Atomic origin of the coexistence of high critical current density and high Tc in CuBa2Ca3Cu4O10+δ superconductors

For cuprate superconductors, a high critical transition temperature (Tc) can be realized in compounds containing multiple CuO2 layers in the unit cell, while a high critical current density (Jc) is rarely sustained above liquid nitrogen temperature. The CuBa2Ca3Cu4O10+δ (Cu-1234) superconductors synthesized under high oxygen pressure incredibly exhibit high Tc (~117 K) and high Jc (>104 A/cm2, 100 K) values. Here, the “double high” traits of Cu-1234 were investigated with advanced scanning transmission electron microscopy. It was revealed that ordering vacancies and plate-like 90° microdomains induced efficient microstructure pinning centers that suppressed vortex flux flow and enhanced Jc. Furthermore, metallic charge-reservoir blocks [Ba2CuO3+δ] were composed of unique compressed [CuO6] octahedra, which induced many holes with 2pz symmetry that significantly decreased the superconducting anisotropy and dramatically enhanced the interlayer coupling that guaranteed a high Jc. On the other hand, optimally doped CuO2 planes inside the thick superconducting blocks [Ca3Cu4O8] maintained a high Tc. Our results are applicable to design and synthesis of new superconductors with “double high” traits. In this work, a high-Tc (~117 K) joined with a high-Jc (>104 A/cm2, 100 K) are reported in the CuBa2Ca3Cu4O10+δ (Cu-1234) superconductor. Studies have shown that the ordering vacancies and platelike 90° micro-domains serve as efficient microstructure pinning centers which suppress the vortex flux flow and enhance Jc. And plenty of holes with 2pz symmetry owing to unique compressed [CuO6] octahedrons decrease superconducting anisotropy and enhance the interlayer coupling that guarantee a high-Jc.


Introduction
Critical-current density (J c ) is a parameter of primary importance for potential applications of high-temperature superconductors (HTSCs), and it is limited principally by breakdown of zero-resistive current due to thermally activated flux flow under high temperature and high magnetic fields 1,2 . The "intrinsic" J c at liquid nitrogen temperature is limited by the strong two-dimensional (2D) anisotropy of HTSCs, as well as the short coherence length, which is unfavorable for vortex pinning [3][4][5] . Among cuprate superconductors, application of Bi-based compounds at liquid nitrogen temperature is primarily limited by sharp decreases in J c values due to the strong anisotropy 6,7 . For Tl-and Hg-based compounds, the high anisotropy as well as the toxic Tl and Hg elements constrain applications 8,9 . Furthermore, the nontoxic YBa 2 -Cu 3 O 7−δ (YBCO) superconductor with relatively low anisotropy (γ~5), which has a high T c (∼90 K) and a high J c (å 10 4 A/cm 2 at 77 K), is best in terms of comprehensive properties 10,11 . The absolute value of J c is also determined extrinsically by the microstructure, which introduces efficient pinning centers into crystals suppressing the flux flow 4,12-15 . It has already been shown that overdoping HTSCs is effective in decreasing the anisotropies of HTSCs and increasing the irreversibility fields (H irr ) 5,16,17 . However, the T c values drop drastically with increasing carrier concentration in the overdoped region. The tradeoff between T c and J c or H irr in the overdoped region is a crucial problem for HTSCs.
Cu-1234 is a heavily overdoped superconductor that belongs to the CuBa 2 Ca n-1 Cu n O 2n+2+δ (n = 2, 3, 4…) family. In previous studies, Cu-1234 has been reported to have the following features: (I) a high T c above 117 K at ambient pressure near that of Hg-1223, which has the highest T c in cuprates; (II) excellent critical current densities at liquid nitrogen temperature, which are superior to Bi cuprate homologous superconductors and comparable to the classical Y-based system 18,19 . The persistent J c (T) relative to its value at absolute zero decreases roughly exponentially as exp(−T/T 0 ) because of flux creep 20 . The values of T 0 reported are~7 and 4-5 K for Hg systems and Bi-2212, respectively, which caused the J c values to drop rapidly to near zero at liquid nitrogen temperature 6,8,20 . While the values of T 0 reported to date were 16-20 K and~23 K for Cu-1234 and YBCO, respectively, the values of J c for both reached >10 4 A/cm 2 at 77 K 10,19-21 ; and (III) it contains alkaline earth copper oxides only but is stable in air 19 . However, the origin of this excellent superconducting behavior in Cu-1234, especially the high J c above liquid nitrogen temperature, has rarely been reported and is not understood. In this paper, we report systematic studies on the lattice and electronic structure of Cu-1234 by using Cscorrected STEM combined with neutron powder diffraction (NPD) and X-ray adsorption spectroscopy (XAS) and reveal the interaction between lattice and charge that may be intimately related to the excellent "double high" performance of Cu-1234. Our results are applicable to design and synthesis of new multilayered superconductors with high T c as well as high J c .

