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1.
Sci Rep ; 13(1): 13451, 2023 Aug 18.
Article in English | MEDLINE | ID: mdl-37596292

ABSTRACT

The role of spin-orbit interaction has been recently reconsidered in high-[Formula: see text] cuprates, stimulated by the recent experimental observations of spin-polarized electronic states. However, due to the complexity of the spin texture reported, the origin of the spin polarization in high-[Formula: see text] cuprates remains unclear. Here, we present the spin- and angle-resolved photoemission spectroscopy (ARPES) data on the facing momentum points that are symmetric with respect to the [Formula: see text] point, to ensure the intrinsic spin nature related to the initial state. We consistently found the very weak spin polarization only along the nodal direction, with no indication of spin-splitting of the band. Our findings thus call for a revision of the simple application of the spin-orbit interaction, which has been treated within the standard framework of the Rashba interaction in high-[Formula: see text] cuprates.

2.
Nature ; 618(7967): 940-945, 2023 Jun.
Article in English | MEDLINE | ID: mdl-37380689

ABSTRACT

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry1-4. Experimental evidence for such a state exists in high magnetic field5-8 and in some materials that feature density-wave orders that explicitly break translational symmetry9-13. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe4As4, a material that features co-existing superconductivity (superconducting transition temperature (Tc) ≈ 37 kelvin) and magnetism (magnetic transition temperature (Tm) ≈ 15 kelvin)14,15. Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to Tc. When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above Tm, indicating that the PDW is a smectic order.

3.
Adv Mater ; 35(15): e2209964, 2023 Apr.
Article in English | MEDLINE | ID: mdl-36661255

ABSTRACT

Graphite intercalation compounds (GICs) have a variety of functions due to their rich material variations, and thus, innovative methods for their synthesis are desired for practical applications. It is discovered that Na has a catalytic property that dramatically accelerates the formation of GICs. It is demonstrated that LiC6 n (n = 1, 2), KC8 , KC12 n (n = 2, 3, 4), and NaCx are synthesized simply by mixing alkali metals and graphite powder with Na at room temperature (≈25 °C), and AE C6 (AE  = Ca, Sr, Ba) are synthesized by heating Na-added reagents at 250 °C only for a few hours. The NaCx , formed by the mixing of C and Na, is understood to act as a reaction intermediate for a catalyst, thereby accelerating the formation of GICs by lowering the activation energy of intercalation. The Na-catalyzed method, which enables the rapid and mass synthesis of homogeneous GIC samples in a significantly simpler manner than conventional methods, is anticipated to stimulate research and development for GIC applications.

4.
Inorg Chem ; 61(31): 12149-12154, 2022 Aug 08.
Article in English | MEDLINE | ID: mdl-35880851

ABSTRACT

Enriching the material variation often contributes to the progress of materials science. We have discovered for the first time antiperovskite arsenide SrPd3As and revealed a hidden structural and superconducting phase in Sr(Pd1-xPtx)3As. The Pd-rich samples (0 ≤ x ≤ 0.2) had the same noncentrosymmetric (NCS) tetragonal structure (a space group of I41md) as SrPd3P. For the samples with 0.3 ≤ x ≤ 0.7, a centrosymmetric (CS) tetragonal structure (P4/nmm) identical to that of SrPt3P was found to appear, accompanied by superconductivity at a transition temperature (Tc) up to 3.7 K. In the samples synthesized with Pt-rich nominal compositions (0.8 ≤ x ≤ 1.0), Sr2(Pd,Pt)8-yAs1+y with an intergrowth structure (CS-orthorhombic with Cmcm) was crystallized. The phase diagram obtained for Sr(Pd,Pt)3As was analogous to that of (Ca,Sr)Pd3P in which superconductivity (Tc ≥ 2 K) occurred in the CS phases induced by substitutions to the NCS phases. This study indicates the potential for further material variation expansion and the importance of elemental substitutions to reveal hidden phases in related antiperovskites.

5.
Nature ; 601(7894): 562-567, 2022 01.
Article in English | MEDLINE | ID: mdl-35082417

ABSTRACT

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap1. In the high-transition-temperature (high-Tc) cuprates, although the transport, magnetic and thermodynamic signatures of Tc have been known since the 1980s2, the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)2Sr2CaCu2O8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at Tc, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across Tc. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.

