Imaging atomic-scale effects of high-energy ion irradiation on superconductivity and vortex pinning in Fe(Se,Te)

Topologically trivial gap-filling in superconducting Fe(Se,Te) by one-dimensional defects

Structural distortions and imperfections are a crucial aspect of materials science, on the macroscopic scale providing strength, but also enhancing corrosion and reducing electrical and thermal conductivity. At the nanometre scale, multi-atom imperfections, such as atomic chains and crystalline domain walls have conversely been proposed as a route to topological superconductivity, whose most prominent characteristic is the emergence of Majorana Fermions that can be used for error-free quantum computing. Here, we shed more light on the nature of purported domain walls in Fe(Se,Te) that may host 1D dispersing Majorana modes. We show that the displacement shift of the atomic lattice at these line-defects results from sub-surface impurities that warp the topmost layer(s). Using the electric field between the tip and sample, we manage to reposition the sub-surface impurities, directly visualizing the displacement shift and the underlying defect-free lattice. These results, combined with observations of a completely different type of 1D defect where superconductivity remains fully gapped, highlight the topologically trivial nature of 1D defects in Fe(Se,Te).

Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba0.2K0.8Fe2As2 Superconductor

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba1-xKxFe2As2, x = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting Tc, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

Nanoscale Manipulation of Wrinkle-Pinned Vortices in Iron-Based Superconductors

The controlled manipulation of Abrikosov vortices is essential for both fundamental science and logical applications. However, achieving nanoscale manipulation of vortices while simultaneously measuring the local density of states within them remains challenging. Here, we demonstrate the manipulation of Abrikosov vortices by moving the pinning center, namely one-dimensional wrinkles, on the terminal layers of Fe(Te,Se) and LiFeAs, by utilizing low-temperature scanning tunneling microscopy/spectroscopy (STM/S). The wrinkles trap the Abrikosov vortices induced by the external magnetic field. In some of the wrinkle-pinned vortices, robust zero-bias conductance peaks are observed. We tailor the wrinkle into short pieces and manipulate the wrinkles by using an STM tip. Strikingly, we demonstrate that the pinned vortices move together with these wrinkles even at high magnetic field up to 6 T. Our results provide a universal and effective routine for manipulating wrinkle-pinned vortices and simultaneously measuring the local density of states on the iron-based superconductor surfaces.

Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors

Bound states in superconductors are expected to exhibit a spatially resolved electron-hole asymmetry which is the hallmark of their quantum nature. This asymmetry manifests as oscillations at the Fermi wavelength, which is usually tiny and thus washed out by thermal broadening or by scattering at defects. Here we demonstrate theoretically and confirm experimentally that, when coupled to magnetic impurities, bound states in a vortex core exhibit an emergent axial electron-hole asymmetry on a much longer scale, set by the coherence length. We study vortices in 2H-NbSe2 and in 2H-NbSe1.8S0.2 with magnetic impurities, characterizing these with detailed Hubbard-corrected density functional calculations. We find that the induced electron-hole imbalance depends on the band character of the superconducting material. Our results show that coupling between quantum bound states in superconductors is remarkably robust and has a strong influence in tunneling measurements.

Scaling laws for ion irradiation effects in iron-based superconductors

We report on ion irradiation experiments performed on compounds belonging to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BaFe}_2\hbox {As}_2$$\end{document}BaFe2As2 family, each one involving the partial substitution of an atom of the parent compound (K for Ba, Co for Fe, and P for As), with an optimal composition to maximize the superconducting critical temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_c$$\end{document}Tc. Employed ion beams were 3.5-MeV protons, 250-MeV Au ions, and 1.2-GeV Pb ions, but additional data from literature are also considered, thus covering a wide range of ions and energies. Microwave characterization based on the use of a coplanar waveguide resonator allowed us to investigate the irradiation-induced \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_c$$\end{document}Tc degradation, as well as the increase of normal state resistivity and London penetration depth. The damage was quantified in terms of displacements per atom (dpa). From this broad and comprehensive set of experimental data, clear scaling laws emerge, valid in the range of moderate irradiation-induced disorder (dpa up to 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}× 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-3}$$\end{document}-3 were investigated). In these conditions, linear trends with dpa were found for all the modification rates, while a power law dependence on the ion energy was found for heavy-ion irradiation. All these scaling laws are reported and discussed throughout the paper.

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

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.

Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)

Majorana quasiparticles in condensed matter are important for topological quantum computing^1-3, but remain elusive. Vortex cores of topological superconductors may accommodate Majorana quasiparticles that appear as the Majorana bound state (MBS) at zero energy^4,5. The iron-based superconductor Fe(Se,Te) possesses a superconducting topological surface state^6-9 that was investigated by scanning tunnelling microscopy (STM) studies, which suggest such a zero-energy vortex bound state (ZVBS)^10,11. Here we present ultrahigh energy-resolution spectroscopic imaging (SI)-STM to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 ± 20 μeV, which constrained its MBS origin, and showed that some vortices host the ZVBS but others do not. We show that the fraction of vortices hosting the ZVBS decreases with increasing magnetic field and that local quenched disorders are not related to the ZVBS. Our observations elucidate the necessary conditions to realize the ZVBS, which paves the way towards controllable Majorana quasiparticles.

