Fe-based Superconductors Research Articles

Observation of Zero-Energy Modes with Possible Time-Reversal Symmetry Breaking on Step Edge of CaKFe4As4

Abstract Topologically nontrivial Fe-based superconductors attract extensive attentions due to their ability of hosting Majorana zero modes (MZMs) which could be used for topological quantum computation. Topological defects such as vortex lines are required to generate MZMs. Here, we observe the robust edge states along the surface steps of CaKFe4As4. Remarkably, the tunneling spectra show a sharp zero-bias peak (ZBP) with multiple integer-quantized states at the step edge under zero magnetic field. We propose that the increasing hole doping around step edges may drive the local superconductivity into a state with possible spontaneous time-reversal symmetry breaking. Consequently, the ZBP can be interpreted as an MZM in an effective vortex in the superconducting topological surface state by proximity to the center of a tri-junction with different superconducting order parameters. Our results provide new insights into the interplay between topology and unconventional superconductivity, and pave a new path to generate MZMs without magnetic field.

Seebeck and Nernst effects in the mixed state of strongly fluctuating superconductors

We study Seebeck and Nernst effects in strongly fluctuating superconductors by calculating the Seebeck and Nernst coefficients in the Ginzburg–Landau Lawrence–Doniach model with thermal noise. Strongly thermal fluctuations are represented by the Langevin thermal noise. To capture the interesting fluctuation effects, we use the self-consistent Gaussian approximation to treat cubic term in the equation of motion. Our results including all Landau levels are to treat arbitrary magnetic fields. The Seebeck and Nernst coefficients are calculated for arbitrary temperature and magnetic field. The results are compared to experimental data on Fe-based superconductor Fe1+yTe0.6Se0.4 in both the superconducting state below the critical temperature Tc and the normal state above Tc. Our calculation supports the picture of phase disordering of fluctuations above Tc in Fe-based superconductors.

Investigating the role of anion polarizability in Fe-based superconductors via light-matter interaction

Investigating the role of anion polarizability in Fe-based superconductors via light-matter interaction

Evidence of electron interaction with an unidentified bosonic mode in superconductor CsCa2Fe4As4F2

The kink structure in band dispersion usually refers to a certain electron-boson interaction, which is crucial in understanding the pairing in unconventional superconductors. Here we report the evidence of the observation of a kink structure in Fe-based superconductor CsCa2Fe4As4F2 using angle-resolved photoemission spectroscopy. The kink shows an orbital selective and momentum dependent behavior, which is located at 15 meV below Fermi level along the Γ−M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma -{{\\rm{{M}}}}$$\\end{document} direction at the band with dxz orbital character and vanishes when approaching the Γ−X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma -{{\\rm{{X}}}}$$\\end{document} direction, correlated with a slight decrease of the superconducting gap. Most importantly, this kink structure disappears when the superconducting gap closes, indicating that the corresponding bosonic mode (~9±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9\\pm 1$$\\end{document} meV) is closely related to superconductivity. However, the origin of this mode remains unidentified, since it cannot be related to phonons or the spin resonance mode (~15 meV) observed by inelastic neutron scattering. The behavior of this mode is rather unique and challenges our present understanding of the superconducting paring mechanism of the bilayer FeAs-based superconductors.

Enhancement of superconductivity and structural phase transitions under pressure in FeTe0.89S0.11

The ternary iron chalcogenide, FeTe0.89S0.11 is a prominent member of the family of Fe-based superconductors with an ambient pressure Tc of around 8 K and a simple structure formed by layers of edge-sharing distorted tetrahedra separated by a van der Waals gap. Upon compression to 6 GPa, the Tc increases monotonically to 11 K. The superconductivity disappeared at about 6 GPa which was correlated to a softening of a Raman mode. High-resolution synchrotron X-ray diffraction shows that the FeTe0.89S0.11 started to transform from the monoclinic phase described by space group Cm to a disordered triclinic phase described by space group P1 at around 10 GPa (theoretical) - 14 GPa (experimental). Due to the phase transition the studied material transforms from a layered compound to a polymer, which is accompanied by a volume collapse of 4.65 %, indicating a discontinuous first-order phase transition. The disappearance of Raman modes, along with pressure independent resistivity, and ab initio calculations results support the structural and electronics phase transition. According to our results Fe(Te,S) may be useful for future high-field power applications being formed of relatively inexpensive and nontoxic elements.