6.
Inorg Chem ; 60(23): 18017-18023, 2021 Dec 06.
Article in English | MEDLINE | ID: mdl-34779197

ABSTRACT

Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd3P, following our recent synthesis of APd3P (A = Ca, Sr, Ba). While APd3P and (Ca,Sr)Pd3P were found to be tetragonal or orthorhombic systems, LaPd3P is a new prototype cubic system (a = 9.0317(1) Å) with a noncentrosymmetric space group (I4̅3m). LaPd3P exhibited superconductivity with a transition temperature (Tc) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant (γ) were determined to be 0.305(8) kOe, 267(1) K, and 6.06(4) mJ mol-1 K-2 f.u.-1, respectively. We performed first-principles electronic band structure calculations for LaPd3P and compared the theoretical and experimental results. The calculated Sommerfeld constant (2.24 mJ mol-1 K-2 f.u.-1) was much smaller than the experimental value of γ because the Fermi energy (EF) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at EF due to the approximately 5 atom % La deficiency (hole doping) in the sample. The observed Tc value was much lower than that estimated using the Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the possibility of an unconventional superconductivity in LaPd3P arising from the lack of space inversion symmetry.

7.
Proc Natl Acad Sci U S A ; 118(37)2021 Sep 14.
Article in English | MEDLINE | ID: mdl-34493664

ABSTRACT

Magnetic superconductors are specific materials exhibiting two antagonistic phenomena, superconductivity and magnetism, whose mutual interaction induces various emergent phenomena, such as the reentrant superconducting transition associated with the suppression of superconductivity around the magnetic transition temperature (T m), highlighting the impact of magnetism on superconductivity. In this study, we report the experimental observation of the ferromagnetic order induced by superconducting vortices in the high-critical-temperature (high-T c) magnetic superconductor EuRbFe4As4 Although the ground state of the Eu2+ moments in EuRbFe4As4 is helimagnetism below T m, neutron diffraction and magnetization experiments show a ferromagnetic hysteresis of the Eu2+ spin alignment. We demonstrate that the direction of the Eu2+ moments is dominated by the distribution of pinned vortices based on the critical state model. Moreover, we demonstrate the manipulation of spin texture by controlling the direction of superconducting vortices, which can help realize spin manipulation devices using magnetic superconductors.

8.
Phys Chem Chem Phys ; 23(35): 19827-19833, 2021 Sep 15.
Article in English | MEDLINE | ID: mdl-34525149

ABSTRACT

We investigated the defect structures of polycrystalline CaKFe4As4 (CaK1144) superconductors by scanning transmission electron microscopy (STEM). The STEM studies revealed the presence of a one-layer CaFe2As2 (∼1 nm size) defect along the ab-plane, as observed in single crystalline CaK1144. Step-like CaFe2As2 defects are also observed. These nanoscale defects generate fine-sized stacking faults, a lattice mismatch, and stress field defects in the matrix of CaK1144 owing to the different sizes. Correlation of the defects in polycrystalline and single crystalline samples suggests that the defects type and their density depend on the synthesis conditions. A self-field critical current density (Jc) of 15.2 kA cm-2 was obtained at 5 K, and the curves were sustained above 30 K with a considerable Jc value of 1.4 kA cm-2. We investigated the relationship between the observed intrinsic defects and the behavior of the field dependence of Jc. The intrinsically intergrown planar defects, even in polycrystalline samples, are expected to be advantageous for various high-field applications of bulk CaK1144 superconductors.

9.
Inorg Chem ; 59(19): 14290-14295, 2020 Oct 05.
Article in English | MEDLINE | ID: mdl-32921044

ABSTRACT

It is generally difficult to quantify the amount of light elements in materials because of their low X-ray-scattering power, as this means that they cannot be easily estimated via X-ray analyses. Meanwhile, the recently reported layered superconductor, Sc20C8-xBxC20, requires a small amount of boron, which is a light element, for its structural stability. In this context, here, we quantitatively evaluate the optimal x value using both experimental and computational approaches. Using the high-pressure synthesis approach, which can maintain the starting composition even after sintering, we obtain the Sc20(C,B)8C20 phase by the reaction of the previously reported Sc15C19 and B (Sc15ByC19). Our experiments demonstrate that an increase in y values promotes the phase formation of the Sc20(C,B)8C20 structure; however, there appears to be an upper limit to the nominal y value to form this phase. The maximum critical temperature (Tc = 7.6 K) is found to correspond with the actual x value of x ≈ 5 under the assumption that the sample with the same Tc as the reported value (7.7 K) possesses the optimal x amount. Moreover, we construct the energy convex hull diagram by calculating the formation enthalpy based on first principles. Our computational results indicate that the composition of Sc20C4B4C20 (x = 4) is the most thermodynamically stable, which is reasonably consistent with the experimentally obtained value.

