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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Discovery of spontaneous mesoscopic strain waves in nematic domains using dark-field x-ray microscopy

Electronic nematic order arises when correlated electrons spontaneously break the rotational symmetry of a crystal lattice. When electronic nematic order couples bilinearly to symmetry-breaking lattice strain, both appear together at a single ferroelastic phase transition, producing structural twin domains with distinct orientations of the nematic director. While the effects of applied strain on these domains are well established, the intrinsic behavior of spontaneous subdomain strain fields has remained unexplored. Here, we report the discovery of spontaneous mesoscopic strain waves within individual nematic domains of an iron-based superconductor, observed using dark-field x-ray microscopy (DFXM). Using this advanced full-field imaging technique, we visualize subdomain strain modulations emerging concurrently with nematic order. Elastic compatibility relations governing inhomogeneous strains provide a natural mechanism for the strain waves. Our findings reveal a broadly relevant form of strain self-organization and position DFXM as a powerful probe of the local interplay between lattice strain and electronic order.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A mesoscopic device for a realization of the topological Kondo effect

The search for anyons is a field of immense interest owing to its potential application in the field of quantum information. Quantum critical Kondo impurities constitute one possible platform for their realization and topological Kondo effect (TKE) by virtue of remaining critical in the presence of perturbations, seems to be especially promising in this regard. In this paper we discuss practical steps for a realization of TKE with a relatively high Kondo temperature $\mathbf{T}$ k . Its central feature is the so-called Majorana-Cooper box (MCB) and we argue that a particular type of iron-based topological superconductor is especially suitable for realization of TKE. Once MCB is available one needs to connect it to external metallic leads to produce TKE. A relatively high value of the Kondo temperature $\mathbf{T}$ k is then aided by a large superconducting gap of the iron-based superconductor. We give estimates for $\mathbf{T}$ k , for the cases of both isotropic and anisotropic exchange couplings of MCB with the leads.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Microscopic origin of ultranodal superconducting states in spin- 1 2 systems

Several unconventional superconductors show indications of zero-energy excitations in the superconducting state consistent with the existence of a so-called Bogoliubov-Fermi surface (BFS). In particular, FeSe isovalently substituted with S seems to acquire a nonzero density of states at zero energy at low temperatures as the system goes into the tetragonal phase, consistent with a previously proposed phenomenological theory assuming an anisotropic spin singlet pairing gap coexisting with a nonunitary interband triplet component. Here we search for a microscopic model that can support the coexistence of singlet pairing with other orders, including interband nonunitary triplet pairing with magnetization, and discuss several candidates that indeed stabilize ground states with BFS. We show that with proper choice of the coupling strength of the various orders in our model, spontaneous breaking of C 4 rotational symmetry is realized at low temperatures. This feature resembles the findings of recent angle-resolved photoemission experiments in Fe(Se,S) in the tetragonal phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Universal Superconductivity in FeTe and All‐Iron‐Based Ferromagnetic Superconductor Heterostructures

Abstract Ferromagnetism (FM) and superconductivity (SC) are two of the most famous macroscopic quantum phenomena. However, nature normally does not allow SC and FM to coexist without significant degradation. Here, the first fully iron‐based SC/FM heterostructures, composed of Fe(Te,Se) and Fe 3 GeTe 2 , are introduced, and it is shown that this system exhibits both strong FM and high‐temperature SC with an atomically sharp interface. From this study, it is also discovered that minute level of various cationic dopants can drive otherwise non‐superconducting FeTe films into a SC state. This suggests that the ground state of FeTe is so close to the SC state that it can be driven in and out of the SC state with various other perturbations. Altogether, this shows that Fe‐Te‐based heterostructures provide a unique opportunity to manipulate magnetism, superconductivity, and topological physics, paving the way toward new superconducting technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2023

