The electron-pairing mechanism of iron-based superconductors

Enhanced Superconductivity and Critical Current Density Due to the Interaction of InSe2 Bonded Layer in (InSe2)0.12NbSe2

Superconductivity was discovered in (InSe2)xNbSe2. The materials are crystallized in a unique layered structure where bonded InSe2 layers are intercalated into the van der Waals gaps of 2H-phase NbSe2. The (InSe2)0.12NbSe2 superconductor exhibits a superconducting transition at 11.6 K and critical current density of 8.2 × 105 A/cm2. Both values are the highest among all transition metal dichalcogenide superconductors at ambient pressure. The present finding provides an ideal material platform for further investigation of superconducting-related phenomena in transition metal dichalcogenides.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question “is room temperature really achieved?” is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences.

Competing Vortex Topologies in Iron-Based Superconductors

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

Pressure Evolution of Ultrafast Photocarrier Dynamics and Electron-Phonon Coupling in FeTe0.5Se0.5

Understanding the coupling between electrons and phonons in iron chalcogenides FeTexSe1-x has remained a critical but arduous project in recent decades. The direct observation of the electron-phonon coupling effect through electron dynamics and vibrational properties has been lacking. Here, we report the first pressure-dependent ultrafast photocarrier dynamics and Raman scattering studies on an iron chalcogenide FeTe0.5Se0.5 to explore the interaction between electrons and phonons in this unconventional superconductor. The lifetime of the excited electrons evidently decreases as the pressure increases from 0 to 2.2 GPa, and then increases with further compression. The vibrational properties of the A1g phonon mode exhibit similar behavior, with a pronounced frequency reduction appearing at approximately 2.3 GPa. The dual evidence reveals the enhanced electron-phonon coupling strength with pressure in FeTe0.5Se0.5. Our results give an insight into the role of the electron-phonon coupling effect in iron-based superconductors.

Dimensional crossovers in the Gaussian critical fluctuations above Tc of two-layer and three-layer superconductors

By using a Ginzburg–Landau functional in the Gaussian approximation, we calculate the energy of superconducting fluctuations above the transition, at zero external magnetic field, of a system composed by a small number N of parallel two-dimensional superconducting planes, each of them Josephson coupled to its first neighbour, with special focus in the N = 2 and 3 cases. This allows us to obtain expressions for the critical contributions to various observables (fluctuation specific heat and magnetic susceptibility and Aslamazov–Larkin paraconductivity). Our results suggest that these systems may display deviations from pure 2D behaviour and interesting crossover effects, with both similitudes and differences to those known to occur in infinite-layers superconductors. Some challenges for future related research are also outlined.

Iron pnictides and chalcogenides: a new paradigm for superconductivity

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Optical conductivity and superconductivity in highly overdoped La2-x Ca x CuO4 thin films

Chemical substitution is widely used to modify the charge-carrier concentration (“doping”) in complex quantum materials, but the influence of the associated structural disorder on the electronic phase behavior remains poorly understood. We synthesized thin films of the high-temperature superconductor La2−xCaxCuO4 with minimal structural disorder and characterized their doping levels through measurements of the optical conductivity. We find that superconductivity with Tc = 15 to 20 K is stable up to much higher doping levels than previously found for analogous compounds with stronger disorder. The results imply that doping-induced disorder is the leading cause of the degradation of superconductivity for large carrier concentration, and they open up a previously inaccessible regime of the phase diagram of high-temperature superconductors to experimental investigation.

We have used atomic layer-by-layer oxide molecular beam epitaxy to grow epitaxial thin films of La2−xCaxCuO4 with x up to 0.5, greatly exceeding the solubility limit of Ca in bulk systems (x∼0.12). A comparison of the optical conductivity measured by spectroscopic ellipsometry to prior predictions from dynamical mean-field theory demonstrates that the hole concentration p is approximately equal to x. We find superconductivity with Tc of 15 to 20 K up to the highest doping levels and attribute the unusual stability of superconductivity in La2−xCaxCuO4 to the nearly identical radii of La and Ca ions, which minimizes the impact of structural disorder. We conclude that careful disorder management can greatly extend the “superconducting dome” in the phase diagram of the cuprates.