Towards revealing intrinsic vortex-core states in Fe-based superconductors through statistical discovery

In type-II superconductors, electronic states within magnetic vortices hold crucial information about the paring mechanism and can reveal non-trivial topology. While scanning tunneling microscopy/spectroscopy (STM/S) is a powerful tool for imaging superconducting vortices, it is challenging to isolate the intrinsic electronic properties from extrinsic effects like subsurface defects and disorders. Here we combine STM/STS with basic machine learning to develop a method for screening out the vortices pinned by embedded disorder in iron-based superconductors. Through a principal component analysis of large STS data within vortices, we find that the vortex-core states in Ba(Fe0.96Ni0.04)2As2 start to split into two categories at certain magnetic field strengths, reflecting vortices with and without pinning by subsurface defects or disorders. Our machine-learning analysis provides an unbiased approach to reveal intrinsic vortex-core states in novel superconductors and shed light on ongoing puzzles in the possible emergence of a Majorana zero mode.

Particle-hole mixed Bogoliubov quasiparticles and Cooper instability in single-unit-cell FeSe/SrTiO3 films

In conventional superconductors, Bogoliubov quasiparticles and Cooper instability provide a paradigm to describe the superconducting state and the superconducting transition, respectively. However, whether these concepts can be adapted to describe Fe-based superconductors requires rigorous examinations from experiments. Here, we report angle-resolved photoemission studies on single-layer FeSe films grown on SrTiO3 substrate. Due to the improved clarity, our results reveal both particle and hole branches of the energy band with clear quasiparticles. The dispersion and coherence factors are extracted, which unveil the particle-hole mixed Bogoliubov quasiparticles in the superconducting state of the FeSe/STO films. Effective pairing susceptibility is also deduced as a function of temperature, which indicates the persistence of Cooper instability in Fe-based superconductors.

Enhancement of the critical current by surface irregularities in Fe-based superconductors

The critical current Ic of single crystals of the iron pnictide superconductor BaFe2(As 1−x P x )2 has been studied through measurements of magnetic hysteresis cycles. We show that the introduction of micrometer-scale irregularities on the surface significantly increases Ic , primarily near the irreversibility magnetic field Hirr . The observed increase can be attributed to a non-dissipative surface current that arises from the collective bending of the vortex lattice at the sample surface, enabled by the surface irregularities. This mechanism, which is not pinning in the proper sense, has previously been studied in clean, low- Tc , metallic superconductors, but had not been investigated in Fe-based superconductors. The observed increase in Ic is consistent with a theoretical estimate based on the Mathieu-Simon continuum theory of the vortex state.

Phase diagram simulations incorporating the gap anisotropy with AFM spin and charge density wave under spin-orbital coupling in Fe-based superconductors

For over a decade, iron-based superconductors (IBSCs) have been the subject of intense scientific research, yet the underlying principle of their pairing mechanism remains elusive. To address this, we have developed a simulation tool that reasonably predicts the regional superconducting phase diagrams of key IBSCs, incorporating factors such as anisotropic superconducting gap, spin-orbital coupling, electron-phonon coupling, antiferromagnetism, spin density wave, and charge transfer. Our focus has been on bulk FeSe, LiFeAs, NaFeAs, and FeSe films on SrTiO3 substrates. By incorporating angle-resolved photoemission spectroscopy (ARPES) data to fine-tune the electron concentration in the superconducting state, our simulations have successfully predicted the theoretical superconducting transition temperature (Tc) of these compounds, closely matching experimental results. Our research not only aids in identifying patterns and establishing correlations with Tc but also provides a simulation tool for potentially predicting high-pressure phase diagrams.