London penetration depth of electron-irradiated Ba 0 . 47 K 0 . 53 Fe 2 As 2

We have characterized an electron-irradiated Ba 1-x K x Fe 2 As 2 (x = 0.53) single-crystal using two different experimental techniques: magneto-optic measurements and microwave measurements. The crystal has been measured before as well as after the 2.5 MeV electron irradiation process. After irradiation it was annealed in a number of steps, between 90 °C and 180 °C, and measured after each annealing step. Most microwave measurements were performed by means of a copper cavity, taking advantage of the TE 011 and TM 110 modes, allowing for the determination of the London penetration depths changes δλ ab (T) and δλ c (T), ie perpendicular and parallel to the sample c-axis. Appropriate equations, based on perturbation theory, were derived to calculate the penetration depths changes δλ ab and δλ c for a rectangular prism geometry. The sample showed a full recovery of its T c , however the observed behavior of δλ c and δλ ab was not monotonic vs annealing temperature, displaying a minimum of δλ c and δλ ab at 120 °C. In conclusion, this finding was confirmed by magneto-optic measurements, where besides verifying the sample uniformity and the absence of visible defects, the lower critical field H c1 of the Ba 1-x K x Fe 2 As 2 single-crystal was obtained and the London penetration depth λab(0) was calculated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Antiferromagnetic order and its interplay with superconductivity in CaK(Fe$_{1-x}$Mn$_x$) 4 As 4

The magnetic order for several compositions of CaK(Fe$_{1-x}$Mn$_x$) 4 As 4 has been studied by nuclear magnetic resonance (NMR), Mössbauer spectroscopy, and neutron diffraction. Our observations for the Mn-doped 1144 compound are consistent with the hedgehog spin vortex crystal (hSVC) order which has previously been found for Ni-doped CaKFe 4 As 4 . The hSVC state is characterized by the stripe-type propagation vectors $(\pi\,0)$ and $(0\,\pi)$ just as in the doped 122 compounds. The hSVC state preserves tetragonal symmetry at the Fe site, and only this SVC motif with simple antiferromagnetic (AFM) stacking along $\ c$ is consistent with all our observations using NMR Mössbauer spectroscopy, and neutron diffraction. We find that the hSVC state in the Mn-doped 1144 compound coexists with superconductivity (SC), and by combining the neutron scattering and Mössbauer spectroscopy data we can infer a quantum phase transition, hidden under the superconducting dome, associated with the suppression of the AFM transition temperature ($T_N$) to zero for $x$ ≈ 0.01. In addition, unlike several 122 compounds and Ni-doped 1144, the ordered magnetic moment is not observed to decrease at temperatures below the superconducting transition temperature ($T_c$).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Understanding vortex dynamics in CaK(Fe,Ni) 4 As 4 and Ba(Fe,Co) 2 As 2 single crystals under the influence of random point disorder

We report on the influence of doping on vortex dynamics in 3 MeV proton-irradiated single crystals of CaK(Fe 1–x Ni x ) 4 As 4 (1144, x = 0.015, 0.025, and 0.03) and Ba(Fe 1–x Co x ) 2 As 2 (x = 0.04, 0.062, 0.066 and 0.074). Non-irradiated crystals of the 1144 system display superconducting critical temperatures ranging from 31 K for x = 0.015–20.5 K, as doping increases to 0.03. On the other hand, pristine crystals of the 122 system show T c values between 14.6 and 23.6 K, with the maximum T c occurring at intermediate doping levels. The fluence was set at 3 × 10 16 p cm –2 , resulting in a decrease in the T c by around 1.5 K for all samples and significantly affecting the vortex dynamics by reducing the flux creep relaxation compared to previously reported values for unirradiated crystals. Parameters such as vortex pinning energy U 0 and the glassy exponent μ dependencies on doping and magnetic field strength are identified. For the 1144 system, U 0 reaches values approaching 500 K for small fields in samples with T c = 29.3 K (x = 0.015), systematically decreasing to around 200 K as T c falls below 20 K. Furthermore, U 0 decreases as the field increases to 3 T for the same sample, varying from approximately 250 K to 100 K as T c decreases. These changes are typically accompanied by modifications in μ, gradually increasing from values around 1 towards 1.5, corresponding to small bundle relaxation in the collective creep theory. Despite differences in the substitutional disorder and magnetic phase diagram with respect to the 1144 system, the results for 122 single crystals follow a similar tendency in which U 0 usually reduces and μ increase rise as the applied magnetic field is increased. Due to moderate U 0 in these systems (few hundreds of kelvins), the resulting decay of persistent current at liquid helium temperatures is primarily determined by a balance between U 0 and bundle size contribution. Furthermore, these findings provide valuable insights for potential applications of these systems, particularly in the context of intrinsic superconducting parameters and the resulting pinning landscape.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Interrelationships between nematicity, antiferromagnetic spin fluctuations, and superconductivity: Role of hotspots in FeSe 1 - x S x revealed by high pressure Se 77 NMR study

