**1. Introduction**

High-*T*<sup>c</sup> superconductors have attracted considerable research activity, especially for electric power applications at high magnetic fields and temperatures, because the zero-resistive current and the high superconducting transition temperature *T*<sup>c</sup> enable us to operate zero-resistance devices at liquid-nitrogen temperature. Nowadays, coated conductors based on biaxially textured REBa2Cu3O*<sup>y</sup>* (REBCO, RE: rare earth elements) thin films have been significantly developed as second generation high-*T*<sup>c</sup> superconducting tapes and have become commercially available now [1,2].

The critical current density *J*<sup>c</sup> in magnetic field (in-field *J*c), which is a maximum current density with zero-resistivity, is the most important parameter in REBCO-coated conductors for the practical applications. The absolute values of *J*<sup>c</sup> for REBCO-coated conductors, however, have still remained below the practical level for high magnetic field applications [3]. In addition, the electronic mass anisotropy in the layered structure of CuO<sup>2</sup> planes for high-*T*<sup>c</sup> superconductors induces a large anisotropy of *J*<sup>c</sup> against a magnetic field orientation [4], which gives rise to obstacles to the superconducting magnet applications: a minimum in the magnetic field angular variation of *J*c, which is usually located at the magnetic field *B* parallel to the *c*-axis, limits the operation current [5,6].

The in-field *J*<sup>c</sup> can be controlled by immobilization of nano-sized quantized-magneticflux-lines (flux lines) penetrating into superconductors in a magnetic field. The motion of

flux lines is suppressed by crystalline defects and impurities in the specimen, which are called pinning centers (PCs). Thus, artificially embedding crystalline defects as effective PCs is just a key strategy to improve the in-field performance of superconductors [1,3,7]. For the last fifteen years or so, doping of non-superconducting secondary phases such as BaMO<sup>3</sup> (M = Zr, Sn, Hf, etc.) and RE2O<sup>3</sup> has been attempted to form those into effective PCs in REBCO thin films [8–12]. which are called pinning centers (PCs). Thus, artificially embedding crystalline defects as effective PCs is just a key strategy to improve the in-field performance of superconductors [1,3,7]. For the last fifteen years or so, doping of non-superconducting secondary phases such as BaMO3 (M = Zr, Sn, Hf, etc.) and RE2O3 has been attempted to form those into effective PCs in REBCO thin films [8–12]. The flux pinning effect depends on the shape (dimensionality), orientation, size, and

The in-field *J*c can be controlled by immobilization of nano-sized quantized-magnetic-flux-lines (flux lines) penetrating into superconductors in a magnetic field. The motion of flux lines is suppressed by crystalline defects and impurities in the specimen,

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 2 of 22

The flux pinning effect depends on the shape (dimensionality), orientation, size, and distribution of PCs. In particular, the dimensionality of PCs significantly affects the feature of flux pinning, as shown in Figure 1. For example, one-dimensional PCs such as columnar defects (CDs) exhibit a preferential direction for the flux pinning: the strong flux pinning occurs in the magnetic field direction along their long axis. Three-dimensional PCs such as nano-particles, on the other hand, have the morphology with no correlated orientation for flux pinning, resulting in the isotropic pinning force against any direction of magnetic field. These features of PCs play an important role in the modification of the *J*<sup>c</sup> properties in REBCO films: those parameters of PCs such as their shape and size, should be designed to meet the requirements for each application. distribution of PCs. In particular, the dimensionality of PCs significantly affects the feature of flux pinning, as shown in Figure 1. For example, one-dimensional PCs such as columnar defects (CDs) exhibit a preferential direction for the flux pinning: the strong flux pinning occurs in the magnetic field direction along their long axis. Three-dimensional PCs such as nano-particles, on the other hand, have the morphology with no correlated orientation for flux pinning, resulting in the isotropic pinning force against any direction of magnetic field. These features of PCs play an important role in the modification of the *J*c properties in REBCO films: those parameters of PCs such as their shape and size, should be designed to meet the requirements for each application. Swift-heavy-ion irradiation to high-*T*c superconductors produces amorphous CDs of

