Nodeless electron pairing in CsV3Sb5-derived kagome superconductors

The newly discovered kagome superconductors represent a promising platform for investigating the interplay between band topology, electronic order and lattice geometry^1-9. Despite extensive research efforts on this system, the nature of the superconducting ground state remains elusive^10-17. In particular, consensus on the electron pairing symmetry has not been achieved so far^18-20, in part owing to the lack of a momentum-resolved measurement of the superconducting gap structure. Here we report the direct observation of a nodeless, nearly isotropic and orbital-independent superconducting gap in the momentum space of two exemplary CsV₃Sb₅-derived kagome superconductors-Cs(V_0.93Nb_0.07)₃Sb₅ and Cs(V_0.86Ta_0.14)₃Sb₅-using ultrahigh-resolution and low-temperature angle-resolved photoemission spectroscopy. Remarkably, such a gap structure is robust to the appearance or absence of charge order in the normal state, tuned by isovalent Nb/Ta substitutions of V. Our comprehensive characterizations of the superconducting gap provide indispensable information on the electron pairing symmetry of kagome superconductors, and advance our understanding of the superconductivity and intertwined electronic orders in quantum materials.

Genuine electronic structure and superconducting gap structure in (Ba0.6K0.4)Fe2As2 superconductor

The electronic structure and superconducting gap structure are prerequisites to establish microscopic theories in understanding the superconductivity mechanism of iron-based superconductors. However, even for the most extensively studied optimally-doped (Ba_0.6K_0.4)Fe₂As₂, there remain outstanding controversies on its electronic structure and superconducting gap structure. Here we resolve these issues by carrying out high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements on the optimally-doped (Ba_0.6K_0.4)Fe₂As₂ superconductor using both Helium lamp and laser light sources. Our results indicate the "flat band" feature observed around the Brillouin zone center in the superconducting state originates from the combined effect of the superconductivity-induced band back-bending and the folding of a band from the zone corner to the center. We found direct evidence of the band folding between the zone corner and the center in both the normal and superconducting state. Our resolution of the origin of the flat band makes it possible to assign the three hole-like bands around the zone center and determine their superconducting gap correctly. Around the zone corner, we observe a tiny electron-like band and an M-shaped band simultaneously in both the normal and superconducting states. The obtained gap size for the bands around the zone corner (~5.5 meV) is significantly smaller than all the previous ARPES measurements. Our results establish a new superconducting gap structure around the zone corner and resolve a number of prominent controversies concerning the electronic structure and superconducting gap structure in the optimally-doped (Ba_0.6K_0.4)Fe₂As₂. They provide new insights in examining and establishing theories in understanding superconductivity mechanism in iron-based superconductors.

Fluctuations and pairing in Fe-based superconductors: light scattering experiments

Inelastic scattering of visible light (Raman effect) offers a window into properties of correlated metals such as spin, electron and lattice dynamics as well as their mutual interactions. In this review we focus on electronic and spin excitations in Fe-based pnictides and chalcogenides, in particular but not exclusively superconductors. After a general introduction to the basic theory including the selection rules for the various scattering processes we provide an overview over the major experimental results. In the superconducting state below the transition temperatureTcthe pair-breaking effect can be observed, and the gap energies may be derived and associated with the gaps on the electron and hole bands. In spite of the similarities of the overall band structures the results are strongly dependent on the family and may even change qualitatively within one family. In some of the compounds strong collective modes appear belowTc. In Ba1-xKxFe2As2, which has the most isotropic gap of all Fe-based superconductors, there are indications that these modes are exciton-like states appearing in the presence of a hierarchy of pairing tendencies. The strong in-gap modes observed in Co-doped NaFeAs are interpreted in terms of quadrupolar orbital excitations which become undamped in the superconducting state. The doping dependence of the scattering intensity in Ba(Fe1-xCox)2As2is associated with a nematic resonance above a quantum critical point and interpreted in terms of a critical enhancement at the maximalTc. In the normal state the response from particle-hole excitations reflects the resistivity. In addition, there are strongly temperature-dependent contributions from presumably critical fluctuations in the energy range ofkBTwhich can be compared to the elastic properties. Currently it is not settled whether the fluctuations observed by light scattering are related to spin or charge. Another controversy relates to putative two-magnon excitations, typically in the energy range below 0.5 eV. Whereas this response presumably originates from charge excitations in most of the Fe-based compounds theory and experiment suggest that the excitations in the 60 meV range in FeSe stem from localized spins in a nearly frustrated system.

