layer of FeSe bulk crystal

A superconducting transition temperature (T_c) as high as 100 K was recently discovered in one monolayer FeSe grown on SrTiO₃. The discovery ignited efforts to identify the mechanism for the markedly enhanced T_c from its bulk value of 8 K. There are two main views about the origin of the T_c enhancement: interfacial effects and/or excess electrons with strong electron correlation. Here, we report the observation of superconductivity below 20 K in surface electron-doped bulk FeSe. The doped surface layer possesses all the key spectroscopic aspects of the monolayer FeSe on SrTiO₃. Without interfacial effects, the surface layer state has a moderate T_c of 20 K with a smaller gap opening of 4.2 meV. Our results show that excess electrons with strong correlation cannot induce the maximum T_c, which in turn reveals the need for interfacial effects to achieve the highest T_c in one monolayer FeSe on SrTiO₃.

Thin FeSe film on SrTiO₃ substrate becomes a superconductor with a transition temperature over 100 K, yet the origin remains controversial. Here, Seo et al. show superconductivity below 20 K on the electron-doped surface of an FeSe crystal, suggesting a decisive role of interfacial effects in the enhancement of superconductivity.

Scrutinizing the double superconducting gaps and strong coupling pairing in (Li(1-x)Fe(x))OHFeSe

In the field of iron-based superconductors, one of the frontier studies is about the pairing mechanism. The recently discovered (Li(1-x)Fe(x))OHFeSe superconductor with the transition temperature of about 40 K provides a good platform to check the origin of double superconducting gaps and high transition temperature in the monolayer FeSe thin film. Here we report a scanning tunnelling spectroscopy study on the (Li(1-x)Fe(x))OHFeSe single crystals. The tunnelling spectrum mimics that of the monolayer FeSe thin film and shows double gaps at about 14.3 and 8.6 meV. Further analysis based on the quasiparticle interference allows us to rule out the d-wave gap, and for the first time assign the larger (smaller) gap to the outer (inner) Fermi pockets (after folding) associating with the dxy (dxz/dyz) orbitals, respectively. The gap ratio amounts to 8.7, which demonstrates the strong coupling mechanism in the present superconducting system.