Swift-heavy-ion irradiation to high-*T*<sup>c</sup> superconductors produces amorphous CDs of damaged material parallel to the projectile direction through the electron excitation process rather than the nuclear collision process. The CDs produced by the irradiation effectively work as one-dimensional PCs [13–15]. The orientation of one-dimensional PCs determines the preferential direction of flux pinning [13,16]. Therefore, heavy-ion irradiation can be expected to modify the anisotropy of *J*<sup>c</sup> in high-*T*<sup>c</sup> superconductors by tuning the irradiation direction. In addition, the size and shape of CDs strongly depends on the electronic stopping power *S*e, which is defined as energy loss of the incident ion per unit length via electronic excitation in the target material [17]: continuous CDs with thick diameter are formed at higher *S*<sup>e</sup> than a certain value and discontinuous CDs with thin diameter are located at intervals along the ion path at lower *S*<sup>e</sup> [18–20]. In particular, discontinuous CDs may provide more effective flux pinning in a wide magnetic field angular range, because the ends of discontinuous CDs can act as PCs even in magnetic field directions tilted from their long axis [21,22]. Thus, the discontinuity of CDs is also one of the important factors for the modification of the *J*<sup>c</sup> anisotropy in high-*T*<sup>c</sup> superconductors, as well as the direction-dispersion of CDs. damaged material parallel to the projectile direction through the electron excitation process rather than the nuclear collision process. The CDs produced by the irradiation effectively work as one-dimensional PCs [13–15]. The orientation of one-dimensional PCs determines the preferential direction of flux pinning [13,16]. Therefore, heavy-ion irradiation can be expected to modify the anisotropy of *J*c in high-*T*c superconductors by tuning the irradiation direction. In addition, the size and shape of CDs strongly depends on the electronic stopping power *S*e, which is defined as energy loss of the incident ion per unit length via electronic excitation in the target material [17]: continuous CDs with thick diameter are formed at higher *S*e than a certain value and discontinuous CDs with thin diameter are located at intervals along the ion path at lower *S*e [18–20]. In particular, discontinuous CDs may provide more effective flux pinning in a wide magnetic field angular range, because the ends of discontinuous CDs can act as PCs even in magnetic field directions tilted from their long axis [21,22]. Thus, the discontinuity of CDs is also one of the important factors for the modification of the *J*c anisotropy in high-*T*c superconductors, as well as the direction-dispersion of CDs.

**Figure 1.** Sketch of the different dimensional categories for PCs: (**a**) 1D columnar (linear) defects, (**b**) 2D planar defects such as twin boundaries, and (**c**) 3D nano-particles. **Figure 1.** Sketch of the different dimensional categories for PCs: (**a**) 1D columnar (linear) defects, (**b**) 2D planar defects such as twin boundaries, and (**c**) 3D nano-particles.

A major advantage of using heavy-ion irradiation for the formation of CDs is that any CD configuration can be prepared by tuning the irradiation energy and the incident direction [23,24], independently from a fabrication process of samples (see Figure 2): the pinning structure can be efficiently designed to meet the requirements for different applications, which would be valuable for the development of high-performance coated conductors. In addition, unique pinning structures architected by the irradiations may enable us to find new physics of flux line dynamics. Therefore, heavy-ion irradiation to high-*T*<sup>c</sup> A major advantage of using heavy-ion irradiation for the formation of CDs is that any CD configuration can be prepared by tuning the irradiation energy and the incident direction [23,24], independently from a fabrication process of samples (see Figure 2): the pinning structure can be efficiently designed to meet the requirements for different applications, which would be valuable for the development of high-performance coated conductors. In addition, unique pinning structures architected by the irradiations may enable us to find new physics of flux line dynamics. Therefore, heavy-ion irradiation to high-*T*<sup>c</sup> superconductors can provide the design criteria for the supreme pinning landscape making the most of the potential for flux pinning, which leads to *J*<sup>c</sup> close to the theoretical limit of critical current density, i.e., the pair-breaking critical current density.

superconductors can provide the design criteria for the supreme pinning landscape making the most of the potential for flux pinning, which leads to *J*c close to the theoretical limit

of critical current density, i.e., the pair-breaking critical current density.