10.
Inorg Chem ; 59(17): 12397-12403, 2020 Sep 08.
Article in English | MEDLINE | ID: mdl-32845611

ABSTRACT

In this study, we succeeded in synthesizing new antiperovskite phosphides MPd3P (M = Ca, Sr, Ba) and discovered the appearance of a superconducting phase (0.17 ≤ x ≤ 0.55) in a solid solution (Ca1-xSrx)Pd3P. Three perovskite-related crystal structures were identified in (Ca1-xSrx)Pd3P, and a phase diagram was built on the basis of experimental results. The first phase transition from centrosymmetric (Pnma) to noncentrosymmetric orthorhombic (Aba2) occurred in CaPd3P near room temperature. The phase transition temperature decreased as Ca2+ was replaced with a larger-sized isovalent Sr2+. Bulk superconductivity at a critical temperature (Tc) of approximately 3.5 K was observed in a range of x = 0.17-0.55; this was associated with the centrosymmetric orthorhombic phase. Thereafter, a noncentrosymmetric tetragonal phase (I41md) remained stable for 0.6 ≤ x ≤ 1.0, and superconductivity was significantly suppressed as samples with x = 0.75 and 1.0 showed Tc values as low as 0.32 K and 57 mK, respectively. For further substitution with a larger-sized isovalent Ba2+, namely, (Sr1-yBay)Pd3P, the tetragonal phase continued throughout the composition range. BaPd3P no longer showed superconductivity down to 20 mK. Since the inversion symmetry of structure and superconductivity can be precisely controlled in (Ca1-xSrx)Pd3P, this material may offer a unique opportunity to study the relationship between inversion symmetry and superconductivity.

11.
Proc Natl Acad Sci U S A ; 117(12): 6424-6429, 2020 Mar 24.
Article in English | MEDLINE | ID: mdl-32165540

ABSTRACT

Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics), resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba1-x Rb x Fe2As2 iron-based superconductors. While for [Formula: see text], the nematic director points along the in-plane diagonals of the tetragonal lattice, for [Formula: see text], it points along the horizontal and vertical axes. Remarkably, for intermediate doping, the susceptibilities of these two symmetry-irreducible nematic channels display comparable Curie-Weiss behavior, thus revealing a nearly XY-nematic state. This opens a route to assess this elusive electronic quantum liquid-crystalline state.

12.
Inorg Chem ; 58(22): 15629-15636, 2019 Nov 18.
Article in English | MEDLINE | ID: mdl-31661255

ABSTRACT

The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature (Tc) in materials containing light elements, we explored new superconducting phases in a scandium borocarbide system. Here, we report the observation of superconductivity in a new ternary Sc-B-C compound. The crystal structure, which was determined through a Rietveld analysis, belongs to tetragonal space group P4/ncc. By complementarily using the density functional theory calculations, a chemical formula of the compound was found to be expressed as Sc20C8-xBxC20 (x = 1 or 2). Interestingly, a small amount of B is essential to stabilize the present structure. Our experiments revealed the typical type-II superconductivity at Tc = 7.7 K. Additionally, we calculated the density of states within a first-principles approach and found that the contribution of the Sc-3d orbital was mainly responsible for the superconductivity.

13.
J Phys Chem Lett ; 10(5): 1018-1023, 2019 Mar 07.
Article in English | MEDLINE | ID: mdl-30767536

ABSTRACT

We report synthesis, crystal structure, and superconductivity in ThCr2Si2-type LaFe2As2 (La122). La122 was synthesized at 960 °C for 1.5 h under a pressure of 3.4 GPa. An as-synthesized La122 (nonsuperconductor) had a collapsed tetragonal structure with a short c-axis length of 11.0144(4) Å as observed in CaFe2As2 under pressure. The collapsed tetragonal structure transformed into an uncollapsed tetragonal structure by annealing the as-synthesized La122 at 500 °C. The c-axis length remarkably extended to 11.7317(4) Å, and superconductivity emerged at 12.1 K in the uncollapsed tetragonal La122. A cylindrical hole-like Fermi surface around the Γ point that plays an important role for an s± wave pairing in iron-based superconductors was missing in the uncollapsed tetragonal La122 because of heavy electron doping. Superconductivity in La122 may be closely related to that induced in CaFe2As2 under pressure.