A Review of Recent Applications of Ion Beam Techniques on Nanomaterial Surface Modification: Design of Nanostructures and Energy Harvesting

Nanomaterials have gained plenty of research interest because of their excellent performance, which is derived from their small size and special structure. In practical applications, to acquire nanomaterials with high performance, many methods have been used to modulate the structure and components of materials. To date, ion beam techniques have extensively been applied for modulating the performance of various nanomaterials. Energetic ion beams can modulate the surface morphology and chemical components of nanomaterials. In addition, ion beam techniques have also been used to fabricate nanomaterials, including 2D materials, nanoparticles, and nanowires. Compared with conventional methods, ion beam techniques, including ion implantation, ion irradiation, and focused ion beam, are all pure physical processes; these processes do not introduce any impurities into the target materials. In addition, ion beam techniques exhibit high controllability and repeatability. Here, recent progress in ion beam techniques for nanomaterial surface modification is systematically summarized and existing challenges and potential solutions are presented.

Glassy Dynamics in a heavy ion irradiated NbSe2 crystal

Fascination with glassy states has persisted since Fisher introduced the vortex-glass as a new thermodynamic phase that is a true superconductor that lacks conventional long-range order. Though Fisher's original model considered point disorder, it was later predicted that columnar defects (CDs) could also induce glassiness - specifically, a Bose-glass phase. In YBa2Cu3O7-x (YBCO), glassy states can cause distinct behavior in the temperature (T ) dependent rate of thermally activated vortex motion (S). The vortex-glass state produces a plateau in S(T ) whereas a Bose-glass can transition into a state hosting vortex excitations called double-kinks that can expand, creating a large peak in S(T ). Although glass phases have been well-studied in YBCO, few studies exist of other materials containing CDs that could contribute to distinguishing universal behavior. Here, we report on the effectiveness of CDs tilted ~30° from the c-axis in reducing S in a NbSe2 crystal. The magnetization is 5 times higher and S is minimized when the field is parallel to the defects versus aligned with the c-axis. We see signatures of glassiness in both field orientations, but do not observe a peak in S(T ) nor a plateau at values observed in YBCO. Finally, we discuss the possibility that competing disorder induces a field-orientation-driven transition from a Bose-glass to an anisotropic glass involving both point and columnar disorder.

Evidence for Majorana bound states in an iron-based superconductor

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe_0.55Se_0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

Observation of topological superconductivity on the surface of an iron-based superconductor

Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. By using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe_1-x Se _x (x = 0.45; superconducting transition temperature T_c = 14.5 kelvin) hosts Dirac-cone-type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below T_c Our study shows that the surface states of FeTe_0.55Se_0.45 are topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.

Discrete energy levels of Caroli-de Gennes-Matricon states in quantum limit in FeTe0.55Se0.45

Caroli-de Gennes-Matricon (CdGM) states were predicted in 1964 as low-energy excitations within vortex cores of type-II superconductors. In the quantum limit, the energy levels of these states were predicted to be discrete with the basic levels at ±μΔ2/EF (μ = 1/2, 3/2, 5/2, …) with Δ the superconducting energy gap and EF the Fermi energy. However, due to the small ratio of Δ/EF in most type-II superconductors, it is very difficult to observe the discrete CdGM states, but rather a symmetric peak which appears at zero bias at the vortex center. Here we report the clear observation of these discrete energy levels of CdGM states in FeTe0.55Se0.45. The rather stable energies of these bound state peaks vs. space clearly validate our conclusion. Analysis based on the energies of these CdGM states indicates that the Fermi energy in the present system is very small.

Effects of disorder induced by heavy-ion irradiation on (Ba1-x K x )Fe2As2 single crystals, within the three-band Eliashberg s± wave model

One of the open issues concerning iron-based superconductors is whether the s± wave model is able to account for the overall effects of impurity scattering, including the low rate of decrease of the critical temperature with the impurity concentration. Here we investigate Ba_1-x K _x Fe₂As₂ crystals where disorder is introduced by Au-ion irradiation. Critical temperature, T _c , and London penetration depth, λ _L , were measured by a microwave resonator technique, for different values of the irradiation fluence. We compared experimental data with calculations made on the basis of the three-band Eliashberg equations, suitably accounting for the impurity scattering. We show that this approach is able to explain in a consistent way the effects of disorder both on T _c and on λ _L (T), within the s± wave model. In particular, a change of curvature in the low-temperature λ _L (T) curves for the most irradiated crystals is fairly well reproduced.

Vortices in high-performance high-temperature superconductors

The behavior of vortex matter in high-temperature superconductors (HTS) controls the entire electromagnetic response of the material, including its current carrying capacity. Here, we review the basic concepts of vortex pinning and its application to a complex mixed pinning landscape to enhance the critical current and to reduce its anisotropy. We focus on recent scientific advances that have resulted in large enhancements of the in-field critical current in state-of-the-art second generation (2G) YBCO coated conductors and on the prospect of an isotropic, high-critical current superconductor in the iron-based superconductors. Lastly, we discuss an emerging new paradigm of critical current by design-a drive to achieve a quantitative correlation between the observed critical current density and mesoscale mixed pinning landscapes by using realistic input parameters in an innovative and powerful large-scale time dependent Ginzburg-Landau approach to simulating vortex dynamics.

Topological Superconductivity on the Surface of Fe-Based Superconductors

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.