Band-dependent superconducting gap in SrFe2(As0.65P0.35)2 studied by angle-resolved photoemission spectroscopy

The isovalent-substituted iron pnictide compound SrFe₂(As_1−xP_x)₂ exhibits multiple evidence for nodal superconductivity via various experimental probes, such as the penetration depth, nuclear magnetic resonance and specific heat measurements. The direct identification of the nodal superconducting (SC) gap structure is challenging, partly because the presence of nodes is not protected by symmetry but instead caused by an accidental sign change of the order parameter, and also because of the three-dimensionality of the electronic structure. We have studied the SC gaps of SrFe₂(As_0.65P_0.35)₂ in three-dimensional momentum space by synchrotron and laser-based angle-resolved photoemission spectroscopy. The three hole Fermi surfaces (FSs) at the zone center have SC gaps with different magnitudes, whereas the SC gaps of the electron FSs at the zone corner are almost isotropic and k_z-independent. As a possible nodal SC gap structure, we propose that the SC gap of the outer hole FS changes sign around the Z-X [(0, 0, 2π) − (π, π, 2π)] direction.

Analyzing scanning tunneling spectroscopy for Fe-based superconductors and extracting sample density of states

We extract the density of states (DOS) from the scanning tunneling spectroscopy data for Ba_1-x K _x Fe₂As₂ superconductor. The obtained sample DOS is composed of two ordinary s-wave types from the band at [Formula: see text] point and a linear-like DOS within the s-wave gap from the band at M point in the Brillouin zone, and is consistent with the corresponding data from angle-resolved photoemission spectroscopy. We clarify that the major peak of the tunneling conductance is not related to the DOS but is rather the effect of nonequilibrium coherent tunneling including all coherent spins in the tip and sample.

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.

Atomic-scale visualization of surface-assisted orbital order

Orbital-related physics attracts growing interest in condensed matter research, but direct real-space access of the orbital degree of freedom is challenging. We report a first, real-space, imaging of a surface-assisted orbital ordered structure on a cobalt-terminated surface of the well-studied heavy fermion compound CeCoIn₅. Within small tip-sample distances, the cobalt atoms on a cleaved (001) surface take on dumbbell shapes alternatingly aligned in the [100] and [010] directions in scanning tunneling microscopy topographies. First-principles calculations reveal that this structure is a consequence of the staggered d _xz -d _yz orbital order triggered by enhanced on-site Coulomb interaction at the surface. This so far overlooked surface-assisted orbital ordering may prevail in transition metal oxides, heavy fermion superconductors, and other materials.

Antiferroic electronic structure in the nonmagnetic superconducting state of the iron-based superconductors

A major problem in the field of high-transition temperature (T_c) superconductivity is the identification of the electronic instabilities near superconductivity. It is known that the iron-based superconductors exhibit antiferromagnetic order, which competes with the superconductivity. However, in the nonmagnetic state, there are many aspects of the electronic instabilities that remain unclarified, as represented by the orbital instability and several in-plane anisotropic physical properties. We report a new aspect of the electronic state of the optimally doped iron-based superconductors by using high-energy resolution angle-resolved photoemission spectroscopy. We find spectral evidence for the folded electronic structure suggestive of an antiferroic electronic instability, coexisting with the superconductivity in the nonmagnetic state of Ba_1-x K _x Fe₂As₂. We further establish a phase diagram showing that the antiferroic electronic structure persists in a large portion of the nonmagnetic phase covering the superconducting dome. These results motivate consideration of a key unknown electronic instability, which is necessary for the achievement of high-T_c superconductivity in the iron-based superconductors.

Unconventional Superconductivity in the BiS_{2}-Based Layered Superconductor NdO_{0.71}F_{0.29}BiS_{2}

We investigate the superconducting-gap anisotropy in one of the recently discovered BiS_{2}-based superconductors, NdO_{0.71}F_{0.29}BiS_{2} (T_{c}∼5  K), using laser-based angle-resolved photoemission spectroscopy. Whereas the previously discovered high-T_{c} superconductors such as copper oxides and iron-based superconductors, which are believed to have unconventional superconducting mechanisms, have 3d electrons in their conduction bands, the conduction band of BiS_{2}-based superconductors mainly consists of Bi 6p electrons, and, hence, the conventional superconducting mechanism might be expected. Contrary to this expectation, we observe a strongly anisotropic superconducting gap. This result strongly suggests that the pairing mechanism for NdO_{0.71}F_{0.29}BiS_{2} is an unconventional one and we attribute the observed anisotropy to competitive or cooperative multiple paring interactions.