Spin-charge-lattice couplings and Co doping effect in Ba(Fe 1−x Co x )2As2: an ab initio molecular dynamics study

As one of the typical iron-based superconductors, Ba(Fe 1−x Co x )2As2 exhibits a dome-like evolution of superconducting transition temperature T c with the Co doping (x), which provides an ideal platform to explore the mechanism of unconventional superconductivity. Through ab initio molecular dynamics (AIMD) studies, we find that the spin, charge, and lattice degrees of freedom in Ba(Fe 1−x Co x )2As2 are intimately coupled with a characteristic frequency around 5.5 THz, which originates from the A1g phonon mode of the As atoms. Compared with the undoped BaFe2As2, the spin dynamics in Ba(Fe 1−x Co x )2As2 (x = 0.0625, 0.1250, 0.1875) shows enhanced spatial inhomogeneities, though the features of the charge dynamics are rarely modified. Along with the increasing Co doping, the spatial inhomogeneities of Fe spin dynamics display nonmonotonic changes, meanwhile the lattice vibrational spectra first show peak broadening and then restore the main peak around 5.5 THz, being both consistent with the nonmonotonic behavior of superconducting T c. Our study provides a molecular dynamics approach to investigate the couplings of spin, charge, and lattice in doped BaFe2As2, which could also be applied to explore the dome-like evolution of superconductivity in other Fe-based superconductors.

Uniaxial stress effect on the electronic structure of quantum materials

Uniaxial stress has proven to be a powerful experimental tuning parameter for effectively controlling lattice, charge, orbital, and spin degrees of freedom in quantum materials. In addition, its ability to manipulate the symmetry of materials has garnered significant attention. Recent technical progress to combine uniaxial stress cells with quantum oscillation and angle-resolved photoemission techniques allowed to study the electronic structure as function of uniaxial stress. This review provides an overview on experimental advancements in methods and examines studies on diverse quantum materials, encompassing the semimetal WTe2, the unconventional superconductor Sr2RuO4, Fe-based superconductors, and topological materials.

Superconductivity in a Layered Cobalt Oxychalcogenide Na2CoSe2O with a Triangular Lattice.

Unconventional superconductivity in bulk materials under ambient pressure is extremely rare among the 3d transition metal compounds outside the layered cuprates and iron-based family. It is predominantly linked to highly anisotropic electronic properties and quasi-two-dimensional (2D) Fermi surfaces. To date, the only known example of a Co-based exotic superconductor is the hydrated layered cobaltate, NaxCoO2·yH2O, and its superconductivity is realized in the vicinity of a spin-1/2 Mott state. However, the nature of the superconductivity in these materials is still a subject of intense debate, and therefore, finding a new class of superconductors will help unravel the mysteries of their unconventional superconductivity. Here, we report the discovery of superconductivity at ∼6.3 K in our newly synthesized layered compound Na2CoSe2O, in which the edge-shared CoSe6 octahedra form [CoSe2] layers with a perfect triangular lattice of Co ions. It is the first 3d transition metal oxychalcogenide superconductor with distinct structural and chemical characteristics. Despite its relatively low TC, this material exhibits very high superconducting upper critical fields, μ0HC2(0), which far exceeds the Pauli paramagnetic limit by a factor of 3-4. First-principles calculations show that Na2CoSe2O is a rare example of a negative charge transfer superconductor. This cobalt oxychalcogenide with a geometrical frustration among Co spins shows great potential as a highly appealing candidate for the realization of unconventional and/or high-TC superconductivity beyond the well-established Cu- and Fe-based superconductor families and opens a new field in the physics and chemistry of low-dimensional superconductors.

Electronic, optical, and thermoelectric characteristics of (Ae)xFBiS2 (Ae=Sr, Ba, and x=1.7) layered materials useful in optical modulator devices