Materials and methods
The Cu-1234 sample was synthesized by a solid-state reaction method under high pressure and high temperature conditions. The detailed experimental procedure is described in the literature 18 . The starting materials were CaO (99.95% pure, Alfa Aesar), CuO (99.995% pure, Alfa Aesar), and BaO 2 (95% pure, Alfa Aesar). All of the operations were performed under argon gas in a glove box with oxygen and vapor levels of less than 1 ppm due to the highly hygroscopic nature of alkaline-earth metallic oxides. High-pressure experiments were performed with a cubic anvil-type high-pressure apparatus. After the pressure was gradually increased to 6 GPa, the sample was heated to 1273 K and maintained there for 30 min. Then, the temperature was reduced to ambient before releasing the pressure. After the high-pressure and hightemperature process, the superconductive Cu-1234 sample was obtained. Cross-sectional TEM specimens were prepared by a standard procedure that included mechanical grinding, tripod polishing, and argon ion beam milling in a stage cooled with liquid nitrogen. The thickness of the sample was less than 20 nm.
Atomic scale structures of Cu-1234 samples were studied by using a combination of selected area electron diffraction and high-angle annular dark field (HAADF) and annular bright field (ABF) imaging methods. Aberration-corrected STEM studies were performed on an FEI Titan Cubed Themis 60-300 (operating at 300 kV), which was capable of recording high-resolution STEM images with a spatial resolution of ≈ 0.06 nm. The microscopy equipment included a high brightness electron gun (X-FEG with a monochromator), a C S probe corrector, a C S image corrector, and a postcolumn imaging energy filter (Gatan Quantum 965 Spectrometer). ABF and HAADF images were acquired at acceptance angles of 12-45 and 64-200 mrad, respectively. The SI data and the ADF signal in the STEM-EELS experiments were simultaneously acquired with a beam current of~40 to 50 pA, a convergence semiangle of 25 mrad, a GIF collection semiangle of 55 mrad, and a pixel dwell time of 25 ms to maximize the signal while minimizing drift and beam damage artifacts. The orientation-dependent EELS measurements for the O-K edge in the TEM diffraction mode used a GIF collection semiangle of 0.362 mrad, an entrance aperture of 2.5 mm and a total sum time of 50 s to maximize the signal. NPD studies were performed on a GPPD (general purpose powder diffractometer) time-offlight diffractometer at the CSNS (China Spallation Neutron Source), Dongguan, China. The obtained NPD data were analyzed by the Rietveld method with the GSAS/EXPGUI package 22 . The magnetic properties of the sample were measured using a superconducting quantum interference device magnetometer (Quantum Design MPMS3-7T). The magnetization hysteresis loop was measured with a Cu-1234 powder sample. The Cu-1234 sample was finely ground and sealed in a nonmagnetic capsule. Soft X-ray absorption spectroscopy (XAS) at the O-K edge was measured at the BL08B beamline of the National Synchrotron Radiation Research Center (NSRRC) in Taiwan.

