Table of contents

The past four years of incredibly intense research into Fe-based superconductors have brought about many unexpected surprises. Our understanding of their behavior and physical properties is constantly evolving. Unlike any other superconductors, those containing iron span diverse groups of materials: pnictides, chalcogenides, intermetallics and oxides. Some major properties of the materials are quite similar, yet each group has its own distinct features. Significant effort has been put into identifying new superconducting compositions, modifying the existing ones with new dopants and treatments, and producing single crystals, thin films, wires and polycrystalline bulk material. A wide array of experimental techniques was applied to study Fe-based superconductors and the result is a tremendous amount of data collected over a period of less than four years. Theoretical debates are still lively, and there is an ongoing search for possible universalities and commonalities with other unconventional superconductors, like high-T_c cuprates or heavy fermion materials.

The three-dimensional electronic structures of Fe-based superconductors, as well as their extreme sensitivity to disorder, present serious challenges for both theoretical analysis and the interpretation of experiments. However, some key properties emerge from multiple studies. Unconventional, multiband superconductivity originating from an electronic mechanism has found both experimental and theoretical support. There has been great progress in the understanding of various anisotropies of superconducting gap structures, including the possibility of gap nodes even if the gap symmetry is s-wave. Similar to high-T_c cuprates, the superconducting phase has a dome-like shape on T-doping or T-pressure phase diagrams. The anisotropy of the superconducting gap evolves with doping and is likely to become stronger at the dome's edge. In many Fe-based superconductors there is a range where superconductivity coexists and competes with long-range magnetic order, and magnetic fluctuations are considered by some to be of the utmost importance for the pairing mechanism. Others argue that orbital fluctuations, possibly in combination with phonons, are crucial for the pairing.

Fe-based superconductors show extremely large upper critical fields and relatively low electronic anisotropy, which are crucial aspects for power applications. The expectations are high, though it remains unclear what maximal current densities can be supported by a properly designed bulk material with optimal pinning centers.

This focus issue of Superconductor Science and Technology is a snapshot of some of the recent progress in materials preparation, experiments and theory. It includes articles on the search for new Fe-based superconductors and on the search for superconductivity at extreme conditions. Particular attention is devoted to: the effects of chemical substitutions; the development of thin films; the introduction of artificial defects to increase critical current density; and a general analysis of vortex physics. The articles on fundamental aspects of superconductivity include: the discussion of various experimental problems; an in-depth analysis of the nodal and nodeless pairing states; the discussion of the pairing mechanism; and the effects of pair-breaking due to disorder. Also discussed are nematic correlations and the coexistence of magnetism and superconductivity.

The papers collected in this issue present a detailed review of the accomplishments of the last four years of research into Fe-based superconductors, up to and including last-minute developments. We hope that this combination will make this special section of Superconductor Science and Technology both interesting and useful to a broad spectrum of physicists and materials scientists.

We present a theoretical description of the London penetration depth of a multiband superconductor in the case when both superconducting and spin-density wave orders coexist. We focus on clean systems and zero temperature to emphasize the effect of the two competing orders. Our calculation shows that the superfluid density closely follows the evolution of the superconducting order parameter as doping is increased, saturating to a BCS value in the pure superconducting state. Furthermore, we predict a strong anisotropic in-plane penetration depth induced by the spin-density wave order.

We reexamined the experimental evidence for the possible existence of superconducting (SC) gap nodes in the three most suspected Fe-pnictide SC compounds: LaFePO, BaFe₂(As_0.67P_0.33)₂, and KFe₂As₂. We showed that while the T-linear temperature dependence of the penetration depth λ(T) of these three compounds indicates extremely clean nodal gap superconductors, the thermal conductivity data lim_T,H→0 κ_S(H,T)/T unambiguously showed that LaFePO and BaFe₂(As_0.67P_0.33)₂ are extremely dirty, while KFe₂As₂ can possibly be clean. These apparently conflicting experimental data cast a serious doubt on the nodal gap possibility for LaFePO and BaFe₂(As_0.67P_0.33)₂.

