Properties and Applications of Iron–Chalcogenide Superconductors

Abstract

Iron–chalcogenide superconductors continue to captivate researchers due to their diverse crystalline structures and intriguing superconducting properties, positioning them as both a valuable platform for theoretical investigations and promising candidates for practical applications. This review begins with a comprehensive overview of the fabrication techniques employed for various iron–chalcogenide superconductors, accompanied by a summary of their phase diagrams. Subsequently, it delves into the upper critical field, anisotropy, and critical current density. Furthermore, it discusses the successful fabrication of meters-long coated conductors and explores their applications in superconducting radio-frequency cavities and coils. Finally, several prospective avenues for future research are proposed.

1. Introduction

Iron-based superconductors [1], discovered in 2008, are considered to be a new platform to study high-temperature superconducting mechanisms and potential candidates for practical applications [2,3,4]. From the crystalline structure point of view, iron-based superconductors can be divided into two major categories, iron–pnictides with the [FeAs]⁻¹ layer and iron–chalcogenides with the electroneutral FeSe layer. The [FeAs]⁻¹ layers in iron–pnictides are responsible for charge carrier transfer, which is alternated by the charge reservoir layers, e.g., the [ReO]⁺¹, Ae²⁺, and A⁺¹ layers (Re = rare earth elements, Ae = alkaline earth elements, A = alkaline elements) [5]. Consequently, there are varieties of iron–pnictides with multiple structures and abbreviations, such as 111, 122, 1111, 12,442, et al., as shown in Figure 1a. On the contrary, the iron–chalcogenides’ 11 system contains non-toxic elements and possesses the simplest crystal structure among iron-based superconductors, making them more attractive for theoretical studies and practical applications. Here, in this review, we start with the fabrication methods for iron–chalcogenide and discuss the superconducting transition temperatures related to different crystal structures and charge carrier densities. Then, the important factors for determining the applications, the upper critical field and the critical current density, are summarized for single crystals and films. At last, recent applications of FeTe_1−xSe_x-coated conductors are discussed.

2. Fabrications, Crystal Structures, and Superconducting Transition Temperature of Iron–Chalcogenide Superconductors

The substitution of Se by Te or S induces novel superconductivity with higher superconducting transition temperatures, T_c [14,15]. However, there is a common characteristic in the 11 system, which is the excess Fe atoms (Fe(2) in Figure 1a) existing between the FeSe layers, as shown by the bright spots in the Scanning Tunneling Microscope (STM) images in Figure 2b,i [16]. They cause carrier localization and provide magnetic order deteriorating superconductivity in the Fe(1) plane [17], which masks the intrinsic superconductivity. It was soon found that annealing in air, O₂, S, Se, Te, P, As, Sb, and I atmospheres can effectively remove the excess iron [18], as shown in Figure 2c,d. Correspondingly, the semiconductor-like normal state, namely, the resistivity (ρ), increases with cooling and changes to metallic-like behavior [19] with the increased annealing temperature, as shown in Figure 2a. Moreover, the T_c is enhanced from 9 K to 14 K, and the superconducting transition becomes sharper. The superconducting volume fraction of FeTe_0.6Se_0.4 approaches 100% after optimizing the annealing conditions. Gu et al. reported that through Mn element doping, the suppressed superconductivity in the pristine FeTe_0.55Se_0.45 single crystals can largely recover. As shown in the inset of Figure 2e, 1% Mn doping into the Fe site increases the T_c^onset to 15 K. The quick saturation of susceptibility and the obvious jump in the temperature dependence of specific heat in Figure 2f,g suggest that bulk superconductivity emerges after the excess Fe atoms are removed, as evidenced by Figure 2j. They are summarized in a Mn-doping phase diagram, as shown in Figure 2h. Minor Mn doping of 0.5% has increased the T_c to a plateau value of 14.5 K, while further doping suppresses T_c and the jump of specific heat.

The interlayer coupling of FeSe is dominated by the Van der Waals Force. The intercalation with metal atoms can be fulfilled through the traditional high-temperature synthesis routes and low-temperature ammonothermal techniques. The (Tl,K,Rb)_xFe_ySe₂ single crystals are usually fabricated through slow cooling from the melt at temperatures exceeding 900 °C. By increasing the Fe content, the normal state of (Tl,K)Fe_ySe₂ was tuned from an insulator to a semiconductor, accompanied by a superconducting transition at T_c~31 K [9]. However, systematic investigation using a scanning electron microscope (SEM) and STM reveals a severe phase separation existing in this system. The filament KFe₂Se₂ superconducting phase (as shown by the rectangles in Figure 3b,c is sandwiched by the insulating K₂Fe₄Se₅ phase with a Néel temperature of 560 K (the dark matrix) [20]. Li et al. found that the STM image in region I of Figure 3d exhibits a centered rectangular lattice structure with very few defects, as shown by Figure 3e. The Scanning Tunneling Spectroscopy (STS) reveals a double-gap structure, which is uniform along the white line in Figure 3e [21]. In region II, the STS indicates an energy gap of 0.43 eV across the Fermi level, suggesting an insulation phase. There are obvious Fe vacancies in the STM images, constructing a so-called $\sqrt{5}\times \sqrt{5}$ superlattice.