The recent discovery of superconductivity behavior in the mother BiS2-layered compounds has captivated the attention of several physicists. The crystal structure of superconductors with alternate layers of BiS2 is homologous to that of cuprates and Fe-based superconductors. The full-potential linearized augmented plane-wave (FP-LAPW) technique was utilized to investigate the electronic structures and density of states in the vicinity of the Fermi energy of SrFBiS2 and BaFBiS2 compounds under the electron carriers doping. The introduction of electron doping (carries doping) reveals that the host compounds SrFBiS2 and BaFBiS2 exhibit features indicative of superconductivity. This carrier doping of SrFBiS2 and BaFBiS2 compounds (electron-doped) has a significant impact on the lowest conduction states near the Fermi level for the emergence of the superconducting aspect. The electron doping modifies and induces changes in the electronic structures with superconducting behavior in (Ae)1.7FBiS2(Ae=Sr,Ba) compounds. A Fermi surface nesting occurred under the modification of electrons (carriers) doping in the host compounds SrFBiS2 and BaFBiS2. Furthermore, the optical characteristics of the carrier-doped SrFBiS2 and BaFBiS2 compounds are simulated. Due to the anisotropic behavior, the optical properties of these materials based on BiS2 demonstrate a pronounced polarization dependency. The starting point at zero photon energy in the infrared region is elucidated by considering the Drude features in the optical conductivity spectra of SrFBiS2 and BaFBiS2 compounds, when the electron carriers doping is applied. It was clearly noticed that the spin-orbit coupling (SOC) influences the electronic band structures, density of states, Femi surface, and optical features because of the heavy Bismuth atom, which may disclose fascinating aspects. Further, we conducted simulations to assess the thermoelectric properties of these mother compounds. The two BiS2-layered compounds could be suitable for practical thermoelectric purposes and are highlighted through assessment of electrical conductivity, thermal conductivity, Seebeck coefficient, and power factor. As a result, we propose that the mechanisms of superconducting behavior in BiS2 family may pave new avenues for investigating the field of unconventional superconductivity. It may also provide new insights into the origin of high-Tc superconductivity nature.

Driven charge density modulation by spin density wave and their coexistence interplay in SmFeAsO: A first-principles study

We use density functional theory to investigate effects of spin-orbit coupling and single-stripe-type antiferromagnetic (sAFM) ordering on the crystal structure and electronic properties of SmFeAsO. The results indicate that AFM ordering causes the crystal structure transition from tetragonal to orthorhombic, along with increase in the height of As atoms from Fe layer due to magnetostriction. It also leads to the opening of partial band gaps, the emergence of a prominent peak near Fermi energy (EF) in the density of states (DOS) and a reduction in Fermi surface nesting. The study finds a correlation between the calculated area under the DOS curve, spanning from EF to the first peak above it, and the optimal electron-doped concentration required for inducing superconductivity in SmFeAsO. The findings suggest that spin and charge density waves can play important roles in the superconducting mechanism of Fe-based superconductors. Our calculations demonstrate that spin-orbit coupling reduces electronic correlation.

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1−xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1−xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

THERMODYNAMIC MAGNETIC FIELD AND SPECIFIC HEAT JUMP OF IRON-BASED SUPERCONDUCTOR BY TWO-BAND GINZBURG-LANDAU APPROACH

In this research, temperature-dependent thermodynamic magnetic field and specific heat jump of Fe-based superconductor were studied by two-band Ginzburg-Landau theory. The analytical form of the thermodynamic magnetic field was investigated by four temperature-dependent models; Chen’s model, Zhu’s model, Shanenko’s model and Changjan & Udomsamuthirun’s model. For the calculation of specific heat jump, we use the Ruthgers expression. Calculation findings indicate an inverse relationship between the critical temperature and the specific heat jump. When compared with various models, the results from Changjan and Udomsamuthirun's models suit experimental data of Ba1-xKxFe2As2 (x = 0.4) and KFe2As2 superconductors better

Influences of quenching treatment and cobalt-doping on the thermally activated flux-flow behavior in KCa2(FeCo )4As4F2

Owing to the unique double-FeAs-layered structure between neighboring insulating layers, the 12442-type Fe-based superconductors are expected to host rich vortex phenomena in the mixed state. Here, we report a systematic investigation on the influences of quenching treatment and cobalt-doping on the magnetic vortex dynamics of KCa2(FeCo x )4As4F2 (x = 0, 0.1) single crystals via electrical transport measurements. It is found that the slopes of the upper critical field near Tc , along both directions ( and ), are doubled by the cobalt-doping with x = 0.1. The activation energy is acquired by analyzing the Arrhenius plots, which shows a H −α dependence with a change in the exponent α at around 3 T, indicating the evolution of the dominant pinning mechanisms in different field regions. Importantly, the quenching treatment obviously enhances the magnitude of activation energy and critical current density J c, which can be suppressed by the introduction of cobalt-doping. Possible mechanisms for such evolutions of these important parameters are discussed. Our results emphasize the important role of quenching treatment in enhancing the activation energy and critical current density in 12442 system.

