*3.4. Modification of J<sup>c</sup> at B || ab by Heavy-Ion Irradiation along the a-Axis*

An in-plane aligned *a*-axis-oriented YBCO film offers an excellent opportunity for further exploration into the influence of CDs on the flux pinning at *B* || *ab*, since we can easily install CDs along the *ab*-plane with the ion-beam normal to the film [43]. We prepared the in-plane aligned *a*-axis-oriented YBCO film by a PLD technique with an ArF excimer laser, where a (100) SrLaGaO<sup>4</sup> substrate with Gd2CuO<sup>4</sup> buffer layer was used to promote the in-plane orientation of YBCO thin film [44]. The film was patterned into the shape of a microbridge so as to make the bridge direction parallel to the *b*-axis, where transport current can be applied along the *ab*-plane (see Figure 14). Both the in-plane-aligned texture of the film and the experimental arrangement enable us to remove the extra effect such as the interlayer Josephson current and the channel flow of flux lines along the CuO<sup>2</sup> plane, providing deeper insights on the nature of flux pinning of CDs along the *ab*-plane. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 13 of 22 promote the in-plane orientation of YBCO thin film [44]. The film was patterned into the shape of a microbridge so as to make the bridge direction parallel to the *b*-axis, where transport current can be applied along the *ab*-plane (see Figure 14). Both the in-planealigned texture of the film and the experimental arrangement enable us to remove the extra effect such as the interlayer Josephson current and the channel flow of flux lines along the CuO2 plane, providing deeper insights on the nature of flux pinning of CDs along the *ab*-plane.

**Figure 14.** Sketch of the experimental arrangement using the in-plane aligned *a*-axis-oriented YBCO film. Reprinted with permission from [43], copyright 2019 by IEEE. **Figure 14.** Sketch of the experimental arrangement using the in-plane aligned *a*-axis-oriented YBCO film. Reprinted with permission from [43], copyright 2019 by IEEE.

The in-plane aligned *a*-axis-oriented YBCO thin film showed good *a*-axis orientations without other orientations for the X-ray *θ*-2*θ* diffraction pattern, as shown in Figure 15. In addition, X-ray diffraction *φ* scanning using the (102) plane of the YBCO film before the irradiation indicated two-fold symmetry, since strong peaks stood out at around 90° and 270° in the inset of Figure 15. Therefore, the in-plane aligned *a*-axis-orientated micro-The in-plane aligned *a*-axis-oriented YBCO thin film showed good *a*-axis orientations without other orientations for the X-ray *θ*-2*θ* diffraction pattern, as shown in Figure 15. In addition, X-ray diffraction *ϕ* scanning using the (102) plane of the YBCO film before the irradiation indicated two-fold symmetry, since strong peaks stood out at around 90◦ and 270◦ in the inset of Figure 15. Therefore, the in-plane aligned *a*-axis-orientated microstructure can be confirmed on the film used in this work.

structure can be confirmed on the film used in this work. A cross-sectional TEM image of the in-plane aligned *a*-axis oriented YBCO film after the irradiation with 200 MeV Xe ions is shown in Figure 16a. The straight CDs along the *a*axis are elongated through the thickness of the YBCO film. Figure 16b shows the plan-view TEM image of the *a*-axis oriented YBCO thin film after the irradiation. The CDs formed by the ion beam along the a-axis are roughly elliptical in shape, whereas CDs parallel to the *c*-axis are usually circular [17,45]. In general, the shape of CDs depends on the direction of the incident ions relative to the crystallographic axes in high-*T*<sup>c</sup> superconductors, because the anisotropy of thermal diffusivity causes more severe irradiation damage for the creation of CDs along the *a*- and/or the *b*-axis [17].

**Figure 15.** X-ray diffraction *θ*-2θscan of the in-plane aligned a-axis oriented YBCO thin film before the irradiation. Inset: X-ray φ scan using (102) plane of the YBCO thin film before the irradiation.

A cross-sectional TEM image of the in-plane aligned *a*-axis oriented YBCO film after the irradiation with 200 MeV Xe ions is shown in Figure 16a. The straight CDs along the *a*-axis are elongated through the thickness of the YBCO film. Figure 16b shows the planview TEM image of the *a*-axis oriented YBCO thin film after the irradiation. The CDs formed by the ion beam along the a-axis are roughly elliptical in shape, whereas CDs parallel to the *c*-axis are usually circular [17,45]. In general, the shape of CDs depends on the

Reprinted with permission from [43], copyright 2019 by IEEE.

structure can be confirmed on the film used in this work.

along the *ab*-plane.