It is known that liquid ammonia dissolves alkali, alkaline earth, and some rare earth elements. Burrard-Lucas et al. first synthesized the Fe_1+δSe polycrystals using the solid-state-reaction method. The Fe_1+δSe and the Li metal were then placed in a Schlenk tube with a magnetic stirrer, which was attached to the ammonia cylinder. The tube was cooled to allow the ammonia to condense onto the reactants. The mixtures were then stirred at −78 °C for half an hour, after which the Schlenk tube was warmed up and the ammonia was evaporated. Finally, the Li_x(NH₂)_y(NH_3)1-yFe₂Se₂ (x~0.6; y~0.2) with T_c = 43 K was obtained [11]. Ying et al., instead, directly poured the liquid ammonia into an autoclave filled with β-FeSe powders and alkali, alkaline earth, Yb, and Eu at liquid nitrogen temperature. The whole device was then kept at room temperature for 2–17 days [22]. Varieties of FeSe-based superconductors intercalated with Li, Na, Ba, Sr, Ca, Yb, and Eu were obtained, as proved by the Rietveld refinement shown in Figure 4a. The highest T_c is 45 K for NaFe₂Se₂. As shown in Figure 4b, the sharp superconducting transition and the large magnetization hysteresis loop indicate bulk superconductivity. By using the high-purity FeSe powders, they continued to intercalate K in FeSe via the ammonothermal route [23]. At least two superconducting phases were discovered, of which the T_c was controlled by the nominal content of K rather than the NH₃. Discrete superconducting regions were revealed with abrupt changes of T_c with doping, as shown in Figure 5a,b. When x in K_xFe₂Se₂(NH₃)_y is below 0.3, T_c^onset is 44 K. When 0.3 < x < 0.6, a two-step transition was observed at T_c1~44 K and T_c2~30 K, indicating the phase separation in this doping region. There is only one superconducting phase with T_c~30 K when x > 0.6. Moreover, there is no sign of antiferromagnetic (AFM) transition in the temperature-dependence of magnetization, indicating that the Fe-vacancy phase, such as the 245 phase, disappears in K_xFe₂Se₂(NH₃)_y. To further investigate the intrinsic superconducting properties, Sun et al. synthesize Li_x(NH₃)_yFe₂Se₂ single crystals through the low-temperature ammonothermal technique. The FeSe single crystals fabricated through the eutectic AlCl₃ and NaCl (=0.52:0.48) flux method were used as the template. The as-synthesized thin plate-like Li_x(NH₃)_yFe₂Se₂ single crystals are shown in the inset of Figure 5d, with sharp (00l) diffraction peaks in the XRD patterns. The lattice parameters are a = 3.7704(6) Å and c = 16.973(7) Å. The T_c^onset is determined to be 44.3 K. Surprisingly, the crystals exhibit a huge anisotropy in resistivity. The ab-plane resistivity ρ_ab exhibits a semiconductor behavior above 150 K, while the c-axis resistivity ρ_c presents a metallic behavior. Furthermore, the ratio ρ_c/ρ_ab increases from 900 at 300 K to 8000 at 50 K, as shown in Figure 5e.

Guo et al. utilized a similar method to synthesize the NH₃-free Na-intercalated FeSe_1-zS_z superconductors. The difference is that the Taiatsu Glass TVS-N₂ high-pressure vessel continued to be evacuated to ~10⁻² Pa using a molecular pump after the reaction was finished [24]. The X-ray diffraction pattern shown in Figure 4c,d can be fitted well by Na_0.65Fe_1.93Se₂ (91.3%), with minor impurities of FeSe (3.5%) and Fe₇Se₈ (5.2%). As depicted in Figure 4e, the NH₃-free phase has a T_c of 37 K, while the NH₃-poor intercalates show a T_c of 45 K. Figure 4f summarizes the S-doping-dependence of T_c for the FeSe_1-zS_z and two intercalates. With S doping, the T_c decreases quicker in the NH₃-free phase than in the NH₃-poor phase, indicating that S doping effect is weaker in the NH₃-poor phase.

Except for the low-temperature ammonothermal method, Hatakeda et al. dissolved lithium and sodium metal in 2-phenethylamine (2-PEA) and reacted them with FeSe powders at 45 °C for 7 and 28 days, respectively [26]. The c-axis length is 19.04(6) Å and 18.0(1) Å for the Li- and Na-cases, respectively, which is the largest among the iron–chalcogenide superconductors. T_c is 39 K for the Li-case, while a two-step transition is observed in the Na-case. The thermalgravimetric measurements show a 27% mass loss below 300 °C, which is ascribed to the deintercalation or desorption of 2-PEA, and a nearly 60% mass loss above 700 °C. This implies a high instability of the intercalated FeSe at high temperatures.

Shi et al. performed an electrochemical intercalation method to successfully synthesize a cetyltrimethyl ammonium (CTA⁺)-intercalated FeSe-based superconductor (CTA)_0.3FeSe with T_c = 45 K [12]. The crystal structure is exhibited in Figure 1b. The FeSe single crystals were used as the starting materials and fixed on an In wire as the positive electrode. The electrolyte is N-methyl-2-pyrrolidone added by hexadecyl trimethyl ammonium bromide (CTAB). The Transmission Electron Microscope (TEM) indicated that the distance between the FeSe layers increased from 0.56 nm for the pristine FeSe to 1.45 nm for the CTA⁺ intercalated FeSe. The CTA⁺ organic layer can be clearly seen, as shown by the darker layer in Figure 6g. Figure 6a shows the temperature dependence of susceptibility measured under the fields of 5 Oe and 40 Oe. At 5 Oe, the T_c is determined to be 45 K, and the small distance between the FC and ZFC branches implies weak flux-pinning properties, confirming the high degree of homogeneity of the intercalated sample. The T_c also exhibits a negative pressure effect up to 1 GPa, which is consistent with other pressure experiments on the intercalated FeSe systems under low pressure. Meng et al. cleaved the FeSe single crystals obtained through the chemical vapor transport (CVT) method into thin flakes with a thickness of ~15 μm [27]. Several crystals were attached to the negative electrode using silver paint. The ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF₄) was used as the electrolyte, as schematized in Figure 6i. By using the optimized voltage 3 V and a temperature of 330 K provided by a thermostatic hot plate, the intercalated FeSe samples with different H⁺ content were obtained after different protonation times. As depicted in Figure 6j–l, the nematic transition at T_s~89 K marked by the black arrows in (j) was gradually suppressed after protonation and totally disappeared after 5 days. Meanwhile, the T_c is enhanced from 10 K for the pristine FeSe single crystals to T_c1 = 25 K at 5 days of protonation. In the intermediate protonation time, there is a coexistence of three superconducting transitions with T_c2 = 25 K, T_c3 = 34 K, and T_c4 = 44 K. After 15 days, only the T_c4 = 44 K phase survived. Moreover, the magnetization measurements prove the 100% volume fraction of superconductivity for all of the samples at 2 K. They also proved that this effect was reversible after deprotonation, as the T_c4 phase gradually transformed to the T_c1 phase, accompanied by the reappearance of the nematic order.

