[en] Ubiquitous in most superconducting materials and a common result of nanofabrication processes, weak links are known for their limiting effects on the transport of electric currents. Still, they are at the root of key features of superconducting technology. By performing quantitative magneto-optical imaging experiments and thermomagnetic model simulations, we correlate the existence of local maxima in the magnetization loops of focused ion beam (FIB)-patterned Nb films to a magnetic field induced weak-to-strong-link transformation increasing their critical current. This phenomenon arises from the nanoscale interaction between quantized magnetic flux lines and FIB-induced modifications of the device microstructure. Under an ac drive field, this leads to a rectified vortex motion along the weak link. The reported tunable effect can be exploited in the development of new superconducting electronic devices, such as flux pumps and valves, to attenuate or amplify the supercurrent through a circuit element and as a strategy to enhance the critical current in weak-link-bearing devices.
Disciplines :
Physics
Author, co-author :
Chaves, Davi A. D. ; Departamento de Física, Universidade Federal de São Carlos, Brazil
Valerio-Cuadros, M.I.; Departamento de Física, Universidade Federal de São Carlos, Brazil ; Departamento de Física, Universidade Estadual de Maringá, Brazil
Jiang, L. ; School of Aeronautics, Northwestern Polytechnical University, Xi'an, China ; Experimental Physics of Nanostructured Materials, Q-MAT, CESAM, Université de Liège, Belgium
Abbey, E.A. ; Departamento de Física, Universidade Federal de São Carlos, Brazil
Colauto, F.; Departamento de Física, Universidade Federal de São Carlos, Brazil
Oliveira, A.A.M.; Instituto Federal de Educação Ciência e Tecnologia de São Paulo, Campus São Carlos, Brazil
De Andrade, A.M.H.; Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
Pinheiro, L.B.L.G. ; Departamento de Física, Universidade Federal de São Carlos, Brazil ; Instituto Federal de Educação Ciência e Tecnologia de São Paulo, Campus São Carlos, Brazil
Johansen, T.H.; Department of Physics, University of Oslo, Oslo, Norway
Xue, C.; School of Mechanics Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, China
Zhou, Y.-H.; School of Aeronautics, Northwestern Polytechnical University, Xi'an, China ; Department of Mechanics and Engineering Sciences, Lanzhou University, Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education of China, Lanzhou, China
Silhanek, Alejandro ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés
Ortiz, W.A. ; Departamento de Física, Universidade Federal de São Carlos, Brazil
Motta, M. ; Departamento de Física, Universidade Federal de São Carlos, Brazil
CAPES - Coordenação de Aperfeicoamento de Pessoal de Nível Superior [BR] FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo [BR] CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico [BR] NSCF - National Natural Science Foundation of China [CN] CSC - China Scholarship Council [CN] LNNano - Laboratório Nacional de Nanotecnologia [BR]
Funding text :
This work was partially supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil (CAPES), Finance Code 001, the São Paulo Research Foundation (FAPESP, Grant No. 2021/08781-8), and the National Council for Scientific and Technological Development (CNPq, Grants No. 431974/2018-7, No. 316602/2021-3, and No. 309928/2018-4). C.X. acknowledges the support by the National Natural Science Foundation of China (Grants No. 11972298 and 12011530143). L.J. was supported by the China Scholarship Council. The authors thank the Laboratory of Structural Characterization (LCE/DEMa/UFSCar) for the EDS and AFM measurements. The research was supported by LNNano, Brazilian Nanotechnology National Laboratory (CNPEM/MCTI) during the use of the Device Manufacturing open access facility.
K. Harada, O. Kamimura, H. Kasai, T. Matsuda, A. Tonomura, and V. V. Moshchalkov, Direct observation of vortex dynamics in superconducting films with regular arrays of defects, Science 274, 1167 (1996) 0036-8075 10.1126/science.274.5290.1167.