**Figure 15.** X-ray diffraction *θ*-2θscan of the in-plane aligned a-axis oriented YBCO thin film before the irradiation. Inset: X-ray φ scan using (102) plane of the YBCO thin film before the irradiation. Reprinted with permission from [43], copyright 2019 by IEEE. **Figure 15.** X-ray diffraction *θ*-2θscan of the in-plane aligned a-axis oriented YBCO thin film before the irradiation. Inset: X-ray ϕ scan using (102) plane of the YBCO thin film before the irradiation. Reprinted with permission from [43], copyright 2019 by IEEE. direction of the incident ions relative to the crystallographic axes in high-*T*c superconductors, because the anisotropy of thermal diffusivity causes more severe irradiation damage for the creation of CDs along the *a*- and/or the *b*-axis [17].

promote the in-plane orientation of YBCO thin film [44]. The film was patterned into the shape of a microbridge so as to make the bridge direction parallel to the *b*-axis, where transport current can be applied along the *ab*-plane (see Figure 14). Both the in-planealigned texture of the film and the experimental arrangement enable us to remove the extra effect such as the interlayer Josephson current and the channel flow of flux lines along the CuO2 plane, providing deeper insights on the nature of flux pinning of CDs

**Figure 14.** Sketch of the experimental arrangement using the in-plane aligned *a*-axis-oriented

The in-plane aligned *a*-axis-oriented YBCO thin film showed good *a*-axis orientations without other orientations for the X-ray *θ*-2*θ* diffraction pattern, as shown in Figure 15. In addition, X-ray diffraction *φ* scanning using the (102) plane of the YBCO film before the irradiation indicated two-fold symmetry, since strong peaks stood out at around 90° and 270° in the inset of Figure 15. Therefore, the in-plane aligned *a*-axis-orientated micro-

YBCO film. Reprinted with permission from [43], copyright 2019 by IEEE.

**Figure 16.** (**a**) Cross-sectional and (**b**) plan-view TEM images of the a-axis oriented YBCO thin film irradiated with 200 MeV Xe ions along the a-axis. The arrows indicate several ion tracks. Reprinted with permission from [43], copyright 2019 by IEEE. **Figure 16.** (**a**) Cross-sectional and (**b**) plan-view TEM images of the a-axis oriented YBCO thin film irradiated with 200 MeV Xe ions along the a-axis. The arrows indicate several ion tracks. Reprinted with permission from [43], copyright 2019 by IEEE.

Figure 17 represents the magnetic field dependence of *J*c at 72 K for the *a*-axis oriented YBCO film before and after the irradiation. The *J*c at *B* || *c* is reduced by the introduction of CDs along the *a*-axis, especially for high magnetic fields. The CDs along the *a*-axis hardly interact with flux lines at *B* || *c*, since the CDs are perpendicular to the magnetic field direction. Moreover, CDs perpendicular to magnetic field direction create easy channel for flux lines to creep along the length of the CDs [46]. In addition to these deterioration effects, the irradiation damage to the host matrix causes the pronounced reduction of Figure 17 represents the magnetic field dependence of *J*<sup>c</sup> at 72 K for the *a*-axis oriented YBCO film before and after the irradiation. The *J*<sup>c</sup> at *B* || *c* is reduced by the introduction of CDs along the *a*-axis, especially for high magnetic fields. The CDs along the *a*-axis hardly interact with flux lines at *B* || *c*, since the CDs are perpendicular to the magnetic field direction. Moreover, CDs perpendicular to magnetic field direction create easy channel for flux lines to creep along the length of the CDs [46]. In addition to these deterioration effects, the irradiation damage to the host matrix causes the pronounced reduction of *J*<sup>c</sup> at *B* || *c*.