Lei et al. applied the electric-double-layer transistor (EDLT) using ionic liquids as the gate dielectric to the single crystalline FeSe flakes with typical thicknesses of ~10 nm [28], as shown in Figure 7a,b. The ionic liquid DEME-TFSI was used as the dielectric, and the cations and anions were DEME⁺ and TFSI^-, respectively. After introducing carriers to the FeSe flakes at 220 K with the application of gate voltages, the sheet resistance was measured, as depicted in Figure 7e. After increasing the gate voltage V_g, the pristine T_c = 5.2 K was enhanced to 7.5 K at V_g = 4.0 V. Further increase of V_g induces a two-step transition. Above V_g > 5.0 V, there is only one superconducting phase with T_c above 40 K. The highest T_c~48.2 K is realized after applying V_g = 6 V. Similar results were observed in the Li/Na intercalated FeSe superconductors by using the ionic gating technique [29]. The lithium-based Li_1+x+yA_x(Ti,Ge)_2−xSi_yP_3−yO₁₂ and the sodium-based Na_3.4Zr_1.8Mg_0.2Si₂PO₁₂ were adopted as the substrates, as shown in Figure 7c,d. The 5–38 nm thick FeSe flake was sandwiched between the solid ionic substrate and a 100 nm SiO₂ layer. The SiO₂ layer is crucial to insulate the electrodes from the substrate to avoid metal accumulation and accurate determination of the content of the intercalated metals. It can be observed that with intercalation of Li cations, the T_c1 = 8 K from the FeSe matrix gradually increases to T_c2 = 36 K and finally enters into the phase with T_c3 = 44 K, accompanied by decreased normal state resistivity. However, the normal state resistance gradually increases upon Li doping, and, finally, the T_c3 = 44 K phase disappears and the sample transforms into an insulator, as shown in Figure 7g. Similar intercalation behavior was found in Na_xFeSe. The common discrete superconducting phase in these systems was found to be robust against S substitution but vulnerable to the Fe site substitution by Cu, implying the importance of the intact Fe plane to the high-temperature superconductivity.

(Li_1−xFe_x)OHFeSe was first prepared through the hydrothermal reaction method. Selenourea, Fe powders, LiOH·H₂O, and de-ionized water were put into an autoclave and heated at 160 °C for 3–10 days [30]. The crystal structure was determined through XRD and Rietveld refinements (Figure 8a). As depicted in Figure 1b, the anti-PbO-type FeSe layers are alternated with the anti-PbO-type LiFeO₂. The crystal lattice parameters are determined to be a = 3.7926(1) Å, c = 9.2845(1) Å. The susceptibility shows a superconducting transition at 40 K. Sun et al. systematically studied the superconducting properties of (Li_1−xFe_x)OHFe_1-ySe with different iron vacancy concentrations [31]. It was found that the synthesized compounds through hydrothermal synthesis lead to x~0.2, but with a variable y. Interestingly, superconductivity emerges when Fe vacancy (y < 0.05) is decreased. The lithiation process reduces y to zero by replacing some Fe ions in the reservoir layer by Li, while the replaced Fe fills into the vacancy in the conducting layer. As a result, a large superconducting volume was reached with the highest T_c. Due to the powder form, the resistivity measurements on the pressed bulk show a low T_c^zero. Dong et al. successfully synthesized single crystalline (Li_0.84Fe_0.16)OHFe_0.98Se via the hydrothermal ion-exchange technique based on the K_0.8Fe_1.6Se₂ (245 insulating phase) single crystals [32]. During the hydrothermal reaction process, the K ions in the 245 single crystals were completely released into the solution, and (Li/Fe)OH layers constructed by ions from the solution were squashed into the matrix, which connects with the adjacent edge-sharing FeSe tetrahedra via weak hydrogen bonding, as schematized in Figure 8c. Despite the sharp superconducting transition at 42 K in the susceptibility data, clear resistivity evidence was also observed, as shown in Figure 8g.