We investigate the interplay of onsite Coulomb repulsion and various mechanisms breaking the fourfold lattice symmetry in a three-band model for the iron planes of iron-based superconductors. Using cluster-perturbation theory allows us to locally break the symmetry between the x and y directions without imposing long-range magnetic order. Previously investigated anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. We find that all three mechanisms for a broken rotational symmetry lead to similar signatures once onsite interactions are strong enough to bring the system close to a spin-density wave. The band distortions near the Fermi level are independent of differences between the total densities found in xz and yz orbitals.

In the present paper, we describe how the band structure and the Fermi surface of iron-based superconductors vary as the Fe–As–Fe bond angle changes. We discuss how these Fermi surface configurations affect the superconductivity mediated by spin fluctuations, and show that, in several situations, frustration in the sign of the gap function arises due to the repulsive pairing interactions that requires a sign change of the order parameter. Such a frustration can result in nodes or very small gaps, and generally works destructively against superconductivity. Conversely, we propose that the optimal condition for superconductivity is realized for the Fermi surface configuration that gives the least frustration while maximizing the Fermi surface multiplicity. This is realized when there are three hole Fermi surfaces, where two of them have d_XZ/YZ orbital character and one has d_X²−Y² for all k_z in the three-dimensional Brillouin zone. Looking at the band structures of various iron-based superconductors, the occurrence of such a 'sweet spot' situation is limited to a narrow window.

We investigate how emergent nematic order and nematic fluctuations affect several macroscopic properties of both the normal and superconducting states of the iron pnictides. Due to its magnetic origin, long-range nematic order enhances magnetic fluctuations, leaving distinctive signatures in the spin–lattice relaxation rate, the spin–spin correlation function, and the uniform magnetic susceptibility. This enhancement of magnetic excitations is also manifested in the electronic spectral function, where a pseudogap can open at the hot spots of the Fermi surface. In the nematic phase, electrons are scattered by magnetic fluctuations that are anisotropic in momentum space, giving rise to a non-zero resistivity anisotropy whose sign changes between electron-doped and hole-doped compounds. We also show that due to the magneto-elastic coupling, nematic fluctuations soften the shear modulus in the normal state, but harden it in the superconducting state. The latter effect is an indirect consequence of the competition between magnetism and superconductivity, and also causes a suppression of the orthorhombic distortion below T_c. We also demonstrate that ferro-orbital fluctuations enhance the nematic susceptibility, cooperatively promoting an electronic tetragonal symmetry-breaking. Finally, we argue that T_c in the iron pnictides might be enhanced due to nematic fluctuations of magnetic origin.

We present a microscopic study of the nuclear magnetic relaxation rate 1/T₁ based on the five-orbital model for iron-based superconductors. We mainly discuss the effect of the 'inelastic' quasi-particle damping rate γ due to many-body interaction on the size of the coherence peak, for both s₊₊ and s_±-wave superconducting states. We focus on Ba(Fe_1−xCo_x)₂As₂, and systematically evaluate γ in the normal state from the experimental resistivity, from optimally to overdoped compounds. Next, γ in the superconducting state is calculated microscopically based on second-order perturbation theory. In optimally doped compounds (T_c ∼ 30 K), it is revealed that the coherence peak on 1/T₁T is completely suppressed due to large γ for both s₊₊ and s_±-wave states. On the other hand, in heavily overdoped compounds with T_c < 10 K, the coherence peak could appear for both pairing states, since γ at T_c is quickly suppressed in proportion to ${T}_{\mathrm{c}}^{2}$. By making careful comparison between theoretical and experimental results, we conclude that it is difficult to discriminate between s₊₊ and s_±-wave states from the present experimental results.

We examine the relevance of several major material-dependent parameters to the magnetic softness in iron-based superconductors by means of first-principles electronic structure analysis of their parent compounds. The results are explained in the spin-fermion model where localized spins and orbitally degenerate itinerant electrons coexist and are coupled by Hund's rule coupling. We found that the difference in strength of the Hund's rule coupling term is the major material-dependent microscopic parameter for determining the ground-state spin pattern. The magnetic softness in iron-based superconductors is essentially driven by the competition between the double-exchange ferromagnetism and the superexchange antiferromagnetism.