*J*c at *B* || *c*. The introduction of CDs along the *a*-axis, on the other hand, hardly reduces the absolute value of *J*<sup>c</sup> at *B* || *a*, even though the *J*<sup>c</sup> is affected by the local irradiation damage to the CuO<sup>2</sup> planes as well as the *J*<sup>c</sup> at *B* || *c*. It should be noted that the normalized *J*<sup>c</sup> by *J*c0 increases after the irradiation, especially for high magnetic fields (see the inset of Figure 17). This behavior suggests that CDs contribute to the flux pinning at *B* || *ab*. For low magnetic fields, by contrast, the pinning effect of CDs along the *a*-axis is hardly visible even on the normalized *J*c. This is attributed to the presence of the naturally growth defects such as stacking faults in the film: Such pre-existing defects act as *ab*-plane correlated PCs both before and after the irradiation, which obscures the pinning effect of CDs, especially for low magnetic fields.

**Figure 17.** Magnetic field dependence of *J*c at *B* || *c* and at *B* || *a* in the *a*-axis oriented YBCO thin film before and after the irradiation. Inset: *J*c normalized by self-field critical current density *J*c0 as a function of magnetic field along the *a*-axis. Reprinted with permission from [43], copyright 2019 by

The introduction of CDs along the *a*-axis, on the other hand, hardly reduces the absolute value of *J*c at *B* || *a*, even though the *J*c is affected by the local irradiation damage to the CuO2 planes as well as the *J*c at *B* || *c*. It should be noted that the normalized *J*c by *J*c0 increases after the irradiation, especially for high magnetic fields (see the inset of Figure 17). This behavior suggests that CDs contribute to the flux pinning at *B* || *ab*. For low

IEEE.

*J*c at *B* || *c*.

printed with permission from [43], copyright 2019 by IEEE.

**Figure 17.** Magnetic field dependence of *J*c at *B* || *c* and at *B* || *a* in the *a*-axis oriented YBCO thin film before and after the irradiation. Inset: *J*c normalized by self-field critical current density *J*c0 as a function of magnetic field along the *a*-axis. Reprinted with permission from [43], copyright 2019 by IEEE. **Figure 17.** Magnetic field dependence of *J*c at *B* || *c* and at *B* || *a* in the *a*-axis oriented YBCO thin film before and after the irradiation. Inset: *J*<sup>c</sup> normalized by self-field critical current density *J*c0 as a function of magnetic field along the *a*-axis. Reprinted with permission from [43], copyright 2019 by IEEE.

direction of the incident ions relative to the crystallographic axes in high-*T*c superconductors, because the anisotropy of thermal diffusivity causes more severe irradiation damage

**Figure 16.** (**a**) Cross-sectional and (**b**) plan-view TEM images of the a-axis oriented YBCO thin film irradiated with 200 MeV Xe ions along the a-axis. The arrows indicate several ion tracks. Re-

Figure 17 represents the magnetic field dependence of *J*c at 72 K for the *a*-axis oriented YBCO film before and after the irradiation. The *J*c at *B* || *c* is reduced by the introduction of CDs along the *a*-axis, especially for high magnetic fields. The CDs along the *a*-axis hardly interact with flux lines at *B* || *c*, since the CDs are perpendicular to the magnetic field direction. Moreover, CDs perpendicular to magnetic field direction create easy channel for flux lines to creep along the length of the CDs [46]. In addition to these deterioration effects, the irradiation damage to the host matrix causes the pronounced reduction of

for the creation of CDs along the *a*- and/or the *b*-axis [17].

#### The introduction of CDs along the *a*-axis, on the other hand, hardly reduces the ab-*3.5. Modification of the J<sup>c</sup> Anisotropy by Controlling the Heavy-Ion Irradiation Energy*

