FeSe Single Crystals Research Articles

Turbulent Structure and Characterization of ‘11’-type Iron-based Superconductors by Magneto-optical Imaging

Magneto-optical imaging is employed to investigate the vortex penetration modes in ‘11’-type iron-based superconductors (IBSs) Fe(Te0.6Se0.4) and FeSe single crystals. In Fe(Te0.6Se0.4), vortices penetrate mostly homogeneously from all edges, forming an unstable turbulent interface with pre-existing anti-vortices, where ‘Meissner hole’ emerges as those have been reported in ‘122’-type IBSs. In FeSe, however, the penetration is restricted to numerous mesoscopic stripe-like regions. Further experiments revealed an inhomogeneous vortex propagation pattern, where vortices are most likely to be channeled along the twin boundaries.

Fracture toughness of Fe–Si single crystals in mode I: Effect of loading rate on an edge crack (–110)[110] at macroscopic and atomistic level

This paper is devoted to an experimental and 3D atomistic study of the influence of loading rate on fracture toughness in dilute Fe–Si alloys and in bcc iron. We analyze new and previous experimental results from fracture tests performed at room temperature on bcc iron–silicon single crystals with edge cracks (1¯10)[110] (crack plane/crack front). The specimens of single edge notch-type were loaded in tension mode I under different loading rates. The ductile–brittle behavior at the crack front was monitored online via optical microscopy together with external force and prolongation of the specimens. About 30% decrease in fracture toughness was monitored in the new experiment under the highest loading rate. The nanoscopic processes produced by the crack itself were studied at room temperature via 3D molecular dynamics (MD) simulations in bcc iron under equivalent boundary conditions as in experiments to reveal (explain) the sensitivity of the crack to loading rate. For this purpose, this MD study utilizes the self-similar character of linear fracture mechanics. The results show that the emission of blunting dislocations from the crack is the most difficult under the highest loading rate, which leads to the reduced fracture toughness of the atomistic sample. This is in a qualitative agreement with the experimental (macro) results. Moreover, MD indicates that there may be some synergetic (resonant) effect between the loading rate and thermal activation that promotes dislocation emission.

Significant enhancement of critical current density in H+-intercalated FeSe single crystal

Superconducting transition temperature (T c) and critical current density (J c) are two key factors that are not only crucial for probing high temperature superconducting mechanism, but also for practical applications. The simple crystal structure of FeSe is very favorable for the fabrication of thin films and wires, but its application is limited by the relatively low T c and small J c. Previous studies have found that the T c of FeSe can be significantly enhanced over 40 K by using protonation method. Here, we present a systematic study of J c and vortex properties of H+-intercalated FeSe (H x -FeSe) single crystals. The value of J c for H x -FeSe single crystal is significantly enhanced, exceeding 1.3 × 106 A cm−2 at 4 K, which is more than two orders of magnitude larger than 1.1 × 104 A cm−2 of pristine FeSe. The vortex pinning mechanism of H x -FeSe is found to be surface pinning, which is different from the dominant strong point-like pinning in pristine FeSe. Moreover, the systematic study of the vortex phase transition and the underlying mechanism provides a wealth of information for the vortex phase diagram of H x -FeSe single crystal. Our results confirm that the introduction of H+ intercalations into FeSe not only enhance the T c but also significantly increases the value of J c, which is favorable for practical applications.

Protonation-induced discrete superconducting phases in bulk FeSe single crystals

The superconducting transition temperature, $T_{\rm{c}}$, of FeSe can be significantly enhanced several-fold by applying pressure, electron doping, intercalating spacing layer, and reducing dimensionality. Various ordered electronic phases, such as nematicity and spin density waves, have also been observed accompanying high-$T_{\rm{c}}$ superconductivity. Investigation on the evolution of the electronic structure with $T_{\rm{c}}$ is essential to understanding electronic behavior and high-$T_{\rm{c}}$ superconductivity in FeSe and its derived superconductors. In this report, we have found a series of discrete superconducting phases, with a maximum $T_{\rm{c}}$ up to 44 K, in H$^+$-intercalated FeSe single crystals using an ionic liquid gating method. Accompanied with the increase of $T_{\rm{c}}$, suppression of the nematic phase and evolution from non-Fermi-liquid to Fermi-liquid behavior was observed. An abrupt change in the Fermi surface topology was proposed to explain the discrete superconducting phases. A band structure that favors the high-$T_{\rm{c}}$ superconducting phase was also revealed.