Results and discussion
The Cu-1234 bulk sample was synthesized via a solidstate reaction run under high pressure and high temperature conditions 18,19,23 . The NPD measurements demonstrated that these samples, in general, had a tetragonal basic structure with lattice parameters a = b = 3.85856(5) Å, c = 17.9544(6) Å, and space group of P4/mmm (No. 123). This structure is similar to the crystal structure of the 1234 phase known for Tl-based or Hg-based superconducting systems, such as HgBa 2 Ca 3 Cu 4 O 10+δ 24 and TlBa 2 Ca 3 Cu 4 O 10+δ 25 . The actual chemical composition of Cu-1234 based on NPD refinement was Cu 0.94 Ba 2 Ca 3 Cu 4 O 10.66 , which indicated that the average valence state of Cu was +2.29 (more details on the refined structural parameters are listed in Table S1). As shown in Fig. 1a Fig. 1c [26][27][28] . Peaks H and U are attributed to transitions from O 1s to the doped hole states and upper Hubbard band, respectively. The spectral weight of U in Cu-1234 was weaker than that in YBa 2 Cu 2.30+ 3 O 6.95 29 but slightly higher than that of Ba 2 Cu 2.40+ O 3. 2 30 , indicating that the doping level in Cu-1234 was slightly smaller than that of Ba 2 Cu 2.40 + O 3.2 but higher than that of YBa 2 Cu 2.30+ 3 O 6.95 ; this confirmed the overdoped nature of Cu-1234. The superconducting transition occurred at 117 K, as indicated by the magnetization measurement (Fig. 1d). The critical current densities J c versus magnetic field at different temperatures were calculated from magnetic hysteresis loops (Fig. S1) by using the Bean model, and these are plotted in Fig. 1e. The values of J c for Cu-1234 were approximately 5.6 × 10 5 A/cm 2 (77 K) in the Earth's field, which are much larger than those of Bi, Hg-, and Tl-based cuprate superconductors and comparable to that of YBCO at liquid nitrogen temperatures 19 . The J c of Cu-1234 in this work reached approximately 1.7 × 10 5 A/cm 2 (100 K), which provides great potential for high-power applications in the temperature range near 100 K. The temperature dependence of J c at 1 and 4 T was normalized against J c (0) and is shown in Fig. 1f. The data from 5 to 60 K fit the relation J c (T) = J c (0)exp(−T/T 0 ), and the fitting parameters T 0 at 1 and 4 T were 17.16 ± 0.45 and 14.49 ± 0.28 K, respectively. The T 0 values for the Y-123 and Hg systems (Hg-1201, Hg-1212, and Hg-1223) and Bi-2212 were 20-23,~7, and 4-5 K, respectively 20,31 . T 0 for the as-synthesized sample in this study (~17.2 K) was relatively large and close to that of Y-123, which can be attributed to the similarity of the CRBs of Cu-1234 and Y-123. The large value of J c and its weak dependence on field and temperature all suggested strong flux pinning by Cu-1234.
Ordering of the copper and oxygen vacancies was discovered to exhibit an a×2b×2c modulated structure and induce periodic lattice distortions in Cu-1234. As shown in Fig. 2a, the copper and oxygen vacancies were situated at Cu1a, O1a, and O2a sites, while the Cu1b, O1b, and O2b sites were fully occupied, resulting in doubling of the b axis and a loss of tetragonal symmetry. Specifically, the corresponding HAADF and ABF images were taken along the [100] zone axis. In Fig. 2b, due to the copper and oxygen vacancies in Cu1a and O1a sites, Cu1a(O1a) columns showed much weaker intensity than those of Cu1b (O1b). The arrangement of atomic columns in the red frame is -Cu1aO1a (overlap)-Cu1bO1b (overlap)-Cu1aO1a (overlap)-, which gives 2b periodicity, as clearly illustrated by blue and red arrows. The arrangement of atomic columns in the blue frame is different: -Cu1bO1b (overlap)-Cu1aO1a (overlap)-Cu1bO1b (overlap)-, resulting in 2c periodicity in the modulated structure. In Fig. 2c, the intensity of O2 sites in BaO layers also shows 2b and 2c periodicity. Our a×2b×2c modulated structural model for Cu-1234 with the Ammm space group was also confirmed by the corresponding HAADF and ABF images taken along the [010] zone axis. In Fig. 2d  Cu-O distances were opposite. These alternately occurring maximum and minimum values indicated periodic lattice distortions, which was induced by vacancy ordering and was consistent with the 2b periodicity mentioned above. Varying the Cu-O bond length would profoundly modify the pairing landscape by producing regions of either enhanced or depressed pairing, which is required to induce vortex pinning 16,32 (electron diffraction patterns and structural parameters of Cu-1234 with an a×2b×2c modulated structure are shown in Fig. S2 and Table S2, respectively).