solute value of *J*c at *B* || *a*, even though the *J*c is affected by the local irradiation damage to the CuO2 planes as well as the *J*c at *B* || *c*. It should be noted that the normalized *J*c by *J*c0 increases after the irradiation, especially for high magnetic fields (see the inset of Figure 17). This behavior suggests that CDs contribute to the flux pinning at *B* || *ab*. For low The modification of the *J*<sup>c</sup> anisotropy in high-*T*<sup>c</sup> superconductors is sensitive to direction-dispersions of CDs, as mentioned in the previous sections. Another way to modify the *J*<sup>c</sup> properties by CDs is to tune the morphologies of CDs. Especially for the morphology of short segmented (i.e., discontinuous) CDs, the ends of the discontinuous CDs can provide a variety of additional pinning effects: the ends of the segmented CDs can trap flux lines in magnetic field tilted from their long axis [21,22] and the existence of gaps in the segmented CDs can suppress thermal motion of flux lines, as shown in Figure 18. Furthermore, the volume fraction of CDs relative to the superconducting area can be minimized for discontinuous CDs, since CDs are shortly segmented: the reduction of the volume fraction of the crystalline defects suppresses the degradation of the superconductivity associated with the introduction of PCs, leading to the improvement of the absolute value of *J*<sup>c</sup> in a whole magnetic field angular region [19,20]. For iron-based superconductors, the morphology of CDs formed by heavy-ion irradiation tends to be discontinuous, which induces the remarkable improvement of *J*<sup>c</sup> [47–49]. The morphology of CDs in high-*T*<sup>c</sup> superconductors can be tuned by adjusting the irradiation energy for heavy-ion irradiation. In addition, the pinning effect of discontinuous CDs can be compared directly with that of continuous ones under same irradiation conditions except for the irradiation energy: the heavy-ion irradiations with different irradiation energies enable us to clarify the superiority of discontinuous CDs in the flux pinning effect over continuous CDs.

We first compared the flux pinning properties of discontinuous CDs with those of continuous ones when their long axis is parallel to the *c*-axis: GdBCO-coated conductors were irradiated with 80 MeV and 270 MeV Xe-ions along the *c*-axis, respectively [25]. For the irradiated sample with 270 MeV Xe ions, the straight and continuous CDs with the diameter of 4-11 nm penetrate the superconducting layer along the *c*-axis, as shown in Figure 3a. The value of *S*<sup>e</sup> calculated using SRIM code varies from 3.0 to 2.8 keV/Å through the superconducting layer with the thickness of 2.2 µm for the 270 MeV Xe-ion irradiation, so that the continuous CDs are formed over the whole sample. The 80 MeV Xe-ion irradiation, by contrast, produces short segmented CDs in their longitudinal direction along the *c*-axis, as shown in Figure 3b: the length of the segmented CDs with the diameter of 5-10 nm varies from 15 to 50 nm along their length, while the gaps between the segmented CDs is also variable, ranging between 15 and35 nm. The formation of discontinuous CDs is attributed to the value of *S*<sup>e</sup> changing from 2.0 to 1.4 keV/Å for the 80 MeV Xe ions into REBCO thin films [17,19,20].

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 16 of 22

superiority of discontinuous CDs in the flux pinning effect over continuous CDs.

**Figure 18.** Schematic images of flux pinning peculiar to discontinuous CDs. (**a**) Ends of the discontinuous CDs work as PCs in magnetic field tilted off their long axis, which provide effective flux pinning over a wide magnetic field angular range. (**b**) Existence of gaps in the discontinuous CDs can suppress thermal motion of kinks of flux lines, which further improve *J*c in comparison with continuous CDs. **Figure 18.** Schematic images of flux pinning peculiar to discontinuous CDs. (**a**) Ends of the discontinuous CDs work as PCs in magnetic field tilted off their long axis, which provide effective flux pinning over a wide magnetic field angular range. (**b**) Existence of gaps in the discontinuous CDs can suppress thermal motion of kinks of flux lines, which further improve *J*<sup>c</sup> in comparison with continuous CDs. is also variable, ranging between 15 and35 nm. The formation of discontinuous CDs is attributed to the value of *S*e changing from 2.0 to 1.4 keV/Å for the 80 MeV Xe ions into REBCO thin films [17,19,20].

magnetic fields, by contrast, the pinning effect of CDs along the *a*-axis is hardly visible even on the normalized *J*c. This is attributed to the presence of the naturally growth defects such as stacking faults in the film: Such pre-existing defects act as *ab*-plane correlated PCs both before and after the irradiation, which obscures the pinning effect of CDs, especially