Multiband effects on the upper critical field angular dependence of 122-family iron pnictide superconductors

Detailed measurements of the in-plane resistivity were performed in a high-quality Ba([Formula: see text])[Formula: see text] ([Formula: see text]) single crystal, in magnetic fields up to 9 T and with different orientations [Formula: see text] relative to the crystal c axis. A significant [Formula: see text] rounding is observed just above the superconducting critical temperature [Formula: see text] due to Cooper pairs created by superconducting fluctuations. These data are analyzed in terms of a generalization of the Aslamazov-Larkin approach, that extends its applicability to high reduced-temperatures and magnetic fields. This method allows us to carry out a criterion-independent determination of the angular dependence of the upper critical field, [Formula: see text]. In spite of the relatively small anisotropy of this compound, it is found that [Formula: see text] presents a significant deviation from the single-band 3D anisotropic Ginzburg-Landau (3D-aGL) approach, particularly for large [Formula: see text] (typically above [Formula: see text]). These results are interpreted in terms of the multiband nature of these materials, in contrast with other proposals for similar [Formula: see text] anomalies. Our results are also consistent with an effective anisotropy factor almost temperature independent near [Formula: see text], a result that differs from the ones obtained by using a single-band model.

Neutron Spin Resonance in a Quasi-Two-Dimensional Iron-Based Superconductor

The neutron spin resonance is generally regarded as a key to understanding the magnetically mediated Cooper pairing in unconventional superconductors. Here, we report an inelastic neutron scattering study on the low-energy spin excitations in a quasi-two-dimensional iron-based superconductor KCa_{2}Fe_{4}As_{4}F_{2}. We have discovered a two-dimensional spin resonant mode with downward dispersions, a behavior closely resembling the low branch of the hourglass-type spin resonance in cuprates. While the resonant intensity is predominant by two broad incommensurate peaks near Q=(0.5,0.5) with a sharp energy peak at E_{R}=16  meV, the overall energy dispersion of the mode exceeds the measured maximum total gap Δ_{tot}=|Δ_{k}|+|Δ_{k+Q}|. These results deeply challenge the conventional understanding of the resonance modes as magnetic excitons regardless of underlining pairing symmetry schemes, and it also points out that when the iron-based superconductivity becomes very quasi-two-dimensional, the electronic behaviors are similar to those in cuprates.

Superconductivity in undoped BaFe2As2 by tetrahedral geometry design

Fe-based superconductors exhibit a diverse interplay between charge, orbital, and magnetic ordering. Variations in atomic geometry affect electron hopping between Fe atoms and the Fermi surface topology, influencing magnetic frustration and the pairing strength through changes of orbital overlap and occupancies. Here, we experimentally demonstrate a systematic approach to realize superconductivity without chemical doping in BaFe₂As₂, employing geometric design within an epitaxial heterostructure. We control both tetragonality and orthorhombicity in BaFe₂As₂ through superlattice engineering, which we experimentally find to induce superconductivity when the As-Fe-As bond angle approaches that in a regular tetrahedron. This approach to superlattice design could lead to insights into low-dimensional superconductivity in Fe-based superconductors.

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.

Pairing mechanism in multiband superconductors

It has been a long-standing puzzle why electrons with repulsive interactions can form pairs in unconventional superconductors. Here we develop an analytic solution for renormalization group analysis in multiband superconductors, which agrees with the numerical results exceedingly well. The analytic solution allows us to construct soluble effective theory and answers the pairing puzzle: electrons form pairs resonating between different bands to compensate the energy penalty for bring them together, just like the resonating chemical bonds in benzene. The analytic solutions allow us to explain the peculiar features of critical temperatures, spin uctuations in unconventional superconductors and can be generalized to cuprates where the notion of multibands is replaced by multipatches in momentum space.

Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

Aperiodic structure imaging suffers limitations when utilizing Fourier analysis. The authors report an algorithm that quantitatively overcomes these limitations based on nonconvex optimization, demonstrated by studying aperiodic structures via the phase sensitive interference in STM images.

Higher-Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures

We show, theoretically, that a heterostructure of monolayer FeTe_{1-x}Se_{x}-a superconducting quantum spin Hall material-with a monolayer of FeTe-a bicollinear antiferromagnet-realizes a higher order topological superconductor phase characterized by emergent Majorana zero modes pinned to the sample corners. We provide a minimal effective model for this system, analyze the origin of higher order topology, and fully characterize the topological phase diagram. Despite the conventional s-wave pairing, we find a rather surprising emergence of a novel topological nodal superconductor in the phase diagram. Featured by edge-dependent Majorana flat bands, the topological nodal phase is protected by an antiferromagnetic chiral symmetry. We also discuss the experimental feasibility, the estimation of realistic model parameters, and the robustness of the Majorana corner modes against magnetic and potential disorder. Our work provides a new experimentally feasible high-temperature platform for both higher order topology and non-Abelian Majorana physics.

Gap suppression at a Lifshitz transition in a multi-condensate superconductor

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO₃/SrTiO₃ interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen-Cooper-Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

Machine learning in electronic-quantum-matter imaging experiments

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena¹. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science^2-5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)^6-16, the next challenge is to apply this approach to experimental data-for example, to the arrays of complex electronic-structure images¹⁷ obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals^18,19 are consistent with these observations.

Scaling of the Fano Effect of the In-Plane Fe-As Phonon and the Superconducting Critical Temperature in Ba_{1-x}K_{x}Fe_{2}As_{2}

By means of infrared spectroscopy, we determine the temperature-doping phase diagram of the Fano effect for the in-plane Fe-As stretching mode in Ba_{1-x}K_{x}Fe_{2}As_{2}. The Fano parameter 1/q^{2}, which is a measure of the phonon coupling to the electronic particle-hole continuum, shows a remarkable sensitivity to the magnetic and structural orderings at low temperatures. Most strikingly, at elevated temperatures in the paramagnetic tetragonal state we observe a linear correlation between 1/q^{2} and the superconducting critical temperature T_{c}. Based on theoretical calculations and symmetry considerations, we identify the relevant interband transitions that are coupled to the Fe-As mode. In particular, we show that a sizable xy orbital component at the Fermi level is fundamental for the Fano effect and, thus, possibly also for the superconducting pairing.

Helical Hinge Majorana Modes in Iron-Based Superconductors

Motivated by recent experiments on FeTe_{1-x}Se_{x}, we construct an explicit minimal model of an iron-based superconductor with band inversion at the Z point and nontopological bulk s_{±} pairing. While there has been considerable interest in Majorana zero modes localized at vortices in such systems, we find that our model-without any vortices-intrinsically supports 1D helical Majorana modes localized at the hinges between (001) and (100) or (010) surfaces, suggesting that this is a viable platform for observing "higher-order" topological superconductivity. We provide a general theory for these hinge modes and discuss their stability and experimental manifestation. Our work indicates the possible experimental observability of hinge Majorana modes in iron-based topological superconductors.