Various kinds of energetic particles are irradiated into iron-based superconductors, and their effects on the critical current density (J_c) and vortex dynamics have been systematically studied. It is found that J_c is enhanced and vortex dynamics is strongly suppressed by energetic particles having a sufficient energy deposition rate, similar to the case of high temperature cuprate superconductors. The enhancement of J_c, in general, persists up to much higher irradiation doses than in cuprates. However, details of the effect of irradiation depend on the kind of ion species and their energies. Even with the same ions and energies, the effect is not universal for different kinds of iron-based superconductors. The correlated nature of defects created by heavy-ion irradiation is confirmed by the angular dependence of irreversible magnetization.

We investigate the effect of external pressure on magnetic order in undoped LnFeAsO (Ln =La, Ce, Pr, Sm) by using muon spin relaxation measurements and ab initio calculations. Both the magnetic transition temperature T_m and the Fe magnetic moment decrease with external pressure. The effect is observed to be lanthanide dependent, with the strongest response for Ln =  La and the weakest for Ln =  Sm. The trend is qualitatively in agreement with our density functional theory calculations. The same calculations allow us to assign a value of 0.68(2) μ_B to the Fe moment, obtained from an accurate determination of the muon sites. Our data further show that the magnetic lanthanide order transitions do not follow the simple trend of Fe, possibly as a consequence of the different f-electron overlap.

The field-angular dependence and anisotropy of the critical current density in iron-based superconductors is evaluated using a phenomenological approach featuring distinct anisotropy factors for the penetration depth and the coherence length. Both the weak collective pinning limit and the strong pinning limit relevant for iron-based superconductors at low magnetic fields are considered. It is found that in the more anisotropic materials, such as SmFeAsO and NdFeAsO, the field-angular dependence is completely dominated by the coherence length (upper critical field) anisotropy, thereby explaining recent results on the critical current in these materials. In less anisotropic superconductors, strong pinning can lead to an apparent inversion of the anisotropy. Finally, it is shown that, under all circumstances, the ratio of the c-axis and ab-plane critical current densities for the magnetic field along the ab-plane directly yields the coherence length anisotropy factor ε_ξ.

We have systematically investigated the effect of annealing on the superconductivity of the iron chalcogenide Fe_1+y(Te_1−xSe_x). The atmospheres used for annealing include O₂, N₂, I₂ vapor, air and vacuum. We observed that annealing in O₂, I₂ and air could enhance the superconductivity of underdoped samples, consistent with the results reported in the literature. Interestingly, we found that annealing in N₂ also leads to a superconductivity enhancement, similar to the annealing effects of O₂, I₂ and air. However, vacuum annealing does not enhance the superconductivity, which indicates that the enhanced superconductivity in O₂-, N₂- , I₂- and air-annealed samples is not due to improved homogeneity. In addition, we treated underdoped samples with nitric acid, which is found to enhance the superconductivity as well. Our analyses of these results support the argument that the superconductivity enhancement, caused either by annealing or nitric acid treatment, originates from the variation of interstitial Fe. The interstitial Fe, which is destructive to superconducting pairing, can be reduced by annealing in oxidation agents or nitric acid treatment. We also find that although N₂-, O₂- and air-annealed samples exhibit strong superconducting diamagnetism with −4πχ ∼ 1 (χ, dc magnetic susceptibility) for some samples, their actual superconducting volume fraction probed by specific heat is low, ranging from 10% to 30% for 0.09 < x < 0.3, indicating that the superconductivity suppression remains significant even in annealed samples. The strong diamagnetism is associated with the superconducting shielding effect on the non-superconducting phase. We have also established the phase diagram of the annealed samples and compared it with that of the as-grown samples. The effect of annealing on the interplay between magnetism and superconductivity is discussed.