The modification of the *J*c anisotropy in high-*T*c superconductors is sensitive to direction-dispersions of CDs, as mentioned in the previous sections. Another way to modify the *J*c properties by CDs is to tune the morphologies of CDs. Especially for the morphology of short segmented (i.e., discontinuous) CDs, the ends of the discontinuous CDs can provide a variety of additional pinning effects: the ends of the segmented CDs can trap flux lines in magnetic field tilted from their long axis [21,22] and the existence of gaps in the segmented CDs can suppress thermal motion of flux lines, as shown in Figure 18. Furthermore, the volume fraction of CDs relative to the superconducting area can be minimized for discontinuous CDs, since CDs are shortly segmented: the reduction of the volume fraction of the crystalline defects suppresses the degradation of the superconductivity associated with the introduction of PCs, leading to the improvement of the absolute value of *J*<sup>c</sup> in a whole magnetic field angular region [19,20]. For iron-based superconductors, the morphology of CDs formed by heavy-ion irradiation tends to be discontinuous, which induces the remarkable improvement of *J*c [47–49]. The morphology of CDs in high-*T*<sup>c</sup> superconductors can be tuned by adjusting the irradiation energy for heavy-ion irradiation. In addition, the pinning effect of discontinuous CDs can be compared directly with that of continuous ones under same irradiation conditions except for the irradiation energy: the heavy-ion irradiations with different irradiation energies enable us to clarify the

*3.5. Modification of the Jc Anisotropy by Controlling the Heavy-Ion Irradiation Energy* 

for low magnetic fields.

We first compared the flux pinning properties of discontinuous CDs with those of continuous ones when their long axis is parallel to the *c*-axis: GdBCO-coated conductors were irradiated with 80 MeV and 270 MeV Xe-ions along the *c*-axis, respectively [25]. For the irradiated sample with 270 MeV Xe ions, the straight and continuous CDs with the diameter of 4-11 nm penetrate the superconducting layer along the *c*-axis, as shown in Figure 3a. The value of *S*e calculated using SRIM code varies from 3.0 to 2.8 keV/Å through the superconducting layer with the thickness of 2.2 µm for the 270 MeV Xe-ion irradiation, so that the continuous CDs are formed over the whole sample. The 80 MeV Xe-ion irradiation, by contrast, produces short segmented CDs in their longitudinal direction along the *c*-axis, as shown in Figure 3b: the length of the segmented CDs with the diameter of 5-10 nm varies from 15 to 50 nm along their length, while the gaps between the segmented CDs Figure 19 shows the magnetic field angular dependences of *J*<sup>c</sup> at 70 K and 84 K in GdBCO-coated conductors irradiated with 80 MeV and 270 MeV Xe ions, respectively. The 80 MeV irradiation causes higher *J*<sup>c</sup> in all magnetic field directions compared to the 270 MeV irradiation, which becomes more pronounced at lower temperature of 70 K. The high *J*<sup>c</sup> at *B* || *c* for the 80 MeV irradiation is attributed to the existence of gaps in the segmented CDs, which induce the suppression of thermal motion of flux lines (see Figure 18b). In addition, the ends of discontinuous CDs can trap flux lines in magnetic field tilted from their long axis, as shown in Figure 18a. These flux pinning effects of discontinuous CDs become more remarkable at lower temperature where a core size of flux line approaches the thin diameter of the discontinuous CDs. Moreover, discontinuous CDs more minimize the degradation of the superconductivity associated with the introduction of PCs compared with continuous CDs. Thus, the discontinuity of CDs can contribute to further enhancement of *J*c. Figure 19 shows the magnetic field angular dependences of *J*c at 70 K and 84 K in GdBCO-coated conductors irradiated with 80 MeV and 270 MeV Xe ions, respectively. The 80 MeV irradiation causes higher *J*c in all magnetic field directions compared to the 270 MeV irradiation, which becomes more pronounced at lower temperature of 70 K. The high *J*c at *B* || *c* for the 80 MeV irradiation is attributed to the existence of gaps in the segmented CDs, which induce the suppression of thermal motion of flux lines (see Figure 18b). In addition, the ends of discontinuous CDs can trap flux lines in magnetic field tilted from their long axis, as shown in Figure 18a. These flux pinning effects of discontinuous CDs become more remarkable at lower temperature where a core size of flux line approaches the thin diameter of the discontinuous CDs. Moreover, discontinuous CDs more minimize the degradation of the superconductivity associated with the introduction of PCs compared with continuous CDs. Thus, the discontinuity of CDs can contribute to further enhancement of *J*c.