The highest T_c in iron–chalcogenide superconductors was obtained in the single-layer FeSe film prepared through the Molecular Beam Epitaxy (MBE) method [33,34]. The FeSe single-layer film was grown on the TiO₂-terminated and Nb-doped SrTiO₃ (STO-001) substrate at 450 °C by co-evaporating Fe and Se from Knudsen cells with a flux ratio of 1:10. RHEED was used to monitor the growth process, as shown in Figure 9a. Figure 9b shows the temperature dependence of resistance derived from the I–V curves measured at fixed temperatures. The T_c is determined to be 109 K. Another R–T curve with T_c = 99 K was obtained through measurements conducted while sweeping the temperature, as shown in Figure 9c. As a result, it can be claimed that this is the second high-temperature superconductor with T_c surpassing the liquid nitrogen temperature, indicating great significance not only for the superconducting mechanism but also for potential applications in the liquid nitrogen temperature region. Xue’s group continues to investigate the mechanism [35] of high-temperature superconductivity [35]. They suggest that band bending of STO occurs due to the larger work function of FeSe compared to STO, which contributes to the charge transfer to the FeSe side, as shown in Figure 9d. Moreover, annealing induces stoichiometry of FeSe and shifts the Fermi level upward, thus increasing the electron density (Figure 9e,f). Consequently, the high-temperature superconductivity emerges in the superconducting/dielectric heterostructure, where the dielectric layer enhances the charge density of FeSe and provides the electron–phonon coupling with its intrinsic high-energy phonon mode.

3. Phase Diagram of Iron–Chalcogenide Superconductors

The phase diagrams of iron–chalcogenide superconductors are summarized in Figure 10. The left side of Figure 10a shows the FeSe_1−xS_x single crystals fabricated through the hydrothermal route (0.29 ≤ x ≤ 1) and the CVT method (0 ≤ x ≤ 0.29) [37]. In the nematic phase below T_s, the normal state resistivity presents a linear temperature dependence, namely, the non-Fermi liquid behavior [38]. With S doping, the nematic order is gradually suppressed, and the Fermi liquid behavior is recovered. A small superconducting dome appears within the nematic phase, with the highest T_c~9 K. It reaches a minimum value at x~0.45 and increases again to the FeS end. The right side of Figure 10a shows the Te doping dependence of T_c and T_N. The post-annealing process applied to the high Te content of FeSe_1−xTe_x single crystals prepared through the self-flux method proves the coexistence of long-range AFM order and superconductivity. However, high Se side crystals must be synthesized through the CVT method to avoid phase separation [39,40]. The T_c of FeSe_1−xTe_x presents a minimum around x~0.2 due to the sample disorder. The nematic order is also gradually suppressed by Te doping and disappears at x~0.5, where the T_c reaches the maximum value of 15 K. Zhuang et al. also obtained a full doping phase diagram of FeSe_1−xTe_x by synthesizing the film on the CaF₂ (100) substrate using the Pulsed Laser Deposition (PLD) method [41]. As marked by the green pentagon in Figure 10a, the T_c shows a maximum value of 20 K within 0.6 ≤ x ≤ 0.8, where phase separation should be apparent. High transition temperatures with T_c~24 K were obtained in FeTe_0.8Se_0.2 film [42,43]. The difference between the film and the CVT single crystals may originate from the strain effect induced by the substrate. Figure 10b shows the Te doping phase diagram of FeS_1−xTe_x. Similarly to the doped FeSe, S doping in FeTe gradually suppresses the AFM order, while superconductivity appears when x < 0.95 [44]. There is a region of coexistence of AFM and superconductivity. The maximum T_c is 9 K. However, the solubility limit of S in FeTe prevents further investigation into this system. Zhao et al. prepared the FeS_1−xTe_x single crystals with 0 ≤ x ≤ 0.15 via the hydrothermal technique [45]. The T_c = 4.5 K in FeS [46] was quickly suppressed after Te doping due to the scattering from the impurities, and the superconductivity was totally suppressed when x > 0.1.

Ying et al. summarized a common electron doping phase diagram of the intercalated FeSe superconductors, as shown in Figure 10c. An obvious discreet superconducting phase diagram can be seen [27,29]. The corresponding Fermi surface topologies are also incorporated at the top. For the pristine FeSe system, the hole pockets are at the center of the Brillouin zone (Γ point), and the electron pockets are at the corner (M points). Upon electron doping to a critical level, the Lifshitz transition occurs and leads to an abrupt appearance of the T_c2 phase. Further increasing the doping level induces the enlarged electron pocket and the emergence of the T_c3 phase. Figure 10d depicts T_c as a function of the interlayer distance, d, for all of the FeSe-based superconductors published so far. It seems that the T_c is enhanced with the interlayer distance when d < 9 Å, but it saturates with the higher d. For the protonated FeSe sample, the T_c is enhanced by increasing the electron density, rather than the interlayer distance, as proved by the enhancement from T_c1 to T_c4 with the same interlayer distance. Rebec et al. explain the phase diagram from the viewpoint of the superconducting energy gap, Δ [47]. As schematized in Figure 10e, there is a linear T_c dependence on the gap 2Δ/k_BT_c = 5.87, which demarcates the phase diagram into three regions. For region I, the FeSe/Te bulks exhibit a Δ < 5 meV, and the T_c is less than 20 K. In the second region, a gap of Δ~10 meV is opened at a low temperature, and the T_c of the intercalated or electron-doped FeSe is enhanced to 31–48 K [48]. The 1-unic cell FeSe on the STO substrate belongs to the third group, where interfacial electron–phonon interaction plays an important part in high-temperature superconductivity.