A novel iron-based superconductor synthesized by the ion exchange technique

The superconductivity of the FeSe-based superconductor is extremely sensitive to Fe vacancies in the FeSe plane. In order to reduce the formation of Fe vacancies in the FeSe plane, various low-temperature methods are developed. However, it is still complex and time consuming to control the Fe vacancies concentration. Here, a hybrid iron-based superconductor, Li0.21Se0.05(EG)0.26FeSe (EG: ethylene glycol, C2H6O2), is synthesized by a solvothermal ion-exchange technique using a nearly vacancy-free precursor of (TBA)0.3FeSe as the matrix. Bulk superconductivity with transition temperature (T c) of 30 K is confirmed by the characterization with the magnetic susceptibility and resistivity measurements. Compared with the pristine FeSe single crystal, x-ray photoelectron spectroscopy results show a decrease of the Fe valence, indicating that electron doping to FeSe plane accounts for the increase of the T c. Our result suggests that (TBA)0.3FeSe, a nearly vacancy-free precursor with a large distance between the adjacent FeSe planes, is a good template candidate for the synthesis of other hybrid iron-based superconductors using the ion exchange technique.

Enhanced vortex pinning with possible antiferromagnetic order in FeSe under pressure

The strong coupling between magnetic, structural, and electronic degrees of freedom is a prominent feature of Fe-based superconductors. However, the relationship between the degrees of freedom and vortex dynamics remains unclear. In this paper, we measure the vortex pinning energy ${U}_{0}/{k}_{\mathrm{B}}$ within the thermally activated flux-flow regime with respect to the pressure-induced phases in a FeSe single crystal. We show that the dependence of ${U}_{0}/{k}_{\mathrm{B}}$ on pressure, measured at a magnetic field higher than the crossover field ${H}_{\mathrm{cr}}$, follows a trend like those of critical temperature ${T}_{c}(p)$ and the average Fermi velocity ${\overline{v}}_{\mathrm{F}}(p)$. On the other hand, at magnetic fields lower than ${H}_{\mathrm{cr}}, {U}_{0}/{k}_{\mathrm{B}}$ increases remarkably before reaching the pressure at which antiferromagnetic (AFM) long-range order occurs. Our results suggest the presence of additional pinning sites, possibly AFM domain boundaries, correlated with the enhanced ${U}_{0}/{k}_{\mathrm{B}}$. In addition, in this paper, we provide a universal description of the vortex dynamics in FeSe.

Annealing Effect of FeSe Superconducting Polycrystalline Bulks in Low Oxygen Atmosphere

FeSe superconducting bulks with different Fe contents were prepared by high energy ball milling aided sintering process followed by a post annealing process in low oxygen atmosphere. The influences of Fe content, annealing temperature and oxygen partial pressure have been systematically studied. It was found that both the critical temperature and superconducting phase volume ratio have been obviously improved with annealing. However, the effect of oxygen annealing process on FeSe polycrystalline bulks was different with that on FeSe single crystals. In polycrystalline bulks, the annealing process could further promote the phase transition from nonsuperconducting hexagonal δ-FeSe phase to superconducting tetragonal β-FeSe phase. Meanwhile, the chemical composition uniformity has also been enhanced with no obvious FeO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</sub> phase detected by X-Ray Diffraction. With optimized annealing process under the oxygen partial pressure of 5% at 400 °C for 10 h, FeSe superconducting bulks have reached the critical temperature of 9.1 K.

Disorder-robust high-field superconducting phase of FeSe single crystals

When exposed to high magnetic fields, certain materials manifest an exotic superconducting (SC) phase that has attracted considerable attention. A proposed explanation for the origin of the high-field SC phase is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. This state is characterized by inhomogeneous superconductivity, where the Cooper pairs have finite center-of-mass momenta. Recently, the high-field SC phase was observed in FeSe, and it was deemed to originate from the FFLO state. Here, we synthesize FeSe single crystals with different levels of disorder. The level of disorder is expressed by the ratio of the mean free path to the coherence length and ranges between 35 and 1.2. The upper critical field \textit{B}$_{\rm{c}2}$ was obtained by both resistivity and magnetic torque measurements over a wide range of temperatures, which went as low as $\sim$0.5 K, and magnetic fields, which went up to $\sim$38 T along the \textit{c} axis and in the \textit{ab} plane. In the high-field region parallel to the \textit{ab} plane, an unusual SC phase was confirmed in all the crystals, and the phase was found to be robust against disorder. This result suggests that the high-field SC phase in FeSe is not a conventional FFLO state.