14.
Sci Rep ; 8(1): 16827, 2018 Nov 14.
Article in English | MEDLINE | ID: mdl-30429484

ABSTRACT

We synthesized a Fe-based superconductor (FeSC), (La,Na,K)Fe2As2, and characterized its superconducting properties. It was found that (La,Na,K)Fe2As2 has a 122-type (ThCr2Si2-type) structure with a space group I4/mmm (No. 139), identical to (Ba,K)Fe2As2 and (La,Na)Fe2As2 but distinct from so-called 1144-type FeSCs such as CaKFe4As4 and (La,Na)CsFe4As4. The results demonstrate that the formation of the 1144-type phase necessitates the large ionic radius mismatch among the so-called A-site constituent elements of the AFe2As2 formula. The lattice constants are a = 3.850(1) Å and c = 13.21(1) Å. The La, Na, and K ions occupy the same atomic site of Wyckoff position 1a. Electrical resistivity and magnetic susceptibility show the superconducting transition at 22.5 K. The transition temperature (Tc) of (La,Na,K)Fe2As2 is comparable with that of 122-type (La,Na)Fe2As2 and 1144-type (La,Na)AFe4As4 (A = Rb, Cs), while being more than 10 K lower than those of typical 122- and 1144-type FeSCs. The results suggest that the random distribution of La3+ and Na+ ions is the main reason for lower Tc in the AE = (La,Na) 122-type and 1144-type FeSCs.

15.
Inorg Chem ; 57(15): 9223-9229, 2018 Aug 06.
Article in English | MEDLINE | ID: mdl-30048121

ABSTRACT

Recently, we succeeded in synthesizing (La0.5- xNa0.5+ x)Fe2As2 ((La,Na)122) with a solid solution range of 0 ≤ x ≤ 0.35. Superconductivity was induced for 0.15 ≤ x ≤ 0.35, with the highest transition temperature Tc = 27.0 K for x = 0.3. Here, we report the synthesis and physical properties of analogous compounds ( Ln0.5- xNa0.5+ x)Fe2As2 (( Ln,Na)122) ( Ln = Ce, Pr). Samples were synthesized by precisely tuning the reaction temperature according to Ln and x. The solid solution ranges, 0.1 ≤ x ≤ 0.3 ( Ln = Ce) and 0.15 ≤ x ≤ 0.25 ( Ln = Pr), become narrower with increasing atomic number of Ln (which decreases the ionic radius of Ln3+). Bulk superconductivity emerged for 0.2 ≤ x ≤ 0.3 and 0.15 ≤ x ≤ 0.25 with the highest Tc of 25.6 K ( x = 0.3) and 24.7 K ( x = 0.25) for Ln = Ce and Pr, respectively. Crystal structures refined via the Rietveld analysis method showed that the ( Ln,Na)122 compounds ( Ln = La, Ce, Pr) with the highest Tc have almost the same As-Fe-As bond angles (∼107°) and As heights from Fe planes (∼1.43 Å). In addition to the solid solution ranges, the phases in the samples changed depending on the ionic radius of Ln3+. The ( Ln,Na)122 phase competes with the non-superconducting CaFe4As3(143)-type phase of ( Ln,Na)Fe4As3 for Ln = Ce and Pr, whereas only the ( Ln,Na)122 phase was stable for Ln = La. The 143-type phase alone was observed for Ln = Nd, and neither 122- nor 143-type phases were observed for Ln = Sm and Gd.

16.
J Phys Chem Lett ; 9(4): 868-873, 2018 Feb 15.
Article in English | MEDLINE | ID: mdl-29412667

ABSTRACT

We discovered novel Fe-based superconductors (FeSCs) (La,Na)AFe4As4, where A = Rb or Cs, and characterized their superconducting properties. (La,Na)AFe4As4 is a so-called 1144-type compound with a tetragonal unit cell classified into space group P4/mmm (no. 123). The lattice constants are a = 3.861(1) Å and c = 13.26(1) Å for (La,Na)RbFe4As4 and a = 3.880(1) Å and c = 13.60(1) Å for (La,Na)CsFe4As4. The Rietveld refinement results on the powder X-ray diffraction suggest that the La/Na ratio is rather fixed as La:Na = 0.44(5):0.56(5). The electrical resistivity and magnetic susceptibility show superconducting transition at 25.5 K for (La,Na)RbFe4As4 and 24.0 K for (La,Na)CsFe4As4. The superconducting transition temperature (Tc) of (La,Na)AFe4As4 is comparable with that of 122-type (La,Na)Fe2As2 and lower than that of typical 122-type or 1144-type FeSCs by more than 10 K. The possible reasons for lower Tc are discussed in terms of the structural modification, carrier concentration, and chemical disorder.