4. Upper Critical Field, Anisotropy, and Critical Current Density of Practical Iron–Chalcogenide Superconductors

Two crucial parameters related to practical applications are the upper critical field, above which Cooper pairs are depaired at high magnetic fields, and the anisotropy parameter, γ = B_c2^ab/B_c2^c = (m_c/m_ab)^1/2 = λ_c/λ_ab = ξ_c/ξ_ab, where m, λ, and ξ are the effective mass of electrons, the penetration depth, and the coherence length, respectively. Figure 11a summarizes the temperature dependence of the upper critical field, B_c2. One similarity is that the B_c2 with the field parallel to the ab-plane of the crystal structure is larger than the field parallel to the c-axis. This is caused by the effective mass anisotropy of electrons. For the FeSe (100 nm thick flake), the B_c2 is 16 T at 4 K when the field is parallel to the ab-plane. [49]. The B_c2 with the field parallel to the c-axis is smaller, achieving a B_c2 = 12 T at 2 K. Te doping in the Se site not only enhances the T_c but also increases the B_c2 to 50 T at 2 K. Moreover, the B_c2^ab is closer to the B_c2^c below T_c than FeSe, and there is a crossover between them at 3 K. For the intercalated FeSe superconductors, the enhanced T_c makes the application in liquid hydrogen possible. For the (Li,Fe)OHFeSe single crystals, the B_c2^c is increased to 45 T and 65 T at the liquid hydrogen and liquid helium temperature regions, respectively [50]. The B_c2^ab, on the other hand, is 68 T at 27 K, indicating good application potential. The data of Li_x(NH₃)_yFe₂Se₂ are limited below 14 T, but there is an apparent large gap between the two directions [25].

The anisotropy parameters of the above-mentioned superconductors are depicted as a function of normalized temperature, t = T/T_c, in Figure 11b. For the FeTe_0.6Se_0.4 single crystals, the γ increases from values smaller than 1 (reversed anisotropy with B_c2^ab < B_c2^c) below 0.25 T_c to 1 < γ < 2, and finally above γ = 2 near T_c. The FeSe flakes with infinite conducting layers exhibit more two-dimensional characteristics and exhibit a γ > 2 in the whole studying range. The nearly isotropic behavior of B_c2 is beneficial to the magnet design. For the (Li,Fe)OHFeSe with larger interlayer space, the γ increases from 2.5 to 5.5 when t = T/T_c moves from 0.6 to 0.8. The largest γ is observed in Li_x(NH₃)_yFe₂Se₂, ranging from 8 to 18 above t = 0.38 [25]. The extremely large electronic anisotropy in both (Li,Fe)OH and Li-NH₃ layers of intercalated FeSe compounds is suggested to result from the structure’s characteristics.

In the next section, we will discuss the most important parameter, the critical current density of iron–chalcogenide superconductors, reported so far. Although the J_c has already been studied in the (Tl,K,Rb)_xFe_ySe₂ system [52,53,54], the discussion will not be included here because of the severe phase separation and the small portion of the superconducting phase, which leads to a small J_c~10⁴ A/cm² calculated through the Bean model. Instead, the (Li,Fe)OHFeSe system with an intact Fe plane and 100% volume fraction of superconductivity will be discussed.

Generally, the upper limit of critical current density is determined through the depairing critical current density, which is described by

$$J_d\left(0 K\right)=\frac{{\varphi }_0}{3\sqrt{3}{\mu }_0{\lambda }_{ab}^2\left(0 K\right){\xi }_{ab}(0 K)}$$

where Φ₀ is the flux quantum. The penetration depth and coherence length of three typical iron–chalcogenide superconductors are listed in

Table 1. Penetration depth, coherence length, and critical current density J_c^ab(0 T) of practical iron–chalcogenide superconductors. The anisotropy parameter is derived from Figure 11b. The pristine and irradiated samples are denoted as pri and irr, respectively. The flux pinning efficiency is calculated by η = J_c/J_d at 0 T.

Materials	FeSe		FeTe1−xSex		(Li,Fe)OHFeSe
λab(0 K), nm	445 [55,56]		430		281 [57,58]
ξab(0 K), nm	4.4 [56,59]		1.5 [60]		2.21 [50,58]
Jd(0 K), MA/cm2	11 [56]		36		57.7 [58]
γ = Bc2ab/Bc2c	2–3		1–3		2–5
Jc-single crystal, MA/cm2	0.043 (2 K, pri)	0.2 (2 K, irr) [61]	0.27 (2 K, pri)	0.52 (2 K, irr) [62]	0.24 [63]
Jc-film, MA/cm2	1.7 (2 K, Mono-layer) [34]		1.36 (4.2 K)		\
Jc coated conductor @ 4.2 K, MA/cm2	\		0.43 [64]	1.3 [65]	\
Maximum η	15%		3.7%		0.4%

. The ξ of FeSe is two to three times those of FeTe_0.5Se_0.5 and (Li,Fe)OHFeSe, leading to a small J_d of 11 MA/cm². Comparatively, the J_d of the FeTe_1−xSe_x and (Li,Fe)OHFeSe system achieves 36 and 57 MA/cm² at 0 K.

However, the actual J_c a superconductor can carry is mainly controlled by the flux pinning efficiency of the pinning landscape, in which the dimensionality also determines the J_c anisotropy. As summarized in Table 1, the pristine FeSe single crystals only achieve a small J_c of 0.043 MA/cm². After the irradiation of 2.4 GeV U ions, the J_c approaches the same level of the pristine FeTe_0.61Se_0.39 and (Li,Fe)OHFeSe single crystals [61]. Meanwhile, the irradiated FeTe_0.61Se_0.39 single crystals by 200 MeV Au achieve 0.5 MA/cm² at 0 T and 2 K. The FeTe_1−xSe_x film and coated conductor have a higher J_c above 1 MA/cm² because of the more abundant crystal defects incorporated after the PLD fabrication process.