A. V. Silhanek, L. Van Look, S. Raedts, R. Jonckheere, and V. V. Moshchalkov, Guided vortex motion in superconductors with a square antidot array, Phys. Rev. B 68, 214504 (2003) 0163-1829 10.1103/PhysRevB.68.214504.
O. V. Dobrovolskiy, E. Begun, M. Huth, and V. A. Shklovskij, Electrical transport and pinning properties of Nb thin films patterned with focused ion beam-milled washboard nanostructures, New J. Phys. 14, 113027 (2012) 1367-2630 10.1088/1367-2630/14/11/113027.
G. Shaw, P. Mandal, B. Bag, S. Banerjee, T. Tamegai, and H. Suderow, Properties of nanopatterned pins generated in a superconductor with FIB, Appl. Surf. Sci. 258, 4199 (2012) 0169-4332 10.1016/j.apsusc.2011.05.011.
Y. L. Wang, M. L. Latimer, Z. L. Xiao, R. Divan, L. E. Ocola, G. W. Crabtree, and W. K. Kwok, Enhancing the critical current of a superconducting film in a wide range of magnetic fields with a conformal array of nanoscale holes, Phys. Rev. B 87, 220501 (R) (2013) 1098-0121 10.1103/PhysRevB.87.220501.
O. V. Dobrovolskiy, Abrikosov fluxonics in washboard nanolandscapes, Physica C 533, 80 (2017) 0921-4534 10.1016/j.physc.2016.07.008.
Y. Kalcheim, E. Katzir, F. Zeides, N. Katz, Y. Paltiel, and O. Millo, Dynamic control of the vortex pinning potential in a superconductor using current injection through nanoscale patterns, Nano Lett. 17, 2934 (2017) 1530-6984 10.1021/acs.nanolett.7b00179.
O. V. Dobrovolskiy, V. A. Shklovskij, M. Hanefeld, M. Zörb, L. Köhs, and M. Huth, Pinning effects on flux flow instability in epitaxial Nb thin films, Supercond. Sci. Technol. 30, 085002 (2017) 0953-2048 10.1088/1361-6668/aa73aa.
F. Colauto, M. Motta, and W. A. Ortiz, Controlling magnetic flux penetration in low-(Equation presented) superconducting films and hybrids, Supercond. Sci. Technol. 34, 013002 (2021) 0953-2048 10.1088/1361-6668/abac1e.
K. K. Likharev, Superconducting weak links, Rev. Mod. Phys. 51, 101 (1979) 0034-6861 10.1103/RevModPhys.51.101.
Nanoscience and Engineering in Superconductivity, edited by V. Moshchalkov, R. Woerdenweber, and W. Lang (Springer Berlin, Heidelberg, 2010).
A. Fornieri, A. M. Whiticar, F. Setiawan, E. Portolés, A. C. Drachmann, A. Keselman, S. Gronin, C. Thomas, T. Wang, R. Kallaher, G. C. Gardner, E. Berg, M. J. Manfra, A. Stern, C. M. Marcus, and F. Nichele, Evidence of topological superconductivity in planar Josephson junctions, Nature (London) 569, 89 (2019) 0028-0836 10.1038/s41586-019-1068-8.
I. Holzman and Y. Ivry, Superconducting nanowires for single-photon detection: Progress, challenges, and opportunities, Adv. Quantum Technol. 2, 1800058 (2019) 2511-9044 10.1002/qute.201800058.
A. Murphy, D. V. Averin, and A. Bezryadin, Nanoscale superconducting memory based on the kinetic inductance of asymmetric nanowire loops, New J. Phys. 19, 063015 (2017) 1367-2630 10.1088/1367-2630/aa7331.
L. Chen, L. Wu, Y. Wang, Y. Pan, D. Zhang, J. Zeng, X. Liu, L. Ma, W. Peng, Y. Wang, J. Ren, and Z. Wang, Miniaturization of the superconducting memory cell via a three-dimensional Nb nano-superconducting quantum interference device, ACS Nano 14, 11002 (2020) 1936-0851 10.1021/acsnano.0c04405.