Electronic States and Energy Dissipations of Vortex Core in Pure FeSe Single Crystals Investigated by Microwave Surface Impedance Measurements

In order to clarify electronic states and energy dissipations due to a motion of a vortex core in pure FeSe, which is a candidate superconductor possessing a super-clean core, we measured the microwave surface impedance of pure FeSe single crystals under finite magnetic fields. From the magnetic-field dependence of the flux-flow resistivity, we found that a barometer of electronic states inside the vortex core $\omega_{0}\tau_{\rm core}$ is $1\pm0.5$, suggesting that the vortex core of pure FeSe is in the moderately clean regime contrary to the expectation of the super-clean core. We also found that the mean-free path inside the vortex core is suppressed at the distance of the order of the core radius. Based on observed results and previous reports, we discussed possible origins of rather small $\omega_{0}\tau_{\rm core}$ value in terms of the multiple-bands nature of FeSe and additional mechanisms producing extra energy dissipations specific to the vortex core in motion.

Superconductivity at 44.4 K achieved by intercalating EMIM+ into FeSe* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12061131001 and 52072170) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB25000000).

Superconductivity with transition temperature T c above 40 K was observed in protonated FeSe (H y -FeSe) previously with the ionic liquid EMIM-BF4 used in the electrochemical process. However, the real superconducting phase is not clear until now. And detailed structural, magnetization, and electrical transport measurements are lacking. By using similar protonating technique on FeSe single crystals, we obtain superconducting samples with T c above 40 K. We show that the obtained superconducting phase is not H y -FeSe but actually an organic-ion (C6H11 referred to as EMIM+)-intercalated phase (EMIM) x FeSe. By using x-ray diffraction technique, two sets of index peaks corresponding to different c-axis lattice constants are detected in the obtained samples, which belong to the newly formed phase of intercalated (EMIM) x FeSe and the residual FeSe, respectively. The superconductivity of (EMIM) x FeSe with T c of 44.4 K is confirmed by resistivity and magnetic susceptibility measurements. Temperature dependence of resistivity with different applied magnetic fields reveals that the upper critical field H c2 is quite high, while the irreversibility field H irr is suppressed quickly with increasing temperature till about 20 K. This indicates that the resultant compound has a high anisotropy with a large spacing between the FeSe layers.

Pressure-induced high-temperature superconductivity retained without pressure in FeSe single crystals

To raise the superconducting-transition temperature (Tc) has been the driving force for the long-sustained effort in superconductivity research. Recent progress in hydrides with Tcs up to 287 K under pressure of 267 GPa has heralded a new era of room temperature superconductivity (RTS) with immense technological promise. Indeed, RTS will lift the temperature barrier for the ubiquitous application of superconductivity. Unfortunately, formidable pressure is required to attain such high Tcs. The most effective relief to this impasse is to remove the pressure needed while retaining the pressure-induced Tc without pressure. Here, we show such a possibility in the pure and doped high-temperature superconductor (HTS) FeSe by retaining, at ambient pressure via pressure quenching (PQ), its Tc up to 37 K (quadrupling that of a pristine FeSe at ambient) and other pressure-induced phases. We have also observed that some phases remain stable without pressure at up to 300 K and for at least 7 d. The observations are in qualitative agreement with our ab initio simulations using the solid-state nudged elastic band (SSNEB) method. We strongly believe that the PQ technique developed here can be adapted to the RTS hydrides and other materials of value with minimal effort.