We studied the effects of isoelectronic Ru substitution at the Fe site on the energy gaps of optimally F-doped SmFeAsO by means of point-contact Andreev-reflection spectroscopy. The results show that the SmFe_1−xRu_xAsO_0.85F_0.15 system keeps a multigap character at least up to x = 0.50, and that the gap amplitudes Δ₁ and Δ₂ scale almost linearly with the local critical temperature ${T}_{\mathrm{c}}^{A}$. The gap ratios 2Δ_i/k_BT_c remain approximately constant only as long as T_c ≥ 30 K, and increase dramatically when T_c decreases further. This trend seems to be common to many Fe-based superconductors, irrespective of their family. Based on first-principle calculations of the bandstructure and of the density of states projected on the different bands, we show that this trend, as well as the T_c dependence of the gaps and the reduction of T_c upon Ru doping, can be explained within an effective three-band Eliashberg model as being due to a suppression of the superfluid density at finite temperature that, in turn, modifies the temperature dependence of the characteristic spin-fluctuation energy.

The nature of the pairing state in iron-based superconductors is the subject of much debate. Here we argue that in one material, the stoichiometric iron pnictide KFe₂As₂, there is overwhelming evidence for a d-wave pairing state, characterized by symmetry-imposed vertical line nodes in the superconducting gap. This evidence is reviewed, with a focus on thermal conductivity and the strong impact of impurity scattering on the critical temperature T_c. We then compare KFe₂As₂ to Ba_0.6K_0.4Fe₂As₂, obtained by Ba substitution, where the pairing symmetry is s-wave and the T_c is ten times higher. The transition from d-wave to s-wave within the same crystal structure provides a rare opportunity to investigate the connection between band structure and the pairing mechanism. We also compare KFe₂As₂ with the nodal iron-based superconductor LaFePO, for which the pairing symmetry is probably not d-wave, but more likely s-wave with accidental line nodes.

The effects of aliovalent rare earth substitution on the physical properties of Sr_0.3Ca_0.7Fe₂As₂ solid solutions are explored. Electrical transport, magnetic susceptibility and structural characterization data as a function of La substitution into (Sr_1−yCa_y)_1−xLa_xFe₂As₂ single crystals confirm the ability to suppress the antiferromagnetic ordering temperature from 200 K in the undoped compound down to 100 K approaching the solubility limit of La. Despite up to ∼30% La substitution, the persistence of magnetic order and lack of any signature of superconductivity above 10 K present a contrasting phase diagram to that of Ca_1−xLa_xFe₂As₂, indicating that the suppression of magnetic order is necessary to induce the high-temperature superconducting phase observed in Ca_1−xLa_xFe₂As₂.

This paper reports comprehensive results on thin film growth of 122-type iron-pnictide superconductors, AE(Fe_1−xCo_x)₂As₂ (AE= Ca, Sr, and Ba, AEFe₂As₂:Co) by a pulsed laser deposition method using a neodymium-doped yttrium aluminum garnet laser as an excitation source. The most critical parameter to produce the SrFe₂As₂:Co and BaFe₂As₂:Co phases is the substrate temperature (T_s). It is difficult to produce highly pure CaFe₂As₂:Co phase thin film at any T_s. For BaFe₂As₂:Co epitaxial films, controlling T_s at 800–850 °C and growth rate to 2.8–3.3 Å s⁻¹ produced high-quality films with good crystallinity, flat surfaces, and high critical current densities > 1 MA  cm ⁻², which were obtained for film thicknesses from 100 to 500 nm. The doping concentration x was optimized for Ba(Fe_1−xCo_x)₂As₂ epitaxial films, leading to the highest critical temperature of 25.5 K in the epitaxial films with the nominal x = 0.075.

We present thermodynamic and transport properties of transition-metal (T) arsenides, TAs, with T = Sc to Ni (3d), Zr, Nb, Ru (4d), Hf and Ta (5d). Characterization of these binaries is carried out with powder x-ray diffraction, temperature- and field-dependent magnetization and resistivity, temperature-dependent heat capacity, Seebeck coefficient, and thermal conductivity. All binaries show metallic behavior except TaAs and RuAs. TaAs, NbAs, ScAs and ZrAs are diamagnetic, while CoAs, VAs, TiAs, NiAs and RuAs show approximately Pauli paramagnetic behavior. FeAs and CrAs undergo antiferromagnetic ordering below T_N ≈ 71 K and T_N ≈ 260 K, respectively. MnAs is a ferromagnet below T_C ≈ 317 K and undergoes hexagonal–orthorhombic–hexagonal transitions at T_S ≈ 317 K and 384 K, respectively. For TAs, Seebeck coefficients vary between  + 40 and  − 40 μV  K⁻¹ in the 2–300 K range, whereas thermal conductivity values stay below 18 W m⁻¹ K⁻¹. The Sommerfeld coefficients γ are less than 10 mJ K⁻² mol⁻¹. At room temperature with application of 8 T magnetic field, large positive magnetoresistance is found for TaAs (∼25%), MnAs (∼90%) and NbAs (∼75%).