E. Ilin, X. Song, I. Burkova, A. Silge, Z. Guo, K. Ilin, and A. Bezryadin, Supercurrent-controlled kinetic inductance superconducting memory element, Appl. Phys. Lett. 118, 112603 (2021) 0003-6951 10.1063/5.0040563.
D. A. D. Chaves, L. Nulens, H. Dausy, B. Raes, D. Yue, W. A. Ortiz, M. Motta, M. J. Van Bael, and J. Van de Vondel, Nanobridge SQUIDs as multilevel memory elements, Phys. Rev. Appl. 19, 034091 (2023) 2331-7019 10.1103/PhysRevApplied.19.034091.
Y.-Y. Lyu, J. Jiang, Y.-L. Wang, Z.-L. Xiao, S. Dong, Q.-H. Chen, M. V. Milošević, H. Wang, R. Divan, J. E. Pearson, P. Wu, F. M. Peeters, and W.-K. Kwok, Superconducting diode effect via conformal-mapped nanoholes, Nat. Commun. 12, 2703 (2021) 2041-1723 10.1038/s41467-021-23077-0.
T. Golod and V. M. Krasnov, Demonstration of a superconducting diode-with-memory, operational at zero magnetic field with switchable nonreciprocity, Nat. Commun. 13, 3658 (2022) 2041-1723 10.1038/s41467-022-31256-w.
E. Strambini, A. Iorio, O. Durante, R. Citro, C. Sanz-Fernández, C. Guarcello, I. V. Tokatly, A. Braggio, M. Rocci, N. Ligato, V. Zannier, L. Sorba, F. S. Bergeret, and F. Giazotto, A Josephson phase battery, Nat. Nanotechnol. 15, 656 (2020) 1748-3387 10.1038/s41565-020-0712-7.
T. Yamashita, S. Kim, H. Kato, W. Qiu, K. Semba, A. Fujimaki, and H. Terai, (Equation presented) phase shifter based on NbN-based ferromagnetic Josephson junction on a silicon substrate, Sci. Rep. 10, 1 (2020) 2045-2322 10.1038/s41598-020-70766-9.
T. Golod, R. A. Hovhannisyan, O. M. Kapran, V. V. Dremov, V. S. Stolyarov, and V. M. Krasnov, Reconfigurable Josephson phase shifter, Nano Lett. 21, 5240 (2021) 1530-6984 10.1021/acs.nanolett.1c01366.
C. A. Volkert and A. M. Minor, Focused ion beam microscopy and micromachining, MRS Bull. 32, 389 (2007) 0883-7694 10.1557/mrs2007.62.
M. Wyss, K. Bagani, D. Jetter, E. Marchiori, A. Vervelaki, B. Gross, J. Ridderbos, S. Gliga, C. Schönenberger, and M. Poggio, Magnetic, thermal, and topographic imaging with a nanometer-scale SQUID-on-lever scanning probe, Phys. Rev. Appl. 17, 034002 (2022) 2331-7019 10.1103/PhysRevApplied.17.034002.
F. Sigloch, S. Sangiao, P. Orús, and J. M. de Teresa, Direct-write of tungsten-carbide nanoSQUIDs based on focused ion beam induced deposition, Nanoscale Adv. 4, 4628 (2022) 2516-0230 10.1039/D2NA00602B.
A. M. Datesman, J. C. Schultz, T. W. Cecil, C. M. Lyons, and A. W. Lichtenberger, Gallium ion implantation into niobium thin films using a focused-ion beam, IEEE Trans. Appl. Supercond. 15, 3524 (2005) 1051-8223 10.1109/TASC.2005.849029.
N. De Leo, M. Fretto, V. Lacquaniti, C. Cassiago, L. D'Ortenzi, L. Boarino, and S. Maggi, Thickness modulated niobium nanoconstrictions by focused ion beam and anodization, IEEE Trans. Appl. Supercond. 26, 1 (2016) 1051-8223 10.1109/TASC.2016.2542286.