Infinite-layer nickelates as Ni-eg Hund’s metals

The recent and exciting discovery of superconductivity in the hole-doped infinite-layer nickelate Nd1−δSrδNiO2 draws strong attention to correlated quantum materials. From a theoretical view point, this class of unconventional superconducting materials provides an opportunity to unveil a physics hidden in correlated quantum materials. Here we study the temperature and doping dependence of the local spectrum as well as the charge, spin and orbital susceptibilities from first principles. By using ab initio LQSGW+DMFT methodology, we show that onsite Hund’s coupling in Ni-d orbitals gives rise to multiple signatures of Hund’s metallic phase in Ni-eg orbitals. The proposed picture of the nickelates as an eg (two orbital) Hund’s metal differs from the picture of the Fe-based superconductors as a five orbital Hund’s metal as well as the picture of the cuprates as doped charge transfer insulators. Our finding uncover a new class of the Hund’s metals and has potential implications for the broad range of correlated two orbital systems away from half-filling.

Interplay of Magnetic Interaction and Electronic Structure in New Structure RE-12442 Type Hybrid Fe-Based Superconductors

We present detailed first-principles density functional theory-based studies on RbRE2Fe4As4O2 (RE = Sm, Tb, Dy, Ho) hybrid 12442-type iron-based superconducting compounds with particular emphasis on competing magnetic interactions and their effect on possible magneto-structural coupling and electronic structure. The stripe antiferromagnetic (sAFM) pattern across the xy plane emerges as the most favorable spin configuration for all the four compounds, with close competition among the different magnetic orders along the z-axis. The structural parameters, including arsenic heights, Fe-As-Fe angle, and other relevant factors that influence superconducting Tc and properties, closely match the experimental values in stripe antiferromagnetic arrangement of Fe spins. Geometry optimization with inclusion of explicit magnetic ordering predicts a spin–lattice coupling for all the four compounds, where a weak magneto–structural transition, a tetragonal-to-orthorhombic structural transition, takes place in the relaxed stripe antiferromagnetic spin configuration. Absence of any experimental evidence of such structural transition is possibly an indication of nematic transition in RE-12442 compounds. As a result of structural distortion, the lattice contracts (expands) along the direction with parallel (anti-parallel) alignment of Fe spins. Introduction of stripe antiferromagnetic order in Fe sub-lattice reconstructs the low-energy band structure, which results in significantly reduced number of bands crossing the Fermi level. Moreover, the dispersion of bands and their orbital characteristics also are severely modified in the stripe antiferromagnetic phase similar to BaFe2As2. Calculations of exchange parameters were performed for all the four compounds. Exchange coupling along the anti-parallel alignment of Fe spins J1a is larger than that for the parallel aligned spins J1b. A crossover between the super-exchange-driven in-plane next-nearest-neighbor exchange coupling J2 and in-plane exchange coupling J1a due to lanthanide substitution was found. A large super-exchange-driven next-nearest-neighbor exchange interaction is justified using the construction of 32 maximally localized Wannier functions, where the nearest-neighbor Fe-As hopping amplitudes were found to be larger than the nearest- and the next-nearest-neighbor Fe-Fe hopping amplitudes. We compare the hopping parameters in the stripe antiferromagnetic pattern with non-magnetic configuration, and increased hopping amplitude was found along the anti-parallel spin alignment with more majority-spin electrons in Fe dxz and dxy but not in Fe dyz. On the other hand, the hopping amplitudes are increased in stripe antiferromagnetic phase along the parallel spin alignment with more majority-spin electrons in only Fe dyz. This difference in hopping amplitudes in the stripe antiferromagnetic order enables more isotropic hopping.

Kramers Fulde-Ferrell state and superconducting spin diode effect

We study a novel Fulde-Ferrell equal-spin pairing state with opposite center of mass Cooper pair momentum for each spin polarization. This state respects time-reversal symmetry and is dubbed a Kramers Fulde-Ferrell (KFF) state. It can be realized in a one-dimensional system with spin-orbit coupling and nearest neighbor attraction. We find that the KFF state supports nonreciprocal spin transport for both bulk superconductor and Josephson junctions when inversion symmetry is broken. In addition to the spin Josephson diode effect, the charge transport is controlled by intriguing dynamics of bound states whose transitions can be manipulated by the length of the KFF superconductor. We discuss the relevance of the effective theory to the novel physics observed in monolayer Fe-based superconductor along line defects and domain walls, and the potential for using spins to make dissipationless superconducting spintronics.