The sulfur-substituted FeSe, FeSe 1-x S x , is one of the unique systems that provides an independent tunability of nematicity, antiferromagnetism, and superconductivity under pressure (p). Recently, Rana et al. [K. Rana et al., Phys. Rev. B 101, 180503(R) (2020)] reported, from 77 Se nuclear magnetic resonance (NMR) measurements on FeSe 0.91 S 0.09 under pressure, that there exists a clear role of nematicity in the relationship between antiferromagnetic (AFM) spin fluctuations and the superconducting transition temperature (T c ), where the AFM spin fluctuations are more effective in enhancing T c in the absence of nematicity than with nematicity. Here, motivated by the work, we carried out 77 Se NMR measurements on FeSe 1-x S x with x=0.15 and 0.29 under pressure up to 2.10 GPa to investigate the relationship in a wide range of x in the FeSe 1-x S x system. Based on the new results together with the previously reported data for x=0 [P. Wiecki et al., Phys. Rev. B 96, 180502(R) (2017)] and 0.09 [K. Rana et al. Phys. Rev. B 101, 180503(R) (2020)], we established a p–x–temperature (T) phase diagram exhibiting the evolution of AFM spin fluctuations. From the systematic analysis of the NMR data, we found that the superconducting (SC) state in a nematic state arises from a non-Fermi-liquid state with strong stripe-type AFM spin fluctuations, while the SC state without nematicity comes from a Fermi-liquid state with mild stripe-type AFM spin fluctuations. Furthermore, we show that the previously reported impact of nematicity on the relationship between AFM fluctuations and superconductivity holds throughout the wide range of x from x=0 to 0.29 in FeSe 1-x S x under pressure. We discuss the origin of the role of nematicity in terms of the different numbers of hotspots on Fermi surfaces with and without nematicity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Superconductivity and magnetic and transport properties of single-crystalline CaK ( Fe 1 – x Cr x ) 4 As 4

Members of the CaK (Fe 1–x Cr x ) 4 As 4 series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by x-ray diffraction, elemental analysis, and magnetic and transport measurements. The effects of Cr substitution on the superconducting and magnetic ground states of CaKFe 4 As 4 (T c = 35 K) have been studied. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as x is increased from 0 to 0.038. For x-values greater than 0.012, signatures of a magnetic transition can be detected in magnetic measurements with the associated features in the transport measurements becoming detectable for x ≥ 0.038. The magnetic transition temperature increases in a roughly linear manner as Cr substitution increases. A temperature-composition (T – x) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, T*, appearing near 22 K for x ~ 0.017 and rising slowly up to 60 K for x ~ 0.077. The T – x phase diagrams for CaK (Fe 1–x T x ) 4 As 4 for T = Cr and Mn are essentially the same despite the nominally different band filling; this is in marked contrast to T = Co and Ni series for which the T – x diagrams scale by a factor of 2, consistent with the different changes in band filling Co and Ni would produce when replacing Fe. Superconductivity of CaK (Fe 1–x Cr x ) 4 As 4 is also studied as a function of magnetic field. A clear change in $H^{'}_{c2}$ (T)/T c , where $H^{'}_{c2}$ (T) is dH c2 (T)/dT, at x ~ 0.012 is observed and probably is related to a change of the Fermi surface due to magnetic order. Further, coherence length and the London penetration depths are also calculated based on H c1 and H c2 data. Both of them as a function of x show changes near x = 0.012, again consistent with Fermi surface changes associated with the magnetic ordering seen for higher x-values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Probing putative orbital differentiation effects via Eu 2+ spin dynamics in Sr 1-x Eu x Fe 2 As 2