M. Singh, R. Chaujar, S. Husale, S. Grover, A. P. Shah, M. M. Deshmukh, A. Gupta, V. N. Singh, V. N. Ojha, D. K. Aswal, and R. K. Rakshit, Influence of fabrication processes on transport properties of superconducting niobium nitride nanowires, Curr. Sci. 114, 1443 (2018) 0011-3891 10.18520/cs/v114/i07/1443-1450.
B. Aichner, B. Müller, M. Karrer, V. R. Misko, F. Limberger, K. L. Mletschnig, M. Dosmailov, J. D. Pedarnig, F. Nori, R. Kleiner, D. Koelle, and W. Lang, Ultradense tailored vortex pinning arrays in superconducting (Equation presented) thin films created by focused He ion beam irradiation for fluxonics applications, ACS Appl. Nano Mater. 2, 5108 (2019) 2574-0970 10.1021/acsanm.9b01006.
M. I. Valerio-Cuadros, D. A. D. Chaves, F. Colauto, A. A. M. Oliveira, A. M. H. Andrade, T. H. Johansen, W. A. Ortiz, and M. Motta, Superconducting properties and electron scattering mechanisms in a Nb film with a single weak-link excavated by focused ion beam, Materials 14, 7274 (2021) 1996-1944 10.3390/ma14237274.
D. Larbalestier, A. Gurevich, D. M. Feldmann, and A. Polyanskii, High-(Equation presented) superconducting materials for electric power applications, Nature (London) 414, 368 (2001) 0028-0836 10.1038/35104654.
S. R. Foltyn, L. Civale, J. L. MacManus-Driscoll, Q. X. Jia, B. Maiorov, H. Wang, and M. Maley, Materials science challenges for high-temperature superconducting wire, Nat. Mater. 6, 631 (2007) 1476-1122 10.1038/nmat1989.
H. Hilgenkamp and J. Mannhart, Grain boundaries in high-(Equation presented) superconductors, Rev. Mod. Phys. 74, 485 (2002) 0034-6861 10.1103/RevModPhys.74.485.
S. Graser, P. J. Hirschfeld, T. Kopp, R. Gutser, B. M. Andersen, and J. Mannhart, How grain boundaries limit supercurrents in high-temperature superconductors, Nat. Phys. 6, 609 (2010) 1745-2473 10.1038/nphys1687.
R. P. Reade, P. Berdahl, R. E. Russo, and S. M. Garrison, Laser deposition of biaxially textured yttriastabilized zirconia buffer layers on polycrystalline metallic alloys for high critical current YBaCuO thin films, Appl. Phys. Lett. 61, 2231 (1992) 0003-6951 10.1063/1.108277.
Y. Iijima, K. Onabe, N. Futaki, N. Tanabe, N. Sadakata, O. Kohno, and Y. Ikeno, Structural and transport properties of biaxially aligned (Equation presented) films on polycrystalline Nibased alloy with ionbeammodified buffer layers, J. Appl. Phys. 74, 1905 (1993) 0021-8979 10.1063/1.354801.
X. D. Wu, S. R. Foltyn, P. N. Arendt, W. R. Blumenthal, I. H. Campbell, J. D. Cotton, J. Y. Coulter, W. L. Hults, M. P. Maley, H. F. Safar, and J. L. Smith, Properties of (Equation presented) thick films on flexible buffered metallic substrates, Appl. Phys. Lett. 67, 2397 (1995) 0003-6951 10.1063/1.114559.
A. Goyal, D. P. Norton, J. D. Budai, M. Paranthaman, E. D. Specht, D. M. Kroeger, D. K. Christen, Q. He, B. Saffian, F. A. List, D. F. Lee, P. M. Martin, C. E. Klabunde, E. Hartfield, and V. K. Sikka, High critical current density superconducting tapes by epitaxial deposition of (Equation presented) thick films on biaxially textured metals, Appl. Phys. Lett. 69, 1795 (1996) 0003-6951 10.1063/1.117489.