Evidence for d-Wave Superconductivity in Single Layer FeSe/SrTiO3 Probed by Quasiparticle Scattering Off Step Edges

The de Gennes extrapolation length is a direction dependent measure of the spatial evolution of the pairing gap near the boundary of a superconductor and thus provides a viable means to probe its symmetry. It is expected to be infinite and isotropic for plain s-wave pairing, and finite and anisotropic for d-wave. Here, we synthesize single-layer FeSe films on SrTiO₃(001) (STO) substrates by molecular beam epitaxy and measure the de Gennes extrapolation length by scanning tunneling microscopy/spectroscopy. We find a 40% reduction of the superconducting gap near specular [110]_Fe edges, yielding an extrapolation length of 8.0 nm. However, near specular [010]_Fe edges, the extrapolation length is nearly infinite. These findings are consistent with a phase changing pairing with 2-fold symmetry, indicating d-wave superconductivity. This is further supported by the presence of in-gap states near the specular [110]_Fe edges, but not the [010]_Fe edges. This work provides direct experimental evidence for d-wave superconductivity in single-layer FeSe/STO and demonstrates quasiparticle scattering at boundaries to be a viable phase sensitive probe of pairing symmetry in Fe-based superconductors.

Emergence of superconductivity from fully incoherent normal state in an iron-based superconductor (Ba0.6K0.4)Fe2As2

In unconventional superconductors, it is generally believed that understanding the physical properties of the normal state is a pre-requisite for understanding the superconductivity mechanism. In conventional superconductors like niobium or lead, the normal state is a Fermi liquid with a well-defined Fermi surface and well-defined quasipartcles along the Fermi surface. Superconductivity is realized in this case by the Fermi surface instability in the superconducting state and the formation and condensation of the electron pairs (Cooper pairing). The high temperature cuprate superconductors, on the other hand, represent another extreme case that superconductivity can be realized in the underdoped region where there is neither well-defined Fermi surface due to the pseudogap formation nor quasiparticles near the antinodal regions in the normal state. Here we report a novel scenario that superconductivity is realized in a system with well-defined Fermi surface but without quasiparticles along the Fermi surface in the normal state. High resolution laser-based angle-resolved photoemission measurements have been performed on an optimally-doped iron-based superconductor (Ba_0.6K_0.4)Fe₂As₂. We find that, while sharp superconducting coherence peaks emerge in the superconducting state on the hole-like Fermi surface sheets, no quasiparticle peak is present in the normal state. Its electronic behaviours deviate strongly from a Fermi liquid system. The superconducting gap of such a system exhibits an unusual temperature dependence that it is nearly a constant in the superconducting state and abruptly closes at T_c. These observations have provided a new platform to study unconventional superconductivity in a non-Fermi liquid system.

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.

Orbital Selectivity Enhanced by Nematic Order in FeSe

Motivated by the recent low-temperature experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual observation of strong orbital selectivity in the nematic phase of FeSe, uncover new clues on the nature of the nematic order, and set the stage to elucidate the interplay between superconductivity and nematicity in iron-based superconductors.

Control of Epitaxial BaFe2As2 Atomic Configurations with Substrate Surface Terminations

Atomic layer controlled growth of epitaxial thin films of unconventional superconductors opens the opportunity to discover novel high temperature superconductors. For instance, the interfacial atomic configurations may play an important role in superconducting behavior of monolayer FeSe on SrTiO₃ and other Fe-based superconducting thin films. Here, we demonstrate a selective control of the atomic configurations in Co-doped BaFe₂As₂ epitaxial thin films and its strong influence on superconducting transition temperatures by manipulating surface termination of (001) SrTiO₃ substrates. In a combination of first-principles calculations and high-resolution scanning transmission electron microscopy imaging, we show that Co-doped BaFe₂As₂ on TiO₂-terminated SrTiO₃ is a tetragonal structure with an atomically sharp interface and with an initial Ba layer. In contrast, Co-doped BaFe₂As₂ on SrO-terminated SrTiO₃ has a monoclinic distortion and a BaFeO_{3- x} initial layer. Furthermore, the superconducting transition temperature of Co-doped BaFe₂As₂ ultrathin films on TiO₂-terminated SrTiO₃ is significantly higher than that on SrO-terminated SrTiO₃, which we attribute to shaper interfaces with no lattice distortions. This study allows the design of the interfacial atomic configurations and the effects of the interface on superconductivity in Fe-based superconductors.

