Superconducting gap anisotropy sensitive to nematic domains in FeSe

Superconductivity and nematic order in a new titanium-based kagome metal CsTi3Bi5 without charge density wave order

The cascade of correlated topological quantum states in the newly discovered vanadium-based kagome superconductors, AV3Sb5 (A = K, Rb, and Cs), with a Z2 topological band structure has sparked immense interest. Here, we report the discovery of superconductivity and electronic nematic order in high-quality single-crystals of a new titanium-based kagome metal, CsTi3Bi5, that preserves the translation symmetry, in stark contrast to the charge density wave superconductor AV3Sb5. Transport and magnetic susceptibility measurements show superconductivity with an onset superconducting transition temperature Tc of approximately 4.8 K. Using the scanning tunneling microscopy/spectroscopy and Josephson scanning tunneling spectroscopy, we demonstrate that the single crystals of CsTi3Bi5 exhibit two distinct superconducting gaps. Furthermore, the superconducting gaps break the six-fold crystal rotational symmetry down to two-fold. At low energies, we find that the quasiparticle interference patterns exhibit rotational-symmetry-breaking C2 patterns, revealing a nematic ordered normal state with the same nematic direction as in the superconducting state. Our findings uncover a novel superconducting state in CsTi3Bi5 and provide new insights for the intrinsic electron liquid crystal phases in kagome superconductors.

Exploring Unconventional Electron Distribution Patterns: Contrasts Between FeSe and FeSe/STO Using an Ab Initio Approach

For more than a decade, the unusual distribution of electrons observed in ARPES (angle-resolved photoemission spectroscopy) data within the energy range of ~30 meV to ~300 meV below the Fermi level, known as the ARPES energy range, has remained a puzzle in the field of iron-based superconductivity. As the electron-phonon coupling of FeSe/SrTiO3 is very strong, our investigation is centered on exploring the synergistic interplay between spin-density waves (SDW) and charge-density waves (CDW) with differential phonons at the interface between antiferromagnetic maxima and minima under wave interference. Our analysis reveals that the synergistic energy is proportional to the ARPES energy range, as seen in the comparison between FeSe and FeSe/SrTiO3. This finding may suggest that the instantaneous interplay between these intricate phenomena may play a role in triggering the observed energy range in ARPES.

Lifting of Gap Nodes by Disorder in Tetragonal FeSe_{1-x}S_{x} Superconductors

The observation of time-reversal symmetry breaking and large residual density of states in tetragonal FeSe_{1-x}S_{x} suggests a novel type of ultranodal superconducting state with Bogoliubov Fermi surfaces (BFSs). Although such BFSs in centrosymmetric superconductors are expected to be topologically protected, the impurity effect of this exotic superconducting state remains elusive experimentally. Here, we investigate the impact of controlled defects introduced by electron irradiation on the superconducting state of tetragonal FeSe_{1-x}S_{x} (0.18≤x≤0.25). The temperature dependence of magnetic penetration depth is initially consistent with a model with BFSs in the pristine sample. After irradiation, we observe a nonmonotonic evolution of low-energy excitations with impurity concentrations. This nonmonotonic change indicates a transition from nodal to nodeless, culminating in gapless with Andreev bound states, reminiscent of the nodal s_{±} case. This points to the accidental nature of the possible BFSs in tetragonal FeSe_{1-x}S_{x}, which are susceptible to disruption by the disorder.

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

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

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

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

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

Bridging Structural Inhomogeneity to Functionality: Pair Distribution Function Methods for Functional Materials Development

The correlation between structure and function lies at the heart of materials science and engineering. Especially, modern functional materials usually contain inhomogeneities at an atomic level, endowing them with interesting properties regarding electrons, phonons, and magnetic moments. Over the past few decades, many of the key developments in functional materials have been driven by the rapid advances in short-range crystallographic techniques. Among them, pair distribution function (PDF) technique, capable of utilizing the entire Bragg and diffuse scattering signals, stands out as a powerful tool for detecting local structure away from average. With the advent of synchrotron X-rays, spallation neutrons, and advanced computing power, the PDF can quantitatively encode a local structure and in turn guide atomic-scale engineering in the functional materials. Here, the PDF investigations in a range of functional materials are reviewed, including ferroelectrics/thermoelectrics, colossal magnetoresistance (CMR) magnets, high-temperature superconductors (HTSC), quantum dots (QDs), nano-catalysts, and energy storage materials, where the links between functions and structural inhomogeneities are prominent. For each application, a brief description of the structure-function coupling will be given, followed by selected cases of PDF investigations. Before that, an overview of the theory, methodology, and unique power of the PDF method will be also presented.

Bose-Einstein condensation superconductivity induced by disappearance of the nematic state

The crossover from the superconductivity of the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime holds a key to understanding the nature of pairing and condensation of fermions. It has been mainly studied in ultracold atoms, but in solid systems, fundamentally previously unknown insights may be obtained because multiple energy bands and coexisting electronic orders strongly affect spin and orbital degrees of freedom. Here, we provide evidence for the BCS-BEC crossover in iron-based superconductors FeSe_{1 - x} S _x from laser-excited angle-resolved photoemission spectroscopy. The system enters the BEC regime with x = 0.21, where the nematic state that breaks the orbital degeneracy is fully suppressed. The substitution dependence is opposite to the expectation for single-band superconductors, which calls for a new mechanism of BCS-BEC crossover in this system.

Negative curvature hollow-core anti-resonant fiber for terahertz sensing

Hollow-core fibers are advantageous for chemical sensing as they facilitate liquid infiltration into the core over conventional porous core fiber. In addition, the requirement of less bulk material significantly decreases the effective material loss (EML). In this paper, a six circular cladding tube negative curvature hollow-core fiber (NC-HCF) is proposed for chemical sensing. Five different chemicals including chloroform, polylactic acid, CCL₃, glycerin, and benzene are proposed to fill the core of the NC-HCF, and sensitivities are evaluated by full vector finite element method-based COMSOL software. Numerical results reveal that the proposed sensor exhibits very high relative sensitivity in a wide range of frequency. The fabrication of the proposed fiber is feasible by existing fabrication facilities as it contains realistic fabrication parameters. Hence, the proposed sensor can potentially be used as a chemical sensor especially in the medical, food, and industrial sectors as the five chemicals mentioned above carry great medical and food significance.

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.

Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals

A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong on site Hund's interactions develop intra-atomic tRVBs between the t_{2g} orbitals. On doping, the presence of two iron atoms per unit cell allows these interorbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of on site pair correlations, detectable as an alternating π phase shift in a scanning Josephson tunneling microscope.

Raman Response in the Nematic Phase of FeSe

Raman experiments on bulk FeSe revealed that the low-frequency part of the B_{1g} Raman response R_{B1g}(Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at T_{n}∼85  K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below T_{n}. We argue that the drop of R_{B1g}(Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B_{1g} Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R_{B1g}(Ω). We also show that the enhancement of the B_{1g} Raman response near T_{n} is consistent with the sign change of the nematic order parameter between hole and electron pockets.

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

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

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

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

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

Superconductivity in FeSe: The Role of Nematic Order

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