**Figure 19.** Magnetic field angular dependence of *J*c at 4 T for the irradiated samples with 80 MeV and 270 MeV Xe ions ((**a**) 84 K and (**b**) 70K). Reprinted with permission from [25], copyright 2015 by IEEE. **Figure 19.** Magnetic field angular dependence of *J*<sup>c</sup> at 4 T for the irradiated samples with 80 MeV and 270 MeV Xe ions ((**a**) 84 K and (**b**) 70K). Reprinted with permission from [25], copyright 2015 by IEEE.

ions, where the incident ion beams were tilted from the *c*-axis by *θ*i to introduce various kinds of direction-dispersed CDs: a parallel configuration composed of CDs parallel to the *c*-axis, bimodal angular configuration composed of CDs tilted at *θ*i = ±45° relative to the *c*-axis, and trimodal angular configuration composed of CDs tilted at *θ*i = 0° and ±45°

Figure 20a shows a cross-sectional TEM image of the GdBaCuO-coated conductor irradiated with 80 MeV Xe-ions at *θ*i = 0° and ±45°. The morphologies of CDs are schematically emphasized in Figure 20b. Interestingly, the 80 Me V Xe-ion beams create CDs with different morphologies depending on the irradiation angles of *θ*i: thick and elongated CDs are formed along the ion path at *θ*i = 45°, whereas the 80 MeV ions at *θ*i = 0° creates short segmented CDs along their length. In general, the morphology of CDs is determined by

[50].

The superior flux pinning effect of discontinuous CDs can be further modified by tuning the direction-dispersion. We irradiated GdBCO coated conductors with 80 MeV Xe ions, where the incident ion beams were tilted from the *c*-axis by *θ*<sup>i</sup> to introduce various kinds of direction-dispersed CDs: a parallel configuration composed of CDs parallel to the *c*-axis, bimodal angular configuration composed of CDs tilted at *θ*<sup>i</sup> = ±45◦ relative to the *c*-axis, and trimodal angular configuration composed of CDs tilted at *θ*<sup>i</sup> = 0◦ and ±45◦ [50].

Figure 20a shows a cross-sectional TEM image of the GdBaCuO-coated conductor irradiated with 80 MeV Xe-ions at *θ*<sup>i</sup> = 0◦ and ±45◦ . The morphologies of CDs are schematically emphasized in Figure 20b. Interestingly, the 80 Me V Xe-ion beams create CDs with different morphologies depending on the irradiation angles of *θ*<sup>i</sup> : thick and elongated CDs are formed along the ion path at *θ*<sup>i</sup> = 45◦ , whereas the 80 MeV ions at *θ*<sup>i</sup> = 0◦ creates short segmented CDs along their length. In general, the morphology of CDs is determined by the value of *S*e, which is the energy transferred from the incident ions for the electronic excitation. A thermal spike model [51,52], which is one of models to interpret the formation of irradiation defects through the electronic excitation, can describes the direction-dependent morphologies of CDs in high-*T*<sup>c</sup> superconductors by considering the anisotropy of thermal diffusivity [17,50]. According to the thermal spike model, the energy of the electronic excitation is converted into the thermal energy of lattice, which is the source for the formation of irradiation defects. In high-*T*<sup>c</sup> superconductors, the thermal diffusivity along the *c*-axis is smaller than that along other crystallographic axes, which results in the suppression of a temperature spread in the planes containing the *c*-axis. Thus, the incident ion beam tilted from the *c*-axis causes more severe structural damage, resulting in the formation of elongated CDs with a thicker diameter. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 17 of 22 the value of *S*e, which is the energy transferred from the incident ions for the electronic excitation. A thermal spike model [51,52], which is one of models to interpret the formation of irradiation defects through the electronic excitation, can describes the directiondependent morphologies of CDs in high-*T*c superconductors by considering the anisotropy of thermal diffusivity [17,50]. According to the thermal spike model, the energy of the electronic excitation is converted into the thermal energy of lattice, which is the source for the formation of irradiation defects. In high-*T*c superconductors, the thermal diffusivity along the *c*-axis is smaller than that along other crystallographic axes, which results in the suppression of a temperature spread in the planes containing the *c*-axis. Thus, the incident ion beam tilted from the *c*-axis causes more severe structural damage, resulting in the formation of elongated CDs with a thicker diameter.