Imaging orbital-selective quasiparticles in the Hund's metal state of FeSe

Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Z_m of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Z_m appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that [Formula: see text], consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.

Fully gapped d-wave superconductivity in CeCu2Si2

Identifying the gap structure of superconductors is vital for understanding the underlying pairing mechanism of the Cooper pairs. The first heavy fermion superconductor to be discovered, CeCu₂Si₂, was thought to be a d-wave superconductor with gap nodes, until recent specific heat measurements provided evidence that the gap is fully open across the Fermi surface. We propose a resolution to this puzzle from measurements of the London penetration depth, which give further evidence for fully gapped superconductivity. We analyze the data using a d-wave band-mixing pairing model, which leads to a fully open superconducting gap. Our model accounts well for the penetration depth and specific heat data, while reconciling the nodeless and sign-changing nature of the gap function.

The nature of the pairing symmetry of the first heavy fermion superconductor CeCu₂Si₂ has recently become the subject of controversy. While CeCu₂Si₂ was generally believed to be a d-wave superconductor, recent low-temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here, we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped d+d band-mixing pairing state for CeCu₂Si₂, which yields very good fits to both the superfluid density and specific heat, as well as accounting for a sign change of the superconducting order parameter, as previously concluded from inelastic neutron scattering results.

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.

Superconductivity Induced by Oxygen Doping in Y2 O2 Bi

When doped with oxygen, the layered Y₂ O₂ Bi phase becomes a superconductor. This finding raises questions about the sites for doped oxygen, the mechanism of superconductivity, and practical guidelines for discovering new superconductors. We probed these questions in terms of first-principles calculations for undoped and O-doped Y₂ O₂ Bi. The preferred sites for doped O atoms are the centers of Bi₄ squares in the Bi square net. Several Bi 6p x/y bands of Y₂ O₂ Bi are raised in energy by oxygen doping because the 2p x/y orbitals of the doped oxygen make antibonding possible with the 6p x/y orbitals of surrounding Bi atoms. Consequently, the condition necessary for the "flat/steep" band model for superconductivity is satisfied in O-doped Y₂ O₂ Bi.

Strong 3D and 1D magnetism in hexagonal Fe-chalcogenides FeS and FeSe vs. weak magnetism in hexagonal FeTe

We present a comparative theoretical study of the hexagonal forms of the Fe-chalcogenides FeS, FeSe and FeTe with their better known tetragonal forms. While the tetragonal forms exhibit only an incipient antiferromagnetism and experimentally show superconductivity when doped, the hexagonal forms of FeS and FeSe display a robust magnetism. We show that this strong magnetism arises from a van Hove singularity associated with the direct Fe-Fe c-axis chains in the generally more three-dimensional NiAs structure. We also find that hexagonal FeTe is much less magnetic than the other two hexagonal materials, so that unconventional magnetically-mediated superconductivity is possible, although a large T_c value is unlikely.

High-temperature superconductivity in one-unit-cell FeSe films

Since the dramatic enhancement of the superconducting transition temperature (T _c) was reported in a one-unit-cell FeSe film grown on a SrTiO₃ substrate (1-UC FeSe/STO) by molecular beam epitaxy (MBE), related research on this system has become a new frontier in condensed matter physics. In this paper, we present a brief review on this rapidly developing field, mainly focusing on the superconducting properties of 1-UC FeSe/STO. Experimental evidence for high-temperature superconductivity in 1-UC FeSe/STO, including direct evidence revealed by transport and diamagnetic measurements, as well as other evidence from scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), are overviewed. The potential mechanisms of the enhanced superconductivity are also discussed. There are accumulating arguments to suggest that the strengthened Cooper pairing in 1-UC FeSe/STO originates from the interface effects, specifically the charge transfer and coupling to phonon modes in the TiO₂ plane. The study of superconductivity in 1-UC FeSe/STO not only sheds new light on the mechanism of high-temperature superconductors with layered structures, but also provides an insight into the exploration of new superconductors by interface engineering.