Here, in this work, we report x-ray powder diffraction, elemental analysis, electrical resistivity, magnetic susceptibility, specific heat, and electron spin resonance (ESR) in single crystals of Sr 1-x Eu x Fe 2 As 2 . We observed a breakdown of the previously reported scaling between the Eu 2+ Korringa relaxation rate obtained from ESR and the spin density wave temperature evolution for Sr-rich samples. This result suggests a distinct evolution of the orbital differentiation of the Fe 3d bands along the Sr-based series when compared to the Ba counterpart. We argue that this difference is related to a larger splitting between the structural (tetragonal-to-orthorhombic) and the Fe-driven spin density wave transitions induced by Eu doping in this series. In fact, our results indicate that the two transitions follow an opposite x-Eu dependence for Sr-concentrated samples. Our work shows that Sr 1-x Eu x Fe 2 As 2 series and the comparison with their Ba-based counterparts are exciting platforms to be explored for understanding the interplay among orbital differentiation, magnetism, and structural distortions in the iron pnictides

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Competing topological superconducting phases in FeSe 0.45 ⁢Te 0.55

We demonstrate that recent angle-resolved photoemission spectroscopy experiments provide strong evidence for the existence of two competing topological superconducting phases in FeSe 0.45⁢ Te 0.55 . The coupling of their underlying microscopic mechanisms—one based on a three-dimensional topological insulator, one based on two-dimensional superconductivity—stabilizes topological superconductivity over a wide range of parameters, and gives rise to two disjoint topological regions in the phase diagram of FeSe 0.45 ⁢Te 0.55 . Here, we show that the topological origin of these regions can be identified by considering the form of Majorana edge modes at domain walls.

Angle-resolved photoemission spectroscopy↗
DOE OSTI2026

Intertwined charge, spin, and orbital degrees of freedom under electronic correlations in the one-dimensional Fe 3+ chalcogenide chain

Motivated by recent developments in the study of quasi-one-dimensional iron systems with Fe 2+ , we comprehensively study an Fe 3+ chalcogenide chain system. Based on first-principles calculations, the Fe 3+ chain has a similar electronic structure to that discussed before for the Fe 2+ chain, because of the similar Fe⁢𝑋 4 (𝑋 = S or Se) tetrahedron-chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation 𝑈/𝑊 region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons (𝑈 is the on-site Hubbard repulsion, while 𝑊 is the electronic bandwidth) based on the orbital-selective behavior observed in the charge fluctuations. Furthermore, we do not observe any obvious pairing tendency in the Fe 3+ chain in the electronic-correlation 𝑈/𝑊 region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the Fe 3+ systems. Finally, our results clearly establish the similarities and differences between Fe 2+ and Fe 3+ iron chains, as well as iron ladders.

density matrix renormalization group↗
DOE OSTI2024

In-plane anisotropic magnetoresistance in detwinned BaFe 2-x Ni x As 2 (x = 0, 0.6)