17.
J Am Chem Soc ; 140(1): 369-374, 2018 01 10.
Article in English | MEDLINE | ID: mdl-29280633

ABSTRACT

(La0.5-xNa0.5+x)Fe2As2 ((La,Na)122) is an interesting system in the sense that either electrons (x < 0) or holes (x > 0) can be doped into the Fe2As2 layers, simply by changing the composition value x. However, only nonbulk superconducting samples (single crystals) with x = 0.1 have been synthesized to date. Here, we successfully synthesize polycrystalline samples with a wide hole-doping composition range of 0 ≤ x ≤ 0.35 via a conventional solid-state reaction, by tuning the reaction temperature according to x. The parent compound, (La0.5Na0.5)Fe2As2 (x = 0), is a nonsuperconductor with a resistivity anomaly at 130 K due to structural and antiferromagnetic transitions. We find that the temperature of the resistivity anomaly decreases with increasing x and that bulk superconductivity emerges for 0.15 ≤ x ≤ 0.35. The maximum transition temperature is 27.0 K, for x = 0.3. An electronic phase diagram for the hole-doping side is constructed. However, electron-doped samples (x < 0) cannot be synthesized; thus, the other half of the electronic phase diagram of (La,Na)122 requires resolution to study the electron-hole symmetry in Fe-based superconductors.

18.
Sci Adv ; 3(8): e1700466, 2017 08.
Article in English | MEDLINE | ID: mdl-28875162

ABSTRACT

A major problem in the field of high-transition temperature (Tc) superconductivity is the identification of the electronic instabilities near superconductivity. It is known that the iron-based superconductors exhibit antiferromagnetic order, which competes with the superconductivity. However, in the nonmagnetic state, there are many aspects of the electronic instabilities that remain unclarified, as represented by the orbital instability and several in-plane anisotropic physical properties. We report a new aspect of the electronic state of the optimally doped iron-based superconductors by using high-energy resolution angle-resolved photoemission spectroscopy. We find spectral evidence for the folded electronic structure suggestive of an antiferroic electronic instability, coexisting with the superconductivity in the nonmagnetic state of Ba1-x K x Fe2As2. We further establish a phase diagram showing that the antiferroic electronic structure persists in a large portion of the nonmagnetic phase covering the superconducting dome. These results motivate consideration of a key unknown electronic instability, which is necessary for the achievement of high-Tc superconductivity in the iron-based superconductors.

19.
Inorg Chem ; 56(14): 8590-8595, 2017 Jul 17.
Article in English | MEDLINE | ID: mdl-28657309

ABSTRACT

We have succeeded in crystallizing a new strontium digermanide (SrGe2-δ) with the ThSi2-type structure (tetragonal SrGe2), which is theoretically predicted to compete with the EuGe2-type one (trigonal SrGe2) under pressure. The tetragonal SrGe2 appeared as a metastable phase in samples at approximately 900 °C under a pressure of 2 GPa. X-ray diffraction studies show that the tetragonal SrGe2 is formed by the reaction between trigonal SrGe2 and excess Sr. The composition of the tetragonal SrGe2 was analyzed to be SrGe1.66(4). Lattice parameters for the tetragonal SrGe2 are determined to be a = 4.559(4) Å and c = 14.42(1) Å. The tetragonal SrGe2 shows metallic resistivity behavior and exhibits superconductivity with a critical temperature (Tc) of 7.3 K, which is the highest among compounds with the ThSi2-type structure. Superconducting properties of the tetragonal SrGe2, such as the upper critical field, and the effect of pressure on Tc, are presented and superconductivity is discussed on the basis of electronic band structure calculations.

20.
Sci Rep ; 6: 26671, 2016 05 25.
Article in English | MEDLINE | ID: mdl-27220461

ABSTRACT

Since the high transition temperature (High-Tc) superconductivity was discovered in the series of materials containing iron (Fe), their potential for the applications has been extensively scrutinized. In particular, a lot of effort has been made in achieving the high current-carrying ability by revealing the vortex pinning behavior. Here, we report on the critical current density (Jc) for the pristine Ba1-xKxFe2As2 single crystals with various K concentrations (0.25 ≤ x ≤ 0.52) determined by the magnetization hysteresis loop measurements. The x-dependence of Jc is characterized by a spike-like peak at x ~ 0.30, which corresponds to the under-doped region. This behavior is distinct from a moderate Tc dome with a broad maximum spanning from x ~ 0.3 to 0.5. For the under-doped samples, with increasing magnetic field (H), a second magnetization peak in Jc is observed, whereas for the optimally- and over-doped samples, Jc monotonically decreases with H. This result emphasizes that fine tuning of doping composition is important to obtain strong flux pinning. The origin of the characteristic doping dependence of Jc is discussed in connection with the orthorhombic phase domain boundary, as well as the chemical inhomogeneity introduced by the dopant substitutions.

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