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.

Low-energy microscopic models for iron-based superconductors: a review

The development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-T _c compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the low-energy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.

Amperean Pairing at the Surface of Topological Insulators

The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards a superconducting state with unusual pairing, dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a ferromagnetic layer deposited on the surface of a topological insulator couple to the electrons as gauge fields. The transverse components of the magnetic gauge fields are unscreened and can mediate an effective interaction between electrons. There is an attractive interaction between electrons with momenta in the same direction which makes the pairing to be of Amperean type. We show that this attractive interaction leads to a p-wave pairing instability of the Fermi surface in the Cooper channel.

Superconductivity in alkali metal intercalated iron selenides

Alkali metal intercalated iron selenide superconductors A x Fe2-y Se2 (where A  =  K, Rb, Cs, Tl/K, and Tl/Rb) are characterized by several unique properties, which were not revealed in other superconducting materials. The compounds crystallize in overall simple layered structure with FeSe layers intercalated with alkali metal. The structure turned out to be pretty complex as the existing Fe-vacancies order below ~550 K, which further leads to an antiferromagnetic ordering with Néel temperature fairly above room temperature. At even lower temperatures a phase separation is observed. While one of these phases stays magnetic down to the lowest temperatures the second is becoming superconducting below ~30 K. All these effects give rise to complex relationships between the structure, magnetism and superconductivity. In particular the iron vacancy ordering, linked with a long-range magnetic order and a mesoscopic phase separation, is assumed to be an intrinsic property of the system. Since the discovery of superconductivity in those compounds in 2010 they were investigated very extensively. Results of the studies conducted using a variety of experimental techniques and performed during the last five years were published in hundreds of reports. The present paper reviews scientific work concerning methods of synthesis and crystal growth, structural and superconducting properties as well as pressure investigations.

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

The mechanism of high-temperature superconductivity in the iron-based superconductors remains an outstanding issue in condensed matter physics. The electronic structure plays an essential role in dictating superconductivity. Recent revelation of distinct electronic structure and high-temperature superconductivity in the single-layer FeSe/SrTiO3 films provides key information on the role of Fermi surface topology and interface in inducing or enhancing superconductivity. Here we report high-resolution angle-resolved photoemission measurements on the electronic structure and superconducting gap of an FeSe-based superconductor, (Li0.84Fe0.16)OHFe0.98Se, with a Tc at 41 K. We find that this single-phase bulk superconductor shows remarkably similar electronic behaviours to that of the superconducting single-layer FeSe/SrTiO3 films in terms of Fermi surface topology, band structure and the gap symmetry. These observations provide new insights in understanding high-temperature superconductivity in the single-layer FeSe/SrTiO3 films and the mechanism of superconductivity in the bulk iron-based superconductors.

Phase diagram of the layered oxide SnO: GW and electron-phonon studies

First-principles calculations are performed to study the electronic properties and the electron-phonon interactions of the layered oxide semiconductor SnO. In addition to the high hole mobility that makes SnO a promising material in electronics, it has recently been reported that the semimetallic phase under pressure is superconducting. The superconducting Tc curve exhibits a dome-like feature under pressure and reaches the maximum of 1.4 K at p = 9.2 GPa. Both its crystal structure and the dome-like Tc curve are reminiscent of the Fe-based superconductor FeSe. Motivated by this observation, we investigate the electronic, phonon, and their interactions in SnO using first-principles schemes. GW approximation is adopted to correct the underestimated band gaps, including real and continuous band gaps in the semiconducting and semimetallic phases. The phase diagram showing the semiconductor-to-semimetal transition and the Tc curve has been successfully reproduced. Detailed analysis of the electron-phonon interactions demonstrate the importance of the out-of-plane motions of O atoms and the Sn-s lone pairs for the superconductivity to occur. Our method combining GW and e-ph calculations can be further extended to the study of other materials that undergo insulator-to-superconductor phase transition.