Hydrogen substitution at the oxygen sites of 1111-type layered nickel oxyarsenides LnNiAsO (Ln=lanthanoid) was successfully performed using a high-pressure synthesis technique using LnH₂ as a key component of the starting mixture. In addition to the superconducting LaNiAsO (T_c = 2.4 K) and non-superconducting CeNiAsO, which have already been reported, PrNiAsO (T_c = 1.6 K) and NdNiAsO (non-superconducting above 0.5 K) were successfully synthesized using this technique. Electron-probe micro-analysis (EPMA) and thermogravimetry analysis-mass spectroscopy (TG-MS) indicated that up to 18% of the oxygen sites could be substituted by hydrogen. Although the T_c of LaNiAsO_1−xH_x increased to 3.7 K for x = 0.07–0.17 and rapidly decreased to 1.7 K at x = 0.18, no enhancement in the T_c value above 2 K was observed in any of the other LnNiAsO_1−xH_x systems. Isovalent substitution at the La sites of La³⁺ for either Pr³⁺ or Nd³⁺ and hydrogen substitution of the oxygen sites produced a chemical pressure effect, causing the lattice parameters to decrease. An enhancement and sudden drop in the T_c values, however, was observed following hydrogen substitution, suggesting that the hydrogen substitution process supplied additional electron density to the NiAs layer, resulting in enhancement of the T_c value.

We have synthesized two iron-pnictide/chalcogenide materials, CuFeTe₂ and Fe₂As, which share crystallographic features with known iron-based superconductors, and carried out high pressure electrical resistivity measurements on these materials to pressures in excess of 30 GPa. Both compounds crystallize in the Cu₂Sb-type crystal structure that is characteristic of LiFeAs (with CuFeTe₂ exhibiting a disordered variant). At ambient pressure, CuFeTe₂ is a semiconductor and has been suggested to exhibit a spin-density-wave transition, while Fe₂As is a metallic antiferromagnet. The electrical resistivity of CuFeTe₂, measured at 4 K, decreases by almost two orders of magnitude between ambient pressure and 2.4 GPa. At 34 GPa, the electrical resistivity decreases upon cooling the sample below 150 K, suggesting the proximity of the compound to a metal–insulator transition. Neither CuFeTe₂ nor Fe₂As superconduct above 1.1 K throughout the measured pressure range.

Optimized, biaxially textured BaFe_1.8Co_0.2As₂ thin films with an in-plane alignment of 1.7° have been realized on high-quality IBAD-textured MgO-coated technical substrates utilizing additional Fe buffer layers. High critical current densities (J_c) were achieved, comparable to films on single crystalline MgO (J_c ≥ 1 MA cm⁻² at 4 K, self-field). Transmission electron microscopy investigations reveal a small number of c-axis correlated defects introduced by the MgO template. The effect of these defects on the J_c anisotropy was determined in angular-dependent electronic transport measurements.

In this work we present preparation details and measurement results for an edge-type hybrid Josephson junction based on Co-doped BaFe₂As₂. The base electrode was formed by ion beam etching of a Ba-122 thin film, while the counter-electrode was patterned by evaporating lead. Finally, an indium protection layer was evaporated. The junction shows asymmetric I–V-characteristics with a total I_C R_N -product of about 12 μV . The characteristics can be fitted within a resistively shunted junction model assuming different fitting parameters for the positive and negative branches. There is a high excess current of unknown origin. The magnetic field dependence of the critical current indicates a non-homogeneous junction network and effects by flux trapping. It shows a variation of I_C in the positive as well as in the negative bias branch, but does not suppress it completely. Also the influence of microwave irradiation on the junctions is shown. Thereby I_C as well as the excess current can be suppressed, while first and higher order Shapiro steps can be observed.