**Figure 20.** (**a**) Cross-sectional TEM image of the GdBCO coated conductor irradiated with 80 MeV Xe ions at θi = 0° and ±45°. Several continuous CDs are indicated by the solid arrows and discontinuous CDs along the *c*-axis are indicated by the dotted arrows. (**b**) Schematic image emphasizing the morphologies of CDs in the cross-sectional TEM image. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics. **Figure 20.** (**a**) Cross-sectional TEM image of the GdBCO coated conductor irradiated with 80 MeV Xe ions at *θ*<sup>i</sup> = 0◦ and ±45◦ . Several continuous CDs are indicated by the solid arrows and discontinuous CDs along the *c*-axis are indicated by the dotted arrows. (**b**) Schematic image emphasizing the morphologies of CDs in the cross-sectional TEM image. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics.

Figure 21 shows the magnetic field angular dependence of *J*c for GdBCO coated conductors irradiated with 80 MeV and 270 MeV Xe ions, where the irradiation angles are *θ*<sup>i</sup> = 0° for the parallel CD configurations and *θ*i = 0°, ±45° for the trimodal angular configuration, respectively. The trimodal angular distribution shows higher *J*c values than the parallel CD configuration at 70 K under the same irradiation energy. This suggests that the direction-dispersion of CDs is more effective to enhance the flux pinning over a wide magnetic field angular region, as mentioned in Section 3.2. It is noteworthy that the trimodal angular configuration produced by 80 MeV Xe ions shows the highest *J*c in all the CD configurations over the whole magnetic field angular region at 70 K. The 80 MeV trimodal configuration consists of short segmented CDs along the *c*-axis and elongated CDs Figure 21 shows the magnetic field angular dependence of *J*<sup>c</sup> for GdBCO coated conductors irradiated with 80 MeV and 270 MeV Xe ions, where the irradiation angles are *θ*<sup>i</sup> = 0◦ for the parallel CD configurations and *θ*<sup>i</sup> = 0◦ , ±45◦ for the trimodal angular configuration, respectively. The trimodal angular distribution shows higher *J*<sup>c</sup> values than the parallel CD configuration at 70 K under the same irradiation energy. This suggests that the direction-dispersion of CDs is more effective to enhance the flux pinning over a wide magnetic field angular region, as mentioned in Section 3.2. It is noteworthy that the trimodal angular configuration produced by 80 MeV Xe ions shows the highest *J*<sup>c</sup> in all the CD configurations over the whole magnetic field angular region at 70 K. The 80 MeV trimodal configuration consists of short segmented CDs along the *c*-axis and elongated CDs

CDs, as shown in Figure 18b. Furthermore, continuous CDs crossing at *θ*i = ±45° assist in trapping the unpinned segments of flux lines, as shown in Figure 22a. The pinning of kinks of flux lines is effective for further improvement of *J*c [53,54]. Therefore, the combination of discontinuous CDs and continuous ones crossing at *θ*i = ±45° provides the en-

hancement of *J*c at *B* || *c*.

crossing at *θ*i= ±45◦ , as shown in Figure 20a. For *B* || *c*, the motion of double kinks of flux lines peculiar to one-dimensional PCs is suppressed by the gaps between the segmented CDs, as shown in Figure 18b. Furthermore, continuous CDs crossing at *θ*<sup>i</sup> = ±45◦ assist in trapping the unpinned segments of flux lines, as shown in Figure 22a. The pinning of kinks of flux lines is effective for further improvement of *J*<sup>c</sup> [53,54]. Therefore, the combination of discontinuous CDs and continuous ones crossing at *θ*<sup>i</sup> = ±45◦ provides the enhancement of *J*<sup>c</sup> at *B* || *c*. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 18 of 22

**Figure 21.** Magnetic field angular dependence of *J*c at magnetic field of 4 T and temperatures of (**a**) 84 K, (**b**) 77.3 K, and (**c**) 70 K for GdBCO coated conductors irradiated with 80 MeV and 270 MeV Xe ions, where the irradiation angles are *θ*i = 0° for parallel CD configurations and *θ*i = 0°, ±45° for trimodal angular configurations, respectively. The broken lines for (**b**) 77.3 K and (**c**) 70 K show the *J*c properties of the unirradiated sample as reference data. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics. **Figure 21.** Magnetic field angular dependence of *J*c at magnetic field of 4 T and temperatures of (**a**) 84 K, (**b**) 77.3 K, and (**c**) 70 K for GdBCO coated conductors irradiated with 80 MeV and 270 MeV Xe ions, where the irradiation angles are *θ*<sup>i</sup> = 0◦ for parallel CD configurations and *θ*<sup>i</sup> = 0◦ , ±45◦ for trimodal angular configurations, respectively. The broken lines for (**b**) 77.3 K and (**c**) 70 K show the *J*c properties of the unirradiated sample as reference data. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics.