Tuning emergent magnetism in a Hund's impurity

The recently proposed concept of a Hund's metal--a metal in which electron correlations are driven by Hund's rule coupling-can be used to explain the exotic magnetic and electronic behaviour of strongly correlated electron systems of multi-orbital metallic materials. Tuning the abundance of parameters that determine these materials is, however, experimentally challenging. Here, we show that the basic constituent of a Hund's metal--a Hund's impurity--can be realized using a single iron atom adsorbed on a platinum surface, a system that comprises a magnetic moment in the presence of strong charge fluctuations. The magnetic properties can be controlled by using the tip of a scanning tunnelling microscope to change the binding site and degree of hydrogenation of the 3d transition-metal atom. We are able to experimentally explore a regime of four almost degenerate energy scales (Zeeman energy, temperature, Kondo temperature and magnetic anisotropy) and probe the magnetic excitations with the microscope tip. The regime of our Hund's impurity can be tuned from an emergent magnetic moment to a multi-orbital Kondo state, and the system could be used to test predictions of advanced many-body theories for non-Fermi liquids in quantum magnets or unconventional superconductors.

Slow Spin Dynamics in Superconducting Ca0.9Ce0.1Fe2As2

Slow spin dynamics has been observed in superconducting under-doped Ca0.9Ce0.1Fe2As2 single crystal. Below 100 K, the system exhibits hysteresis in the cooling and warming protocols of temperature dependent resistivity due to first order tetragonal to orthorhombic structural transition with simultaneous magnetic transition from paramagnetic to spin density wave antiferromagnetic state of the iron (Fe) ions. Zero field cooled/field cooled (ZFC/FC) magnetization curves showed splitting at 32 K followed by a sharp increase of the FC curve and then FC plateau at low temperatures. Slow spin relaxation in both the ZFC and FC protocols was observed which is typical for spin-glass system. The system also showed features analogue to spin-glass behavior such as ZFC peak, FC plateau, ZFC slow spin relaxation, magnetic hysteresis, and ZFC ac memory effect. The spin-glass like behavior was rather weak and vanished at higher fields. The origin of the slow spin dynamics could be the inhomogeneous distribution of the cerium (Ce) spins ordered along the c-axis OR interactions between Fe and Ce spins which lead to magnetic frustration of Ce spins. All these findings support the coexistence of slow spin dynamics of Ce spins and superconductivity in Ca0.9Ce0.1Fe2As2 single crystal.

Electronic structure and superconductivity of FeSe-related superconductors

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

Possible electric-field-induced superconducting states in doped silicene

Silicene has been synthesized recently, with experimental evidence showing possible superconductivity in the doped case. The noncoplanar low-buckled structure of this material inspires us to study the pairing symmetry of the doped system under a perpendicular external electric field. Our study reveals that the electric field induces an interesting quantum phase transition from the singlet chiral d + id'-wave superconducting phase to the triplet f-wave one. The emergence of the f-wave pairing results from the sublattice-symmetry-breaking caused by the electric field and the ferromagnetic-like intra-sublattice spin correlations at low dopings. Due to the enhanced density of states, the superconducting critical temperature of the system is enhanced by the electric field remarkably. Furthermore, we design a particular dc SQUID experiment to detect the quantum phase transition predicted here. Our results, if confirmed, will inject a new vitality to the familiar Si-based industry through adopting doped silicene as a tunable platform to study different types of exotic unconventional superconductivities.