Figure 12 summarizes the critical current density of the state-of-the-art iron–chalcogenide superconductors. Generally speaking, the iron–chalcogenide single crystals have much fewer crystalline defects than the film, leading to a weak flux pinning force, strong field dependence, and low J_c at high fields. The FeSe single crystals show a J_c(2 K) = 4 × 10⁴ A/cm² at 0 T, which decreases quickly with the field. The FeTe_1−xSe_x single crystals, on the contrary, exhibit a robust field dependence above 2 T. Irradiation is an effective way to introduce artificial pinning centers into the ‘11’ system, leading to a pronounced enhancement of its current carrying ability. The J_c of FeSe at high fields has been enhanced four times. For the irradiated FeTe_1−xSe_x single crystals, the Au irradiation has increased the J_c below 5 T, above which the J_c before and after irradiation intersect with each other. The (Li,Fe)OHFeSe single crystals have a higher J_c than the FeTe_1−xSe_x single crystals in the testing range due to the intrinsic pinning, which will be discussed below [63]. Comparatively, the iron–chalcogenides in the film form have higher J_c because of the strong flux pinning centers constructed during the film growth [42,64,66,67,68]. The FeTe_1−xSe_x film achieves a high J_c(0 T) = 1.36 MA/cm² and exhibits a rather robust field dependence [69]. Even at 9 T, the J_c remains 0.97 MA/cm². The (Li,Fe)OHFeSe film grown through the hydrothermal method shows a J_c below 10⁵ A/cm² above 20 T [58]. However, the extrapolation to the low field region seems higher than the (Li,Fe)OHFeSe single crystals. Moreover, the Mn doping considerably enhances the high field J_c by nearly 10 times at 33 T, which is ascribed to the extra pinning centers introduced by Mn doping [58]. A similar Mn doping effect on J_c is observed in the FeTe_1−xSe_x [15] and K_xFe_2−ySe₂ [53] systems, but the former is due to the extinguished excess Fe irons. Interestingly, the single-layer FeSe film has a J_c above 1 MA/cm² at self-field. Such a high J_c in the one-unit cell FeSe slowly declines with fields, as shown in the inset.

The flux pinning mechanism is important to unravel the factors governing the critical current density. Figure 13 presents the flux pinning properties of the FeTe_1−xSe_x and (Li,Fe)OHFeSe single crystals and films. The flux pinning type of superconductors is usually studied through the Dew–Hughes model or the angle dependence of J_c. The flux pinning mechanism can be obtained according to the peak of the f_p-h curve, where f_p is the normalized flux pinning force f_p = F_p/F_p^max and h is the reduced magnetic field h = H/H_irr. The Fe_1.04Te_0.6Se_0.4 single crystals have a h_peak = 0.3, indicating mixed pinning from the point and surface defects [70]. After 3at. % Co doping into the Fe sites, the enhanced J_c is still dominated by the point defects [71]. The FeTe_0.5Se_0.5 film deposited on the CaF₂ film also shows a peak at h_peak = 0.33, suggesting a point pinning mechanism, as shown in Figure 13d. The angular J_c at 15 K in Figure 13e has a peak at the fields parallel to the ab-plane [67] due to the intrinsic pinning. As evidenced in Figure 13f, the J_c(Θ, H) curves collapse into one curve when it is plotted against the effective field, H_eff = Hε(Θ), where ε(Θ) = (cos²Θ + γ⁻²sin²Θ)^1/2. The fitted anisotropy parameter is γ = 1.28. It is suggestive that the flux pinning of the film can be attributed to the mixed randomly distributed point defects and mass anisotropy. The f_p-h curves of the (Li,Fe)OHFeSe film before and after Mn doping are both close to the surface pinning [58]. This intrinsic pinning is contributed by the insulating (Li,Fe)OH spacer layer.

The naturally formed pinning centers are quite rare in iron–chalcogenide superconductors, making it necessary to introduce artificial pinning centers. Ion irradiation is considered to be an effective method for introducing point and column defects depending on the type and energy of the irradiation particles [72]. So far, several groups have performed irradiation experiments on the Fe(Te,Se) single crystals and films. As summarized in Figure 14, the large-sized particles, such as U, Xe, and Au ions, created continuous columnar defects in the FeSe (Figure 14a) and FeTe_0.61Se_0.39 (Figure 14b,c) single crystals. As shown in Figure 14d, the U-irradiation suppressed the T_c of FeSe even at a small dose, which demonstrates a nearly linear dependence of T_c on the dose [61]. The quick suppression of T_c when compared with iron pnictides can be explained by the much larger damaged areas (~10 nm) shown in the inset of Figure 14a. In the Ba_0.6K_0.4Fe₂As₂ single crystals, the damaged area is only ~2–5 nm. Consequently, one can observe a peak of the J_c-B_Φ curve at a small B_Φ =2 T, above which the J_c is quickly lowered due to the damaged superconducting matrix.

Ozaki et al. studied the irradiation effect in increasing J_c. For the low-energy Au irradiation, it produces cluster-like defects with sizes of 10–15 nm (Figure 15c,d), much larger than the coherence length [73]. The strong isotropic pinning leads to a nearly 70% increase of J_c at 9 T and 10 K with H//c. The low-energy proton irradiation introduces splayed cascade defects, which are about 1–2 nm in diameter and ~10 nm wide, in the FeTe_1−xSe_x films deposited on the CeO₂ buffer layer, as shown in Figure 15g. The cascade defects cause strained areas [74]. The blue valleys are the highly compressed regions, whereas the yellow peak regions indicate tensile strain (Figure 15h). The nanoscale strain and proximity effect causes an enhanced T_c from 18 K to 18.5 K, as well as the increased H_irr, H_c2, and J_c (Figure 15e,f). A similar proton irradiation effect can be found in the FeSe single crystals. Figure 15a,b show that the h_peak moves from 0.14 to 0.28, indicating the introduction of point defects [75]. The self-field J_c of the irradiated FeSe single crystals was enhanced from 3 × 10⁴ A/cm² to 8 × 10⁴ A/cm².