J. Díez-Sierra, P. López-Domínguez, H. Rijckaert, M. Rikel, J. Hänisch, M. Z. Khan, M. Falter, J. Bennewitz, H. Huhtinen, S. Schäfer, R. Müller, S. A. Schunk, P. Paturi, M. Bäcker, K. D. Buysser, and I. V. Driessche, High critical current density and enhanced pinning in superconducting films of (Equation presented) nanocomposites with embedded (Equation presented), (Equation presented), (Equation presented), and (Equation presented) nanocrystals, ACS Appl. Nano Mater. 3, 5542 (2020) 2574-0970 10.1021/acsanm.0c00814.
I. Ahmad, S. Sarangi, and P. Sarun, Enhanced critical current density and flux pinning of anthracene doped magnesium diboride superconductor, J. Alloys Compd. 884, 160999 (2021) 0925-8388 10.1016/j.jallcom.2021.160999.
M. Rocci, D. Suri, A. Kamra, G. Vilela, Y. Takamura, N. M. Nemes, J. L. Martinez, M. G. Hernandez, and J. S. Moodera, Large enhancement of critical current in superconducting devices by gate voltage, Nano Lett. 21, 216 (2021) 1530-6984 10.1021/acs.nanolett.0c03547.
A. M. Caffer, D. A. D. Chaves, A. L. Pessoa, C. L. Carvalho, W. A. Ortiz, R. Zadorosny, and M. Motta, Optimum heat treatment to enhance the weak-link response of Y123 nanowires prepared by solution blow spinning, Supercond. Sci. Technol. 34, 025009 (2021) 0953-2048 10.1088/1361-6668/abc8d2.
R. Algarni, M. A. Almessiere, Y. Slimani, E. Hannachi, and F. B. Azzouz, Enhanced critical current density and flux pinning traits with (Equation presented) nanoparticles added to (Equation presented) superconductor, J. Alloys Compd. 852, 157019 (2021) 0925-8388 10.1016/j.jallcom.2020.157019.
D. A. D. Chaves, I. M. de Araújo, D. Carmo, F. Colauto, A. A. M. Oliveira, A. M. H. Andrade, T. H. Johansen, A. V. Silhanek, W. A. Ortiz, and M. Motta, Enhancing the effective critical current density in a Nb superconducting thin film by cooling in an inhomogeneous magnetic field, Appl. Phys. Lett. 119, 022602 (2021) 0003-6951 10.1063/5.0058680.
G. Shaw, J. Brisbois, L. B. G. L. Pinheiro, J. Müller, S. Blanco Alvarez, T. Devillers, N. M. Dempsey, J. E. Scheerder, J. Van de Vondel, S. Melinte, P. Vanderbemden, M. Motta, W. A. Ortiz, K. Hasselbach, R. B. G. Kramer, and A. V. Silhanek, Quantitative magneto-optical investigation of superconductor/ferromagnet hybrid structures, Rev. Sci. Instrum. 89, 023705 (2018) 0034-6748 10.1063/1.5016293.
A. Y. Meltzer, E. Levin, and E. Zeldov, Direct reconstruction of two-dimensional currents in thin films from magnetic-field measurements, Phys. Rev. Appl. 8, 064030 (2017) 2331-7019 10.1103/PhysRevApplied.8.064030.
J. I. Vestgården, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, Dynamics and morphology of dendritic flux avalanches in superconducting films, Phys. Rev. B 84, 054537 (2011) 1098-0121 10.1103/PhysRevB.84.054537.
L. Jiang, C. Xue, L. Burger, B. Vanderheyden, A. V. Silhanek, and Y.-H. Zhou, Selective triggering of magnetic flux avalanches by an edge indentation, Phys. Rev. B 101, 224505 (2020) 2469-9950 10.1103/PhysRevB.101.224505.