Electronic evidence of an insulator-superconductor crossover in single-layer FeSe/SrTiO3 films

In high-temperature cuprate superconductors, it is now generally agreed that superconductivity is realized by doping an antiferromagnetic Mott (charge transfer) insulator. The doping-induced insulator-to-superconductor transition has been widely observed in cuprates, which provides important information for understanding the superconductivity mechanism. In the iron-based superconductors, however, the parent compound is mostly antiferromagnetic bad metal, raising a debate on whether an appropriate starting point should go with an itinerant picture or a localized picture. No evidence of doping-induced insulator-superconductor transition (or crossover) has been reported in the iron-based compounds so far. Here, we report an electronic evidence of an insulator-superconductor crossover observed in the single-layer FeSe film grown on a SrTiO3 substrate. By taking angle-resolved photoemission measurements on the electronic structure and energy gap, we have identified a clear evolution of an insulator to a superconductor with increasing carrier concentration. In particular, the insulator-superconductor crossover in FeSe/SrTiO3 film exhibits similar behaviors to that observed in the cuprate superconductors. Our results suggest that the observed insulator-superconductor crossover may be associated with the two-dimensionality that enhances electron localization or correlation. The reduced dimensionality and the interfacial effect provide a new pathway in searching for new phenomena and novel superconductors with a high transition temperature.

Ground state, collective mode, phase soliton and vortex in multiband superconductors

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

Excess conductivity and Berezinskii-Kosterlitz-Thouless transition in superconducting FeSe thin films

Temperature-dependent electronic transport in the vicinity of the superconducting transition is reported for quasi-two-dimensional textured FeSe thin films. The conspicuous rounding of the resistive transitions and large transition widths are indications of excess conductivity due to thermal Cooper-pair fluctuations, which can be well-described by the two-dimensional Aslamazov-Larkin theory. The Halperin-Nelson form of the sheet resistance between the phase-ordering temperature TBKT and the mean-field temperature TMF, and the power-law behaviour of the voltage-current characteristics, with a distinctive jump of the exponent at TBKT, are indicative of a Berezinskii-Kosterlitz-Thouless transition. The complementary results suggest a two-dimensional character of superconductivity in the FeSe films and allow a quantitative estimate of the Ginzburg number Gi.

The anomaly Cu doping effects on LiFeAs superconductors

The Cu substitution effect on the superconductivity of LiFeAs has been studied in comparison with Co/Ni substitution. It is found that the shrinking rate of the lattice parameter c for Cu substitution is much smaller than that of Co/Ni substitution. This is in conjugation with the observation of ARPES that shows almost the same electron and hole Fermi surfaces (FSs) size for undoped and Cu substituted LiFeAs sample, except for a very small hole band sinking below Fermi level with doping. This indicates that there is little doping effect at Fermi surface by Cu substitution, in sharp contrast to the more effective carrier doping effect by Ni or Co.

Electronic structure of Eu(Fe0.79Ru0.21)2As2 studied by angle-resolved photoemission spectroscopy

Eu(Fe(0.79)Ru(0.21))2As2 is suggested to be a nodeless superconductor based on the empirical correlation between pnictogen height (hPn) and superconducting gap behavior, in contrast to BaFe2(As(0.7)P(0.3))2 and Ba(Fe(0.65)Ru(0.35))2As2. We studied the low-lying electronic structure of Eu(Fe(0.79)Ru(0.21))2As2 with angle-resolved photoemission spectroscopy (ARPES). By photon energy dependence and polarization dependence measurements, we resolved the band structure in the three-dimensional momentum space and determined the orbital character of each band. In particular, we found that the dz2 -originated ζ band does not contribute spectral weight to the Fermi surface around Z, unlike BaFe2(As(0.7)P(0.3))2 and Ba(Fe(0.65)Ru(0.35))2As2. Since BaFe2(As(0.7)P(0.3))2 and Ba(Fe(0.65)Ru(0.35))2As2 are nodal superconductors and their hPn's are less than 1.33 Å, while the hPn of Eu(Fe(0.79)Ru(0.21))2As2 is larger than 1.33 Å, our results provide more evidence for a direct relationship between nodes, dz2 orbital character and hPn. Our results help to provide an understanding of the nodal superconductivity in iron-based superconductors.

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

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