5. Practical Applications of Iron–Chalcogenide Superconductors

5.1. Fabrications of FeSe Film for Superconducting Radio-Frequency Applications

Bulk Nb superconducting radio-frequency (SRF) cavities have been widely utilized in accelerators. However, the gradient of acceleration and overall performance are greatly limited by the overheating field (B_sh). Lin et al. fabricated the FeSe-coated Nb as an alternative material. The out-of-plane θ–2θ XRD shows only the (00l) peaks of the FeSe film, indicating excellent c-axis orientation and crystallinity. As shown in Figure 16a–d, SEM and AFM images demonstrate a homogeneous thickness distribution of Nb (117 nm) and FeSe (130 nm) layers throughout the film, with root mean square roughness of 0.773 nm for Nb/CaF₂ and 1.89 nm for FeSe/Nb/CaF₂. This is beneficial to the effectiveness of the Bean–Livingston barrier, which can prevent vortex penetration and increase the B_sh.

As shown in Figure 16k–m, the m(H) curves of the Nb/CaF₂, FeSe/CaF₂, and FeSe/Nb/CaF₂ film deviate at different temperatures and fields. The B_c1(T) is obtained based on the deviation point from the linear background (Figure 16n,o). After the deposition of FeSe on Nb/CaF₂, the B_c1(0) is over ten times higher than that of Nb/CaF₂ and FeSe/CaF₂. In addition, the FeSe layer exhibits excellent bending ability. Figure 16e–h indicate that the FeSe layer maintained a strong adhesion to the surface, even when subjected to varying degrees of inward or outward bending, demonstrating extraordinary resilience. Furthermore, FeSe film can be fabricated on a 10 × 10 mm² curved Nb cut from a cavity, as shown in Figure 16i. The XRD pattern exhibits the (00l) crystal orientation on the polycrystalline Nb substrate (Figure 16j). It suggests that FeSe satisfies the basic requirements and can be an alternative material for SRF cavities.

5.2. Fabrications of Meters-Long FeTe_1−xSe_x-Coated Conductors and the Applications in Coils

Like other siblings of iron-based superconductors, the 11 system exhibits a weak link effect. The critical current density across the junction of the FeSe_0.5Te_0.5 films on the [001]-tilt SrTiO₃ (STO) bicrystals decreases exponentially when the misorientation angle is larger than a critical value of θ_c = 9° [77,78,79]. As a result, the epitaxial film is an accessible option to reach a large supercurrent. The initiative efforts were mainly devoted to growing films on single crystalline substrates. Bellingeri et al. tried growing FeTe_1−xSe_x thin film on (001)-orientated MgO, STO, LaAlO₃ (LAO), and yttria-stabilized zirconia (ZrO:Y) using the PLD method. They found that the T_c is independent on the film thickness but closely correlated to the compressive strain [80]. The highest T_c = 21 K was obtained in the film deposited on the LAO substrates. The CaF₂ substrate was also used, and a 1 MA/cm² critical current density was achieved at 4.2 K and 0 T [70]. The 5–20 nm lattice disorder contributes to the complete isotropy of the current carrying ability. Nowadays, significant progress has been made in research on Fe(Se,Te)-coated conductors (CC). Si et al. significantly enhanced the superconducting performance of Fe(Se,Te) CC by employing a CeO₂ buffer layer [74]. The FeSe_0.5Te_0.5 on a rolling-assisted biaxially textured substrate (RABiTS) exhibited T_c > 20 K. The self-field J_c reached 1 MA/cm² at 4.2 K, and J_c remained around 1 × 10⁵ A/cm² under a high magnetic field of 30 T. Sylva et al. found that the CeO₂ layer plays an important role in preventing the element diffusion from the Ni-W substrate and inducing in-plane texture [81,82]. Song et al. adopted an interface engineering strategy to mitigate the thickness effect, successfully fabricating micron-thick FeSe_0.5Te_0.5 superconducting films on IBAD-LaMnO₃-buffered metal tapes [65]. Unlike the continuous growth mode, the alternating growth of a 10 nm thick seed layer and a 400 nm thick FST superconducting layer ensures the crystalline quality of FeSe_0.5Te_0.5 films (see Figure 17a–c). Apart from the minor pits and droplets, the elemental distribution of the film is uniform, with a smooth surface morphology. Figure 17d depicts the normalized resistance curves of FST films under zero magnetic field, revealing superconductivity across all films. As the film thickness increases, the influence of the LMO buffer layer on T_c diminishes, and the introduction of the seed layer promotes the uniform growth of epitaxy film. Consequently, T_c gradually increases and approaches the bulk value of ~14–15 K. In Figure 17f, the highest J_c appears in the 400 nm thick film, with a self-field J_c of ∼1.3 MA/cm² and J_c(9 T) of 0.71 and 0.5 MA/cm² for H//ab and H//c, respectively. Upon further increasing the thickness, there is a rapid drop down of J_c, suggesting the presence of the thickness effect. But, with the help of the seed layer, the J_c revives to a second peak at 1 μm. A possible reason for the thickness effect is the sensitivity of pinning effects to temperature and thickness in type-II superconductors, where δl pinning contributes more to J_c than δT_c pinning. When the film thickness is 200 nm, δl pinning dominates. With increasing thickness and temperature, δl pinning gradually transforms to δT_c pinning and exhibits a mixed form.