**Figure 2.** Schematic illustration of various configurations of CDs designed by heavy-ion irradiation: (**a**) continuous CDs parallel to the c-axis produced by standard irradiation, (**b**) direction-dispersed CDs installed by tuning the irradiation directions, (**c**) discontinuous CDs formed by adjusting irradiation energy to lower value. **Figure 2.** Schematic illustration of various configurations of CDs designed by heavy-ion irradiation: (**a**) continuous CDs parallel to the c-axis produced by standard irradiation, (**b**) direction-dispersed CDs installed by tuning the irradiation directions, (**c**) discontinuous CDs formed by adjusting irradiation energy to lower value.

In this paper, we describe the results of the modification of the *J*c properties in REBCO thin films and coated conductors, which were obtained by our studies through heavy-ion irradiation under various irradiation conditions. Most of previous works of other researchers using heavy-ion irradiation have focused on the improvement of *J*c at *B* || *c* where *J*c usually shows the minimum [13–15,18,19]. On the other hand, heavy-ion irradiation effects over a wide magnetic field angular range have not been well studied so far. By contrast, we focus especially on modification of the *J*c anisotropy in high-*T*c superconductors by using heavy-ion irradiation: our aim in this review is to improve *J*c in all magnetic field angular range from *B* || *c* to *B* || *ab* by using CDs and to explore breakthroughs for strong and isotropic pinning landscape in REBCO coated conductors. To meet the aim in this paper, we selected Xe ions as the irradiation ion species: the Xe-ion irradiation to REBCO thin films can provide large increase of *J*c without heavily damaging crystallinity even at a large amount of doses, 5.0 × 1011 ions/cm2 [24] and easily enables us to tune the morphology of CDs through the adjustment of the irradiation energy at a tandem accelerator of Japan Atomic Energy Agency (JAEA) used in our works. Firstly, we present the reduction of the *J*c anisotropy by using the direction-dispersed CDs, which are introduced by controlling the irradiation direction. Secondly, we report the influence of CDs tilted at small angle(s) relative to the *ab*-plane on the *J*c properties near *B* || *ab*, which is one of key factors to improve *J*c in all magnetic field directions. In particular, we show the influence of CDs along the *ab*-plane on *J*c at *B* || *ab* by preparing an in-plane aligned *a*-axis-oriented YBCO film. Finally, we clarify the potential of discontinuous CDs for flux pinning in comparison with continuous CDs, where the morphology of CDs is controlled by the irradiation energy. In this paper, we describe the results of the modification of the *J*<sup>c</sup> properties in REBCO thin films and coated conductors, which were obtained by our studies through heavyion irradiation under various irradiation conditions. Most of previous works of other researchers using heavy-ion irradiation have focused on the improvement of *J*<sup>c</sup> at *B* || *c* where *J*<sup>c</sup> usually shows the minimum [13–15,18,19]. On the other hand, heavy-ion irradiation effects over a wide magnetic field angular range have not been well studied so far. By contrast, we focus especially on modification of the *J*<sup>c</sup> anisotropy in high-*T*<sup>c</sup> superconductors by using heavy-ion irradiation: our aim in this review is to improve *J*<sup>c</sup> in all magnetic field angular range from *B* || *c* to *B* || *ab* by using CDs and to explore breakthroughs for strong and isotropic pinning landscape in REBCO coated conductors. To meet the aim in this paper, we selected Xe ions as the irradiation ion species: the Xe-ion irradiation to REBCO thin films can provide large increase of *J*<sup>c</sup> without heavily damaging crystallinity even at a large amount of doses, 5.0 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> [24] and easily enables us to tune the morphology of CDs through the adjustment of the irradiation energy at a tandem accelerator of Japan Atomic Energy Agency (JAEA) used in our works. Firstly, we present the reduction of the *J*<sup>c</sup> anisotropy by using the direction-dispersed CDs, which are introduced by controlling the irradiation direction. Secondly, we report the influence of CDs tilted at small angle(s) relative to the *ab*-plane on the *J*<sup>c</sup> properties near *B* || *ab*, which is one of key factors to improve *J*<sup>c</sup> in all magnetic field directions. In particular, we show the influence of CDs along the *ab*-plane on *J*<sup>c</sup> at *B* || *ab* by preparing an in-plane aligned *a*-axis-oriented YBCO film. Finally, we clarify the potential of discontinuous CDs for flux pinning in comparison with continuous CDs, where the morphology of CDs is controlled by the irradiation energy.