Electrical transport properties of FeSe single crystal under high magnetic field

Electrical transport properties of FeSe single crystal under high magnetic field

Strain tuning of nematicity and superconductivity in single crystals of FeSe

Strain is a powerful experimental tool to explore new electronic states and understand unconventional superconductivity. Here, we investigate the effect of uniaxial strain on the nematic and superconducting phase of single crystal FeSe using magnetotransport measurements. We find that the resistivity response to the strain is strongly temperature dependent and it correlates with the sign change in the Hall coefficient being driven by scattering, coupling with the lattice and multiband phenomena. Band structure calculations suggest that under strain the electron pockets develop a large in-plane anisotropy as compared with the hole pocket. Magnetotransport studies at low temperatures indicate that the mobility of the dominant carriers increases with tensile strain. Close to the critical temperature, all resistivity curves at constant strain cross in a single point, indicating a universal critical exponent linked to a strain-induced phase transition. Our results indicate that the superconducting state is enhanced under compressive strain and suppressed under tensile strain, in agreement with the trends observed in FeSe thin films and overdoped pnictides, whereas the nematic phase seems to be affected in the opposite way by the uniaxial strain. By comparing the enhanced superconductivity under strain of different systems, our results suggest that strain on its own cannot account for the enhanced high $T_c$ superconductivity of FeSe systems.

Normal and superconducting state properties of Cu-doped FeSe single crystals

We report the evolution of the physical properties of FeSe single crystals with Cu substitution. We show that introducing Cu suppresses bulk superconductivity quickly, much faster than the decrease in structural transition temperature, and further doping Cu induces a metal-insulator transition. In contrast, zero-field $ab$-plane resistivity ${\ensuremath{\rho}}_{xx}$ exhibits an unusual temperature dependence ${\ensuremath{\rho}}_{xx}(T)\ensuremath{\sim}A{T}^{n}$, with $n\ensuremath{\sim}$ 1, that is almost unchanged with the variation of Cu content. This result implies that magnetic fluctuations in FeSe are insensitive to the Cu substitution. The field dependence of the Hall resistivity of ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}\mathrm{Se}$ with $x&gt;$ 0 shows a positive slope in the low-temperature region which can be ascribed to the relatively higher hole mobility than the electron one. Therefore, the low-concentration Cu dopant as a strong scattering source can lead to the significant decrease in electron mobility which is detrimental to superconductivity, but it has minor effects on the carrier densities of electrons and holes as well as the shapes of the Fermi surfaces. Correspondingly, the structural transition and magnetic fluctuations in ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}\mathrm{Se}$ change slowly with $x$.

Control of band structure of FeSe single crystals via biaxial strain

We performed systematic transport measurements on FeSe single crystals with applying in-plane biaxial strain $\varepsilon$ ranging from -0.96% to 0.23%. Biaxial strain was introduced by firmly gluing samples to various substrate materials with different thermal expansion. With increasing $\varepsilon$, structural and superconducting transition temperatures monotonically increased and decreased, respectively. We analyzed magneto-transport results using a compensated three-carrier model. The evaluated densities of hole and electron carriers systematically changed with strain. This indicates that we succeeded in controlling the band structure of single-crystalline FeSe.

Electronic transport properties and hydrostatic pressure effect of FeSe0.67Te0.33 single crystals free of phase separation

FeSe1−x Te x superconductors manifest some intriguing electronic properties depending on the value of x. In FeSe single crystal, the nematic phase and Dirac band structure have been observed, while topological surface superconductivity (SC) with the Majorana bound state was found in the crystal of x∼ 0.55. Therefore, the electronic properties of single crystals with 0 < x ⩽ 0.5 are crucial for probing the evolution of those intriguing properties as well as their relations. However, this study is still left blank due to the lack of single crystals because of phase separation. Here, we report the synthesis, magnetization, electronic transport properties, and hydrostatic pressure effect of FeSe0.67Te0.33 single crystals free of phase separation. A structural (nematic) transition is visible at T s = 39 K, below which the resistivity exhibits a Fermi-liquid behavior. Analysis of the upper critical fields suggests that spin-paramagnetic effect should be taken into account for both H || c axis and H || ab plane. A crossover from the low-H quadratic to the high-H quasi-linear behavior is observed in the magnetoresistance, signifying the possible existence of Dirac-cone state. Besides, the strong temperature dependence of Hall coefficient, violation of (modified) Kohler’s rule, and two-band model analysis indicate the multiband effects in FeSe0.67Te0.33 single crystals. Hydrostatic pressure measurements reveal that T s is quickly suppressed with pressure while T c is monotonically increased up to 2.31 GPa, indicating the competition between nematicity and SC. No signature of magnetic order that has been detected in FeSe1−x S x is observed. Our findings fill up the blank of the knowledge on the basic properties of FeSe1−x Te x system with low-Te concentrations.