Epitaxial Fe–Te–Se thin films were deposited by pulsed laser deposition at 250–600 °C on SrTiO₃ (100), MgO (100), LaAlO₃ (100) and CaF₂ (100) single crystal substrates. The best superconducting film was grown on CaF₂: ${T}_{\mathrm{c}}^{\mathrm{onset}}=2 0.0$ K and ${T}_{\mathrm{c}}^{0}=1 6.1 8$ K with T_dep = 300 °C and 3 Hz. Critical current density J_c (T = 4.2 K) was 0.41 × 10⁶ A cm⁻² at 0 T and 0.23 × 10⁶ A cm⁻² at 9 T. The angular dependence of J_c shows a broad c-axis correlated peak when B ≥ 3 T.

From recent literature, it became clear that the crystallographic lattice parameters and the superconducting properties of FeSe_0.5Te_0.5 thin films exhibit a non-trivial dependence on the in-plane lattice constant of the substrates on which they are grown. The strain, which depends on the type of growth, can play an important role both in enhancing the critical temperature T_c and in determining the pinning mechanisms. Here, we present the effects of the substrate on the superconducting properties of FeSe_0.5Te_0.5 thin films. After a comprehensive overview of the different substrates used, i.e. oxides and fluorides, we compare the superconducting properties of films grown on LaAlO₃(001) and SrTiO₃(001). We show that the pinning properties of the two types of film are completely different: the angular dependences of the critical current density are opposite due to the presence of extrinsic pinning along the c-axis on films grown on SrTiO₃. The presence of strong correlated pinning for a field perpendicular to the surface in films grown on SrTiO₃ is confirmed by the analysis of the activation energy for vortex motion U₀ and supported by the observation through scanning tunnelling microscopy of nanoscale threading dislocations possibly induced by the lattice mismatch with the substrate, which are not seen on the films deposited on LaAlO₃.

The interplay between superconductivity, magnetism and crystal structure in iron-based superconductors is a topic of great interest amongst the condensed matter physics community as it is thought to be the key to understanding the mechanisms responsible for high temperature superconductivity. Alkali metal doped iron chalcogenide superconductors exhibit several unique characteristics which are not found in other iron-based superconducting materials such as antiferromagnetic ordering at room temperature, the presence of ordered iron vacancies and high resistivity normal state properties. Detailed microstructural analysis is essential in order to understand the origin of these unusual properties. Here we have used a range of complementary scanning electron microscope based techniques, including high-resolution electron backscatter diffraction mapping, to assess local variations in composition and lattice parameter with high precision and sub-micron spatial resolution. Phase separation is observed in the Cs_xFe_2−ySe₂ crystals, with the minor phase distributed in a plate-like morphology throughout the crystal. Our results are consistent with superconductivity occurring only in the minority phase.

A comparative study of the addition of Pb to polycrystalline Ba_0.6K_0.4Fe₂As₂ has revealed that the Pb should be added after the Ba_0.6K_0.4Fe₂As₂ phase has formed. The uniformly dispersed Pb can ameliorate the Ba_0.6K_0.4Fe₂As₂ grain linkages. In contrast, pre-added Pb in the raw powder congregates to form large particles and has hardly any positive effect on the J_c enhancement. To conglutinate at the grain surface and avoid contamination of the Ba_0.6K_0.4Fe₂As₂, the material added should have a low melting point and inertia to the superconducting phase. This model also enables us to predict desirable dopants for enhancing superconducting properties of Ba_0.6K_0.4Fe₂As₂.

To elucidate the mechanism as to why alcoholic beverages can induce superconductivity in Fe_1+dTe_1−xS_x samples, we performed component analysis and found that a weak acid such as an organic acid has the ability to induce superconductivity. Inductively coupled plasma spectroscopy was performed on weak acid solutions post-annealing. We found that the mechanism of inducement of superconductivity in Fe_1+dTe_1−xS_x is the deintercalation of excess Fe from the interlayer sites.