At the intermediate angles between *B* || *c* and *B* || *ab*, on the other hand, the continuous CDs crossing at *θ*<sup>i</sup> = ±45◦ predominantly trap flux lines. In addition, the flux pinning of CDs crossing at *θ*<sup>i</sup> = ±45◦ is further enhanced through the suppression of the motion of kinks of flux lines by the gaps in discontinuous CDs, as shown in Figure 22b. Thus, the hybrid flux pinning by the two different kinds of PCs causes the large enhancement of *J*<sup>c</sup> even at the intermediate magnetic field angles.

**Figure 22.** Schematic images of flux pinning for the 80 MeV trimodal angular configuration in a magnetic field *B* (**a**) along the *c*-axis and (**b**) in the intermediate angular region between *B* || *c* and *B* || *ab*. The hatched regions in the inclined CDs and the discontinuous ones represent the interaction areas with kinks of flux lines. Reprinted with permission from [50], copyright 2020 by the

Japan Society of Applied Physics.

**Figure 21.** Magnetic field angular dependence of *J*c at magnetic field of 4 T and temperatures of (**a**) 84 K, (**b**) 77.3 K, and (**c**) 70 K for GdBCO coated conductors irradiated with 80 MeV and 270 MeV Xe ions, where the irradiation angles are *θ*i = 0° for parallel CD configurations and *θ*i = 0°, ±45° for trimodal angular configurations, respectively. The broken lines for (**b**) 77.3 K and (**c**) 70 K show the *J*c properties of the unirradiated sample as reference data. Reprinted with permission from

[50], copyright 2020 by the Japan Society of Applied Physics.

**Figure 22.** Schematic images of flux pinning for the 80 MeV trimodal angular configuration in a magnetic field *B* (**a**) along the *c*-axis and (**b**) in the intermediate angular region between *B* || *c* and *B* || *ab*. The hatched regions in the inclined CDs and the discontinuous ones represent the interaction areas with kinks of flux lines. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics. **Figure 22.** Schematic images of flux pinning for the 80 MeV trimodal angular configuration in a magnetic field *B* (**a**) along the *c*-axis and (**b**) in the intermediate angular region between *B* || *c* and *B* || *ab*. The hatched regions in the inclined CDs and the discontinuous ones represent the interaction areas with kinks of flux lines. Reprinted with permission from [50], copyright 2020 by the Japan Society of Applied Physics.

There is a possibility that direction-dispersed CDs with "complete discontinuity" further provide a high and isotropic *J*<sup>c</sup> in high-*T*<sup>c</sup> superconductors. In fact, BaHfO3. nanorods tend to grow discontinuously and to be widely dispersed in the directions, causing a significant improvement of *J*<sup>c</sup> in a wide magnetic field angular range for REBCO thin films [55,56]. The irradiation using lighter ions with lower energy, which provides lower *S*<sup>e</sup> for high-*T*<sup>c</sup> superconductors (e.g., Kr-ion irradiation with 80 MeV, where *S*<sup>e</sup> = 16.0 keV/nm), may produce discontinuous CDs even in directions tilted from the *c*-axis. However, there is a trade-off between the discontinuity of CDs and the thickness of CDs for the formation of CDs by heavy-ion irradiations: discontinuous CDs tend to be thin diameter [18,25], where the elementary pinning force of one segmented column with thin diameter becomes weak. Thus, the discontinuity of CDs does not always provide the strong pinning landscape for the heavy-ion irradiation process. The introduction of direction-dispersed, discontinuous, and thick CDs by the ion irradiation process can be the key to further making high *J*<sup>c</sup> fairly isotropic in high-*T*<sup>c</sup> superconductors.