Structural and electrical transport properties of Cu-doped Fe1–x Cu x Se single crystals* *Project supported by the National Key Research and Development of China (Grant No. 2018YFA0704200), the National Natural Science Foundation of China (Grant No. 11834016), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB25000000).

We report the structural and electrical transport properties of Fe1–x Cu x Se (x = 0, 0.02, 0.05, 0.10) single crystals grown by a chemical vapor transport method. Substituting Cu for Fe suppresses both the nematicity and superconductivity of FeSe single crystal, and provokes a metal–insulator transition. Our Hall measurements show that the Cu substitution also changes an electron dominance at low temperature of un-doped FeSe to a hole dominance of Cu-doped Fe1–x Cu x Se at x = 0.02 and 0.1, and reduces the sign-change temperature (TR ) of the Hall coefficient (R H).

Nontrivial paired states in novel topological superconductors

We report on the superconductive paired states in TbPdBi, β-type FeSe and CaSn3 single crystals through temperature dependence of magnetic penetration depth analysis down to 0.040 K. For half-Heusler TbPdBi, in ultra-low temperature region we traced the T3 power-law behavior of penetration depth indicating the nodeless topological superconductivity with anisotropic gap structure which was confirmed with the analysis of superfluid density. That highlights the role of thermally activated quasi-particles in the pairing mechanism of TBPdBi for which the variation of Δλ(T) wanders off the renown quadratic behavior of penetration depth. In FeSe the contribution of London depth was described with a power law (n ≈ 2.4) and the superfluid density fitted well with two-band d + d model in which the values of both gaps are substantially smaller than the gap size expected by the isotropic BCS model, due to the nodeless anisotropic gap symmetry. In CaSn3, temperature variation of magnetic penetration depth exhibited linear behavior which is ascribed to the topologically nontrivial electronic states. Also, fitting the results of superfluid density exhibited features of multiband pairing allowing the nodal gap in the electronic states which is in good agreement with the expectation of London penetration depth. The complex superconducting order parameter is suggestive of two-dimensional spin singlet or mixing singlet-triplet pairing states behind the signatures of superconductivity in CaSn3. The mechanisms of pairing symmetry uncovered by the temperature dependence of penetration depth study of TbPdBi, FeSe and CaSn3 meet the requirements for topological superconductivity.

Pressure-induced second high-Tc superconducting phase in the organic-ion-intercalated (CTA)0.3FeSe single crystal

Whether the pressure-induced second high- superconducting phase (SC-II) is a universal phenomenon among the intercalated FeSe-derived superconductors deserves further investigations. Here, we report a high-pressure ac magnetic susceptibility study on the newly synthesized organic-ion-intercalated (CTA)0.3 FeSe single crystal, which has a high at ambient pressure. We found that the superconducting transition is quickly suppressed to below 20 K upon increasing pressure to , above which the SC-II phase emerges and its increases gradually to a maximum of ca. 40 K at 5 GPa. For , both and the superconducting volume decline quickly, presumably due to the collapse of the hybrid structure against the higher pressure. Nevertheless, our results indeed evidenced the pressure-induced SC-II phase in (CTA)0.3 FeSe, in reminiscent of the situations observed in (Li,Fe)OHFeSe and Li0.36 (NH3)y Fe2Se2. These results thus demonstrate that pressure-induced SC-II phase should be a universal phenomenon in the electron-doped intercalated FeSe-based superconductors.

Separate tuning of nematicity and spin fluctuations to unravel the origin of superconductivity in FeSe

The interplay of orbital and spin degrees of freedom is the fundamental characteristic in numerous condensed matter phenomena, including high-temperature superconductivity, quantum spin liquids, and topological semimetals. In iron-based superconductors (FeSCs), this causes superconductivity to emerge in the vicinity of two other instabilities: nematic and magnetic. Unveiling the mutual relationship among nematic order, spin fluctuations, and superconductivity has been a major challenge for research in FeSCs, but it is still controversial. Here, by carrying out 77Se nuclear magnetic resonance (NMR) measurements on FeSe single crystals, doped by cobalt and sulfur that serve as control parameters, we demonstrate that the superconducting transition temperature Tc increases in proportion to the strength of spin fluctuations, while it is independent of the nematic transition temperature Tnem. Our observation therefore directly implies that superconductivity in FeSe is essentially driven by spin fluctuations in the intermediate coupling regime, while nematic fluctuations have a marginal impact on Tc.