T. Schuster, M. V. Indenbom, M. R. Koblischka, H. Kuhn, and H. Kronmüller, Observation of current-discontinuity lines in type-II superconductors, Phys. Rev. B 49, 3443 (1994) 0163-1829 10.1103/PhysRevB.49.3443.
T. Schuster, H. Kuhn, and M. V. Indenbom, Discontinuity lines in rectangular superconductors with intrinsic and extrinsic anisotropies, Phys. Rev. B 52, 15621 (1995) 0163-1829 10.1103/PhysRevB.52.15621.
R. G. Mints and A. L. Rakhmanov, Critical state stability in type-II superconductors and superconducting-normal-metal composites, Rev. Mod. Phys. 53, 551 (1981) 0034-6861 10.1103/RevModPhys.53.551.
G. Blatter, M. V. Feigel'man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Vortices in high-temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994) 0034-6861 10.1103/RevModPhys.66.1125.
A. A. Polyanskii, A. Gurevich, A. E. Pashitski, N. F. Heinig, R. D. Redwing, J. E. Nordman, and D. C. Larbalestier, Magneto-optical study of flux penetration and critical current densities in [001] tilt (Equation presented) thin-film bicrystals, Phys. Rev. B 53, 8687 (1996) 0163-1829 10.1103/PhysRevB.53.8687.
T. H. Johansen, F. Colauto, A. M. H. de Andrade, A. A. M. Oliveira, and W. A. Ortiz, Transparency of planar interfaces in superconductors: a critical-state analysis, IEEE Trans. Appl. Supercond. 29, 1 (2019) 1051-8223 10.1109/TASC.2019.2899209.
F. Colauto, D. Carmo, A. M. H. Andrade, A. A. M. Oliveira, W. A. Ortiz, Y. M. Galperin, and T. H. Johansen, Measurement of critical current flow and connectivity in systems of joined square superconducting plates, Physica C 589, 1353931 (2021) 0921-4534 10.1016/j.physc.2021.1353931.
Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Magnetization and critical supercurrents, Phys. Rev. 129, 528 (1963) 0031-899X 10.1103/PhysRev.129.528.
D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, Thin superconducting disk with field-dependent critical current: Magnetization and ac susceptibilities, Phys. Rev. B 61, 9699 (2000) 0163-1829 10.1103/PhysRevB.61.9699.
T. H. Johansen and H. Bratsberg, Critical state magnetization of type II superconductors in rectangular slab and cylinder geometries, J. Appl. Phys. 77, 3945 (1995) 0021-8979 10.1063/1.358576.
E. H. Brandt and M. Indenbom, Type-II-superconductor strip with current in a perpendicular magnetic field, Phys. Rev. B 48, 12893 (1993) 0163-1829 10.1103/PhysRevB.48.12893.
D. V. Shantsev, M. R. Koblischka, Y. M. Galperin, T. H. Johansen, L. Půst, and M. Jirsa, Central peak position in magnetization loops of high-(Equation presented) superconductors, Phys. Rev. Lett. 82, 2947 (1999) 0031-9007 10.1103/PhysRevLett.82.2947.
J. F. Wambaugh, C. Reichhardt, C. J. Olson, F. Marchesoni, and F. Nori, Superconducting fluxon pumps and lenses, Phys. Rev. Lett. 83, 5106 (1999) 0031-9007 10.1103/PhysRevLett.83.5106.
C. J. Olson, C. Reichhardt, B. Jankó, and F. Nori, Collective interaction-driven ratchet for transporting flux quanta, Phys. Rev. Lett. 87, 177002 (2001) 0031-9007 10.1103/PhysRevLett.87.177002.
Y. Togawa, K. Harada, T. Akashi, H. Kasai, T. Matsuda, F. Nori, A. Maeda, and A. Tonomura, Direct observation of rectified motion of vortices in a niobium superconductor, Phys. Rev. Lett. 95, 087002 (2005) 0031-9007 10.1103/PhysRevLett.95.087002.