Understanding the magnetoresistance (MR) of a magnetic material forms the basis for uncovering the orbital mechanisms and charge-spin interactions in the system. Although the parent state of iron-based high-temperature superconductors, including BaFe 2 As 2 , exhibits unusual electron transport properties resulting from spin and charge correlations, there is still valuable insight to be gained by understanding the in-plane MR effect due to twin domains in the orthorhombic antiferromagnetic ordered state. Here, we study the in-plane magnetoresistance anisotropy in detwinned BaFe 2 As 2 and compare the results to the nonmagnetic Ni-doped sample. We find that in the antiferromagnetically ordered state, BaFe 2 As 2 exhibits anisotropic MR that becomes large at low temperatures and high fields. Both transverse and longitudinal MRs are highly anisotropic and dependent on the field and current orientations. Furthermore, these results cannot be fully explained by calculations considering only the anisotropic Fermi surface. Instead, the spin orientation of the ordered moment also affects the MR effect, suggesting the presence of a large charge-spin interaction in BaFe 2 As 2 that is not present in the Ni-doped material.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Elastocaloric evidence for a multicomponent superconductor stabilized within the nematic state in Ba(Fe 1− x Co x ) 2 As 2

The iron-based high-$T_c$ superconductors (SCs) exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity, and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, in this study, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe 1− x Co x ) 2 As 2 near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and reentrant tetragonality as the origin of this transition and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a subdominant pairing instability that competes strongly with the dominant $s^±$ instability. Our results highlight the significant role of nematic order in determining the pairing symmetry close to optimal doping in this extensively studied iron-based SC, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

Ghosh, Sayak [Stanford University, CA (United Stat↗
DOE OSTI2025

Hund's coupling assisted orbital-selective superconductivity in Ba1-xKxFe2As2

While the superconducting transition temperature of hole-doped Ba_{1-x}K_{x}Fe_{2}As_{2} decreases past optimal doping, superconductivity does not completely disappear even for the fully doped KFe_{2}As_{2} compound. In fact, superconductivity is robust through a Lifshitz transition where electron bands become hole-like around the zone corner at around x=0.7, thus challenging the conventional understanding of superconductivity in iron-based systems. High-resolution angle-resolved photoemission spectroscopy is used to investigate the superconducting gap structure, as well as the normal state electronic structure, around optimal doping and across the Lifshitz transition. Our findings reveal a largely orbital-dependent superconducting gap structure, where the more strongly correlated d_{xy} band has a vanishing superconducting gap at higher doping, aligning with the Hund's metal behavior observed in the normal state. Notably, the superconducting gap on the d_{xy} band disappears before the Lifshitz transition, suggesting that the Fermi surface topology may play a secondary role. We discuss how these results point to orbital-selective superconducting pairing and how strong correlations via Hund's coupling may shape superconducting gap structures in iron-based and other multiorbital superconductors.

FOS: Physical sciences↗
DOE OSTI2024

Nodal superconductivity in miassite Rh 17 S 15

Solid state chemistry has produced a plethora of materials with properties not found in nature. For example, high-temperature superconductivity in cuprates is drastically different from the superconductivity of naturally occurring metals and alloys and is frequently referred to as unconventional. Unconventional superconductivity is also found in other synthetic compounds, such as iron-based and heavy-fermion superconductors. Here, we report compelling evidence of unconventional nodal superconductivity in synthetic samples of Rh 17 S 15 (T c = 5.4 K), which is also found in nature as the mineral miassite. We investigated the temperature-dependent variation of the London penetration depth Δλ(T) and the disorder evolution of the critical superconducting temperature T c and the upper critical field H c2 (T) in single crystalline Rh 17 S 15 . We found a T - linear temperature variation of Δλ(T) below 0.3T c , which is consistent with the presence of nodal lines in the superconducting gap of Rh 17 S 15 . The nodal character of the superconducting state is supported by the observed suppression of T c and H c2 (T) in samples with a controlled level of non-magnetic disorder introduced by 2.5 MeV electron irradiation. We propose a nodal sign-changing superconducting gap in the A 1g irreducible representation, which preserves the cubic symmetry of the crystal and is in excellent agreement with the derived superfluid density. To the best of our knowledge, this establishes miassite as the only mineral known so far that reveals unconventional superconductivity in its clean synthetic form, though it is unlikely that it is present in natural crystals because of unavoidable impurities that quickly destroy nodal superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