As further demonstrated by the dark-field experiments and STEM experiments, we also found that the crystal can form 90°microdomains in the above mentioned a×2b×2c modulated structure. Figure 3a displays thin, platelike domains, with longitudinal dimensions varying from 100 to 500 nm and transverse dimensions along the c axis ranging from 2 to 50 nm. The area showing bright contrast is along the [100] zone axis, while the area showing dark contrast is along the [010] zone axis. The atomic structure of the 90°microdomains is shown in Fig. 3b, where their c-axes are parallel while their a-axes are perpendicular to each other. The local strain states between domains were further explored by geometrical phase analysis (GPA) 33,34 carried out on the HAADF-STEM image shown in Fig. 3b. Figure 3c shows the mapping of the in-plane deformation (e xx , along the [010] direction). The ordered copper and oxygen vacancies in CRBs along the [010] direction show periodic tensile and compressive strain, while the disordered vacancies along the [100] direction show no periodicity. Similar to the twin boundaries in YBCO 13,35 or domains in heavily Pbdoped Bi 2 Sr 2 CaCu 2 O 8+δ , these thin, plate-like microdomains in Cu-1234 are believed to disturb flux flow and increase J c 4 since electron scattering at the boundaries may reduce the coherence length locally. Furthermore, we systematically studied the flux pinning force at 77 K and compared it with surface pinning, Δκ pinning, and normal point pinning 36,37 , as shown in Fig. 3d. It is obvious that the experimental data followed the case of surface pinning well, demonstrating that the actual dominant pinning centers are surface pinning centers. Such correlated defects, including vacancy ordering and 90°microdomains in Cu-1234, are believed to suppress the thermal fluctuations of vortices more efficiently than randomly distributed point defects.
The "intrinsic" high-J c seen at liquid nitrogen temperature for heavily overdoped Cu-1234 originated from its special composition and crystal structure. As shown in  characteristics of Cu-1234 were similar to those of Ba 2 CuO 3.2 (Ba-214), in which the in-plane and out-ofplane Cu-O bond lengths were 2.00 and 1.86 Å, respectively. We defined the compression ratio of the [CuO 6 ] local octahedron as σ = d out-of-plane /d in-plane , where d out-ofplane and d in-plane represent the out-of-plane and in-plane Cu-O bond lengths, respectively. According to this definition, the σ for CRBs in Cu-1234 is 0.92, which is very close to that for Ba-214 (σ = 0.93). In compressed octahedron, the energy of the 3d 3z 2 Àr 2 orbital is lifted above that of the 3d x 2 Ày 2 orbital; this leads to significant doping holes in the unconventional 3d 3z 2 Àr 2 orbital, which decrease the superconductivity anisotropy and enhances interlayer coupling. This deduction was further confirmed by orientation-dependent EELS measurements for the O 1s absorption edges, which probed the unoccupied electronic orbitals with 2p symmetry at O sites and their orientations with respect to the crystal axis. We recorded EELS data for the O-K edge using a relatively small collection semiangle (0.362 mrad), with the incident electron beam aligned along the a-, b-, and c-axes for q//a, b, and q//c, respectively. As shown in Fig. 4b, the prepeak at approximately 528.5 eV can be attributed to transitions from the O 1s to O 2p states in the Zhang-Rice singlet band 29,38 . For q//c and q//a, b, a considerable number of holes having 2p z and 2p x,y symmetry were observed, respectively, and the former showed a higher hole concentration than the latter. This is significantly different from all other known cuprate superconductors 26,28,[38][39][40] , for which in-plane orbitals are unanimously predominant, indicating that the apical O 2p z orbitals can play an important role in the intrinsic high-J c .
The coexistence of high T c (~117 K) and high carrier concentration (~0.29 hole/CuO 2 ) in Cu-1234 was investigated by STEM-EELS at atomic resolution and was due to the inhomogeneous carrier distribution among the octahedron", which pushes the 3d x2−y2 orbital energy level above the 3d 3z2−r2 orbital energy level. However, in the compressed "[CuO6] octahedron", the 3d 3z2−r2 orbital energy level is expected to be located above the 3d x2−y2 orbital energy level. c Spatially resolved EELS for Cu-1234 at the O-K edge. These spectra were integrated over the (ab) atomic planes but spatially resolved along the c axis, and intensity is displayed as a color scale. The positions of the O2p hole (H) and upper Hubbard (U) bands are indicated by red and black arrows, respectively. Weighted principal component analysis (PCA) was applied to reduce the noise level. Scale bar = 1 nm. d O-K edge EELS spectra obtained from OPs (red) and IPs (black). Two Gaussian functions were used to model the O2p hole band (red) and the upper Hubbard band (UHB) (blue). The background (gray solid lines) was modeled using a step function 43 .