Enhancement of the Superconducting Gap by Nesting in CaKFe_{4}As_{4}: A New High Temperature Superconductor

We use high resolution angle resolved photoemission spectroscopy and density functional theory with measured crystal structure parameters to study the electronic properties of CaKFe_{4}As_{4}. In contrast to the related CaFe_{2}As_{2} compounds, CaKFe_{4}As_{4} has a high T_{c} of 35 K at stochiometric composition. This presents a unique opportunity to study the properties of high temperature superconductivity in the iron arsenides in the absence of doping or substitution. The Fermi surface consists of several hole and electron pockets that have a range of diameters. We find that the values of the superconducting gap are nearly isotropic (within the explored portions of the Brillouin zone), but are significantly different for each of the Fermi surface (FS) sheets. Most importantly, we find that the momentum dependence of the gap magnitude plotted across the entire Brillouin zone displays a strong deviation from the simple cos(k_{x})cos(k_{y}) functional form of the gap function, proposed by the scenario of Cooper pairing driven by a short range antiferromagnetic exchange interaction. Instead, the maximum value of the gap is observed on FS sheets that are closest to the ideal nesting condition, in contrast to previous observations in other ferropnictides. These results provide strong support for the multiband character of superconductivity in CaKFe_{4}As_{4}, in which Cooper pairing forms on the electron and the hole bands interacting via a dominant interband repulsive interaction, enhanced by band nesting.

Invited Article: High resolution angle resolved photoemission with tabletop 11 eV laser

We developed a table-top vacuum ultraviolet (VUV) laser with 113.778 nm wavelength (10.897 eV) and demonstrated its viability as a photon source for high resolution angle-resolved photoemission spectroscopy (ARPES). This sub-nanosecond pulsed VUV laser operates at a repetition rate of 10 MHz, provides a flux of 2 × 10(12) photons/s, and enables photoemission with energy and momentum resolutions better than 2 meV and 0.012 Å(-1), respectively. Space-charge induced energy shifts and spectral broadenings can be reduced below 2 meV. The setup reaches electron momenta up to 1.2 Å(-1), granting full access to the first Brillouin zone of most materials. Control over the linear polarization, repetition rate, and photon flux of the VUV source facilitates ARPES investigations of a broad range of quantum materials, bridging the application gap between contemporary low energy laser-based ARPES and synchrotron-based ARPES. We describe the principles and operational characteristics of this source and showcase its performance for rare earth metal tritellurides, high temperature cuprate superconductors, and iron-based superconductors.

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

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

Anisotropy of the superconducting gap in the iron-based superconductor BaFe2(As(1-x)P(x))2

We report peculiar momentum-dependent anisotropy in the superconducting gap observed by angle-resolved photoemission spectroscopy in BaFe₂(As_1-xP_x)₂ (x = 0.30, T_c = 30 K). Strongly anisotropic gap has been found only in the electron Fermi surface while the gap on the entire hole Fermi surfaces are nearly isotropic. These results are inconsistent with horizontal nodes but are consistent with modified s_± gap with nodal loops. We have shown that the complicated gap modulation can be theoretically reproduced by considering both spin and orbital fluctuations.

Manipulation of gap nodes by uniaxial strain in iron-based superconductors

In the iron pnictides and chalcogenides, multiple orbitals participate in the superconducting state, enabling different gap structures to be realized in distinct materials. Here we argue that the spectral weights of these orbitals can, in principle, be controlled by a tetragonal symmetry-breaking uniaxial strain, due to the enhanced nematic susceptibility of many iron-based superconductors. By investigating multiorbital microscopic models in the presence of orbital order, we show that not only Tc can be enhanced, but pairs of accidental gap nodes can be annihilated and created in the Fermi surface by an increasing external strain. We explain our results as a mixture of nearly degenerate superconducting states promoted by strain, and show that the annihilation and creation of nodes can be detected experimentally via anisotropic penetration depth measurements. Our results provide a promising framework to externally control the superconducting properties of iron-based materials.

Iron-based high transition temperature superconductors

In a superconductor electrons form pairs and electric transport becomes dissipation-less at low temperatures. Recently discovered iron-based superconductors have the highest superconducting transition temperature next to copper oxides. In this article, we review material aspects and physical properties of iron-based superconductors. We discuss the dependence of transition temperature on the crystal structure, the interplay between antiferromagnetism and superconductivity by examining neutron scattering experiments, and the electronic properties of these compounds obtained by angle-resolved photoemission spectroscopy in link with some results from scanning tunneling microscopy/spectroscopy measurements. Possible microscopic model for this class of compounds is discussed from a strong coupling point of view.