C. C. de Souza Silva, J. Van de Vondel, B. Y. Zhu, M. Morelle, and V. V. Moshchalkov, Vortex ratchet effects in films with a periodic array of antidots, Phys. Rev. B 73, 014507 (2006) 1098-0121 10.1103/PhysRevB.73.014507.
C. C. de Souza Silva, J. Van de Vondel, M. Morelle, and V. V. Moshchalkov, Controlled multiple reversals of a ratchet effect, Nature (London) 440, 651 (2006) 0028-0836 10.1038/nature04595.
J. E. Evetts and B. A. Glowacki, Relation of critical current irreversibility to trapped flux and microstructure in polycrystalline (Equation presented), Cryogenics 28, 641 (1988) 0011-2275 10.1016/0011-2275(88)90147-6.
D. Dimos, P. Chaudhari, and J. Mannhart, Superconducting transport properties of grain boundaries in (Equation presented) bicrystals, Phys. Rev. B 41, 4038 (1990) 0163-1829 10.1103/PhysRevB.41.4038.
M. J. Hogg, F. Kahlmann, Z. H. Barber, and J. E. Evetts, Angular hysteresis in the critical current of (Equation presented) low-angle grain boundaries, Supercond. Sci. Technol. 14, 647 (2001) 0953-2048 10.1088/0953-2048/14/9/301.
J. R. Thompson, H. J. Kim, C. Cantoni, D. K. Christen, R. Feenstra, and D. T. Verebelyi, Self-organized current transport through low-angle grain boundaries in (Equation presented) thin films studied magnetometrically, Phys. Rev. B 69, 104509 (2004) 1098-0121 10.1103/PhysRevB.69.104509.
A. Palau, T. Puig, X. Obradors, E. Pardo, C. Navau, A. Sanchez, A. Usoskin, H. C. Freyhardt, L. Fernández, B. Holzapfel, and R. Feenstra, Simultaneous inductive determination of grain and intergrain critical current densities of (Equation presented) coated conductors, Appl. Phys. Lett. 84, 230 (2004) 0003-6951 10.1063/1.1639940.
A. Palau, T. Puig, X. Obradors, and C. Jooss, Simultaneous determination of grain and grain-boundary critical currents in (Equation presented)-coated conductors by magnetic measurements, Phys. Rev. B 75, 054517 (2007) 1098-0121 10.1103/PhysRevB.75.054517.
K. Guth, V. Born, and C. Jooss, Inhomogeneous current distribution in wide high-temperature superconducting small-angle grain boundaries, Eur. Phys. J. B 42, 239 (2004) 1434-6028 10.1140/epjb/e2004-00384-5.
V. Born, K. Guth, H. C. Freyhardt, and C. Jooss, Self-enhanced flux penetration into small angle grain boundaries in YBCO thin films, Supercond. Sci. Technol. 17, 380 (2004) 0953-2048 10.1088/0953-2048/17/3/015.
Z. Jing, H. Yong, and Y. Zhou, Influences of non-uniformities and anisotropies on the flux avalanche behaviors of type-II superconducting films, Supercond. Sci. Technol. 29, 105001 (2016) 0953-2048 10.1088/0953-2048/29/10/105001.
Z. Jing, H. Yong, and Y. Zhou, Numerical simulation on the flux avalanche behaviors of microstructured superconducting thin films, J. Appl. Phys. 121, 023902 (2017) 0021-8979 10.1063/1.4974000.
Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Critical persistent currents in hard superconductors, Phys. Rev. Lett. 9, 306 (1962) 0031-9007 10.1103/PhysRevLett.9.306.
J. F. Ziegler and J. P. Biersack, The stopping and range of ions in matter, in Treatise on Heavy-Ion Science: Volume 6: Astrophysics, Chemistry, and Condensed Matter, edited by D. A. Bromley (Springer US, Boston, MA, 1985), pp. 93-129.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.214502 to watch the full videos capturing the flux penetration into the samples.