Ye et al. investigated the influence of substrate temperature and thickness on the superconducting properties of FeSe_0.5Te_0.5 CC. Moderate substrate temperatures are conducive to achieving superconducting films with high performance due to the impact on the evaporation of Se and Te, leading to improved texture and stoichiometry. Based on this, increasing the thickness leads to a transition in the deposition mode from heteroepitaxial to homoepitaxial growth, and the prolonged deposition mitigates longitudinal elemental non-uniformity and the attraction of metal ions within the buffer layer, enabling the attainment of good texture even at low temperatures. However, as the thickness increases, the phenomenon of compositional inhomogeneity in the film becomes more severe. Additionally, the actual temperature at the deposition surface may be lower than the set temperature, leading to grain misorientation or the formation of non-superconducting phases, which is detrimental to the superconducting performance of Fe(Se,Te) CC. As shown in Figure 17g–i, the T_c first increases at 450 nm and then decreases for a little bit at 600 nm. The corresponding J_c peaks at 450 nm, but the I_c continues to grow larger with the increasing thickness. The analysis of the pinning mechanism revealed the dominance of point pinning, as proved by the h_peak~0.33 in Figure 17j and 3–10 nm defects in the TEM image in Figure 17k, which do not change with the temperature.

Liu et al. creatively utilized reel-to-reel PLD for the first time to fabricate 1 m long Fe(Se,Te) coated conductors with high superconducting performance [83], as shown in Figure 18a. Figure 18d demonstrates the smooth surface of the CC, except for some particles most likely formed by the condensation of Se vapor. The AFM image in Figure 18e also proves the smooth plane with a small square root mean square roughness of about 1 nm. Figure 18f,g illustrate the high-quality epitaxial growth of Fe(Se,Te) films on CeO₂ buffer layers, where all (00l) planes are clearly visible with distinct interfaces between layers. Figure 18h,i demonstrate that the end-to-end I_c of the samples reached 108 A/cm at 4.2 K and self-field, with good performance observed even under high magnetic fields for short samples. Sharp superconducting transitions occurred in Fe(Se,Te) films under magnetic fields ranging from 0 to 9 T, with T_c reaching up to 17.5 K, and an estimated H_c2(0) = 53 T. The J_c(4.2 K) derived from the Bean model is over 2 MA/cm² at self-field.

Liu et al. optimized the ability of the Fe(Se,Te)-coated conductors to withstand uniaxial tensile pressure by encapsulating them with a copper layer [84]. As illustrated in Figure 19a–c, regardless of considering the cooling process effects, the mechanical and electrical performance of the tape with copper encapsulation under tensile strain is consistently superior to that of the bare tape. As the strain gradually increased from 0% to 0.5%, the I_c of both the bare tape and the copper-coated tape decreased by approximately 58% and 43%, respectively. With the adoption of copper encapsulation, the irreversible tensile strain limit of the FeSe_0.5Te_0.5 tape reached 0.15%. Furthermore, considering the effects of the cooling process, the actual irreversible tensile strain limit was enhanced to 0.29%.

Wei et al. successfully fabricated the world’s first hybrid coil by using FeSe_0.5Te_0.5 CC. The schematic diagram of the FeSe_0.5Te_0.5 hybrid coil and the inserted magnet is shown in Figure 19d–g. This hybrid coil consists of a single-layer FeSe_0.5Te_0.5 coil with an inner diameter of 51 mm and eight double-layer YBCO coils with inner diameters of 45 mm. The YBCO coils are divided into two parts and connected to both sides of the FeSe_0.5Te_0.5 coil. Additionally, a copper layer is used to cover the FeSe_0.5Te_0.5 coil to withstand the high stress during cooling, thereby preventing substrate shrinkage from damaging the superconducting layer. Figure 19i shows that the maximum stress on the coil is less than 1 MPa up to 10 T, which is within the allowable pressure range of the tape. As shown in Figure 19h, based on the quench process of the FeSe_0.5Te_0.5 coil in the first cold test, the self-field I_c reached 108.1 A, and the I_c at a 10T field reached 17.4 A. The J_c was approximately 1.42 × 10⁵ A/cm², which is consistent with the results of the short sample test. Results of repeated cold tests demonstrate the stable performance of the FeSe_0.5Te_0.5 hybrid coil.

6. Conclusions and Prospects

Despite the electroneutral FeSe layer, iron–chalcogenide superconductors present varieties of crystal structures exhibiting different superconducting characteristics. The interesting properties of this system prompt scientists to invent different methodologies to modulate the crystalline and electrical structures through oxidation, intercalation, the electrochemical method, and interface engineering, which greatly enriche the fabrications and investigations of high-temperature superconductors. According to the summarized phase diagram, higher T_c could be achieved through charge transfer and electron–phonon coupling across heterostructures. More importantly, the FeSe_1−xTe_x and the intercalated FeSe have a large upper critical field, which is the precondition for high-field applications. The successful fabrications of meters-long FeSe_1−xTe_x CC facilitate the first fabrications of insert pancake coils. Compared with the poor texture in the iron-based superconducting wires fabricated through the PIT process, the in-plane texture can be easily obtained in the CC, leading to a higher J_c than the FeSe_1−xTe_x wires at high fields [86,87,88]. Due to the larger critical misorientation angle compared to cuprates (θ_c = 5°), less textured substrates are required for the FeSe_1−xTe_x CC. However, the vortex pinning is dominated by the scarce point defects, whether in single crystals or CC. Stronger vortex pinning centers, e.g., nanoparticles and correlated column defects introduced in the ReBa₂Cu₃O_7−δ (Re = rare earth elements) CC by mature techniques, are highly desirable for further enhancement of the current carrying ability of the iron chalcogenide superconductors.