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

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

Imaging the electron-boson coupling in superconducting FeSe films using a scanning tunneling microscope

Scanning tunneling spectroscopy has been used to reveal signatures of a bosonic mode in the local quasiparticle density of states of superconducting FeSe films. The mode appears below Tc as a "dip-hump" feature at energy Ω∼4.7kBTc beyond the superconducting gap Δ. Spectra on strained regions of the FeSe films reveal simultaneous decreases in Δ and Ω. This contrasts with all previous reports on other high-Tc superconductors, where Δ locally anticorrelates with Ω. A local strong coupling model is found to reconcile the discrepancy well, and to provide a unified picture of the electron-boson coupling in unconventional superconductors.

Existence of orbital order and its fluctuation in superconducting Ba(Fe(1-x)Co(x))2As2 single crystals revealed by x-ray absorption spectroscopy

We performed temperature dependent x-ray linear dichroism (XLD) experiments on an iron pnictide system, Ba(Fe(1-x)Co(x))2As2 with x=0.00, 0.05, 0.08, and 0.10 to experimentally verify the existence of orbital ordering (OO). Substantial XLD was observed in polarization dependent x-ray absorption spectra of Fe L edges. By exploiting the difference in the temperature dependent behaviors, OO, and structure contributions to XLD could be clearly separated. The observed OO signal indicates different occupation numbers for d(yz) and d(zx) orbitals and supports the existence of ferro-OO. The results are also consistent with the theoretical prediction. Moreover, we find substantial OO signal well above the structural and magnetic transition temperatures, which suggests the existence of strong OO fluctuations up to high temperatures.

Nematicity as a probe of superconducting pairing in iron-based superconductors

In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here, we show that when both states have comparable free energies, superconducting and nematic degrees of freedom are strongly coupled. Whereas nematic order causes a sharp nonanalytic increase in T(c), nematic fluctuations can change the character of the s-wave to d-wave transition, favoring an intermediate state that does not break time-reversal symmetry but does break tetragonal symmetry. The coupling between superconductivity and nematicity is also manifested in the strong softening of the shear modulus across the superconducting transition. Our results show that nematicity can be used as a diagnostic tool to search for unconventional pairing states in iron pnictides and chalcogenides.

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

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

Self-consistent vertex correction analysis for iron-based superconductors: mechanism of Coulomb interaction-driven orbital fluctuations

We study the mechanism of orbital or spin fluctuations due to multiorbital Coulomb interaction in iron-based superconductors, going beyond the random-phase approximation. For this purpose, we develop a self-consistent vertex correction (VC) method, and find that multiple orbital fluctuations in addition to spin fluctuations are mutually emphasized by the "multimode interference effect" described by the VC. Then, both antiferro-orbital and ferro-orbital (=nematic) fluctuations simultaneously develop for J/U~0.1, both of which contribute to the s-wave superconductivity. Especially, the ferro-orbital fluctuations give the orthorhombic structure transition as well as the softening of shear modulus C(66).

Unraveling orbital correlations with magnetic resonant inelastic x-ray scattering

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition-metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on the symmetry of the orbitals that spins occupy and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital-ordered and ferro-orbital (or orbital liquid) states.

Anisotropy of electrical transport in pnictide superconductors studied using Monte Carlo simulations of the spin-fermion model

An undoped three-orbital spin-fermion model for the Fe-based superconductors is studied via Monte Carlo techniques in two-dimensional clusters. At low temperatures, the magnetic and one-particle spectral properties are in agreement with neutron and photoemission experiments. Our main results are the resistance versus temperature curves that display the same features observed in BaFe(2)As(2) detwinned single crystals (under uniaxial stress), including a low-temperature anisotropy between the two directions followed by a peak at the magnetic ordering temperature, that qualitatively appears related to short-range spin order and concomitant Fermi surface orbital order.

Infrared measurement of the pseudogap of P-doped and Co-doped high-temperature BaFe2As2 superconductors

We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolution of the antiferromagnetic fluctuations associated with the spin-density-wave instability. The strong-coupling analysis of infrared data further reveals the interdependence between the magnetism and the pseudogap in the iron pnictides.

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

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