CuO 2 planes. Figure 4c presents spatially resolved O-K edge EELS spectra, which provide simple layer by layer visualization of changes in the fine structure. Obviously, the strong intensity of peak H appearing for CRBs indicates their metallic conductivity. A high carrier concentration existed in both SCBs and CRBs, which is essential for low superconducting anisotropy and high-J c and high-H irr 5 . Specifically, the O-K edge EELS spectra of OPs and IPs are shown in Fig. 4d. Compared with OPs, considerable spectral weight was transferred from the O 2p peak H (~528.5 eV) to the upper Hubbard peak U (~530 eV) in IPs. Since the spectral weight of this preedge depends on the doping level, OPs show much higher hole concentrations than IPs. The bond valence sum calculation (BVS) 41 based on NPD refinement (Table S3) provided additional evidence for an inhomogeneous hole distribution and showed valence states of +2.45 for Cu1, +2.14 for Cu2, and +2.03 for Cu3. The apical oxygen connects CRBs and SCBs and transfers holes from Cu ions to OPs, thereby enhancing the hole concentration in OPs. The difference in hole concentrations for OPs and IPs increases the average hole concentration, while the IPs maintain a near-optimal doping concentration to maintain T c at approximately 117 K in the heavily overdoped region. Strong superconducting coupling between the thick SCBs mediated by CRBs and overdoped carriers contributes to the intrinsic high J c of Cu-1234.
Although Cu-1234 shows both high-T c and intrinsic intragrain high-J c , the grain boundary has a detriment effect on the critical current density J c of the polycrystalline bulk sample. Actually, the connectivity between grains of the polycrystalline bulk is strongly degraded due to grain boundaries with weak coupling. Therefore, the currents cannot circulate well over the bulk sample, which inhibits the application of bulk high-T c cuprate superconductors. The above problem exists in almost all cuprate superconductors, such as YBCO, BSCCO, and Cu-1234. polycrystalline sample 42 . Therefore, improving or eliminating the weak link problem constitutes further work needed for Cu-1234 polycrystalline samples.

Conclusion
The cuprate superconductor Cu-1234, which is synthesized under high oxygen pressure, has a high T c (~117 K) with a high J c (>10 4 A/cm 2 , 100 K), even in a heavily overdoped state; thus, it provides great potential for application above the liquid nitrogen temperature. The atomic-scale structure and electronic structure of Cu-1234 were revealed to underlie the observed excellent "double high" performance by using a series of techniques based on aberration-corrected STEM. A clear a×2b×2c modulated structure and plate-like microdomains inside the crystal have been commonly observed and are well interpreted by ordering of copper and oxygen vacancies in CRBs. Careful investigation of the alterations in the local atomic structure revealed the strong structural effects of periodic copper and oxygen deficiencies on the basic lattice. These structural features are thought to introduce pinning centers into the crystals, which evidently suppress vortex flux flow and enhance the critical current density. The symmetry and distribution of holes in Cu-1234, which provide a suitable electronic structure for high-J c , were further explored with orientation-dependent EELS and EELS-STEM at atomic resolution. The "intrinsic" high-J c of Cu-1234 at the liquid nitrogen temperature originate from its composition and crystal structure. The charge-reservoir blocks [Ba 2 CuO 3+δ ] with rare compressed [CuO 6 ] octahedra and metallic conductivity give rise to many holes having p z symmetry, which decreases the superconducting anisotropy and enhances the interlayer coupling that guarantees a high-J c . A high carrier concentration in a high-T c superconductor is essential for high J c . The inhomogeneous carrier distribution in thick superconducting layers [Ca 3 Cu 4 O 8 ], with OP overdoping and IPs exhibiting near-optimal doping, maintains the high T c of approximately 117 K even in a heavily overdoped state, which provides the necessary conditions for coexistence of high T c and high J c . Our results are applicable to design and synthesis of new multilayered superconductors with high T c as well as high J c .