Impact of border defects on the magnetic flux penetration in superconducting films

[en] Defects in superconducting systems are ubiquitous and nearly unavoidable. They can vary in nature, geometry, and size, ranging from microscopic-size defects such as dislocations, grain boundaries, twin planes, and oxygen vacancies, to macroscopic-size defects such as segregations, indentations, contamination, cracks, and voids. Irrespective of their type, defects perturb the flow of electric current, forcing it to deviate from its path. In the best-case scenario, the associated perturbation can be damped within a distance of the order of the size of the defect if the rigidity of the superconducting state, characterized by the creep exponent n, is low. In most cases, however, this perturbation spans macroscopic distances covering the entire superconducting sample and thus dramatically influences the response of the system. In this work, we review the current state of theoretical understanding and experimental evidence on the modification of magnetic flux patterns in superconductors by border defects, including the influence of their geometry, temperature, and applied magnetic field. We scrutinize and contrast the picture emerging from a continuous media standpoint, i.e., ignoring the granularity imposed by the vortex quantization, with that provided by a phenomenological approach dictated by the vortex dynamics. In addition, we discuss the influence of border indentations on the nucleation of thermomagnetic instabilities. Assessing the impact of surface and border defects is of utmost importance for all superconducting technologies, including resonators, single-photon detectors, radio frequency cavities and accelerators, cables, metamaterials, diodes, and many others.

Disciplines :

Physics

Author, co-author :

Silhanek, Alejandro ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés

Jiang, Lu ; College of Pipeline and Civil Engineering, China University of Petroleum (East China) 2 , Qingdao 266580,

Xue, Cun ; School of Materials Science and Engineering, Northwestern Polytechnical University 3 , Xi'an 710072,

Vanderheyden, Benoît ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Electronique et microsystèmes

Language :

English

Title :

Impact of border defects on the magnetic flux penetration in superconducting films

Publication date :

01 December 2025

Journal title :

Applied Physics Reviews

eISSN :

1931-9401

Publisher :

AIP Publishing

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://pubs.aip.org/aip/apr/article-pdf/doi/10.1063/5.0282694/20832827/041324_1_5.0282694.pdf

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 09 December 2025

Statistics

Number of views

6 (2 by ULiège)

Number of downloads

15 (0 by ULiège)

More statistics

OpenCitations

OpenAlex citations

Bibliography

A. Gurevich and T. Kubo, “Surface impedance and optimum surface resistance of a superconductor with an imperfect surface,” Phys. Rev. B 96, 184515 (2017). 10.1103/PhysRevB.96.184515
A. Gurevich, “Superconducting radio-frequency fundamentals for particle accelerators,” Rev. Accel. Sci. Technol. 05, 119–146 (2012). 10.1142/S1793626812300058
A. Gurevich and G. Ciovati, “Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong RF fields,” Phys. Rev. B 77, 104501 (2008). 10.1103/PhysRevB.77.104501
W. Weingarten, “On the dependence of the Q-value on the accelerating gradient for superconducting cavities,” Tech. Rep. (CERN, Geneva, 2007).
D. Bothner, T. Gaber, M. Kemmler, D. Koelle, and R. Kleiner, “Improving the performance of superconducting microwave resonators in magnetic fields,” Appl. Phys. Lett. 98, 102504 (2011). 10.1063/1.3560480
D. Bothner, C. Clauss, E. Koroknay, M. Kemmler, T. Gaber, M. Jetter, M. Scheffler, P. Michler, M. Dressel, D. Koelle, and R. Kleiner, “Reducing vortex losses in superconducting microwave resonators with microsphere patterned antidot arrays,” Appl. Phys. Lett. 100, 012601 (2012). 10.1063/1.3673869
D. Bothner, T. Gaber, M. Kemmler, D. Koelle, R. Kleiner, S. Wünsch, and M. Siegel, “Magnetic hysteresis effects in superconducting coplanar microwave resonators,” Phys. Rev. B 86, 014517 (2012). 10.1103/PhysRevB.86.014517
B. Chiaro, A. Megrant, A. Dunsworth, Z. Chen, R. Barends, B. Campbell, Y. Chen, A. Fowler, I. C. Hoi, E. Jeffrey, J. Kelly, J. Mutus, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, and J. M. Martinis, “Dielectric surface loss in superconducting resonators with flux-trapping holes,” Supercond. Sci. Technol. 29, 104006 (2016). 10.1088/0953-2048/29/10/104006
J. Kroll, F. Borsoi, K. van der Enden, W. Uilhoorn, D. de Jong, M. Quintero-Pérez, D. van Woerkom, A. Bruno, S. Plissard, D. Car, E. Bakkers, M. Cassidy, and L. Kouwenhoven, “Magnetic-field-resilient superconducting coplanar-waveguide resonators for hybrid circuit quantum electrodynamics experiments,” Phys. Rev. Appl. 11, 064053 (2019). 10.1103/PhysRevApplied.11.064053
L. Nulens, N. Lejeune, J. Caeyers, S. Marinković, I. Cools, H. Dausy, S. Basov, B. Raes, M. J. Van Bael, A. Geresdi, A. V. Silhanek, and J. Van de Vondel, “Catastrophic magnetic flux avalanches in NbTiN superconducting resonators,” Commun. Phys. 6, 267 (2023). 10.1038/s42005-023-01386-8
A. Badía-Majós, E. Martínez, L. A. Angurel, G. F. de la Fuente, E. Fourneau, S. Marinković, and A. V. Silhanek, “Laser nanostructured metasurfaces in Nb superconducting thin films,” Appl. Surf. Sci. 649, 159164 (2024). 10.1016/j.apsusc.2023.159164
E. Martínez, N. Lejeune, J. Frechilla, L. Porta-Velilla, E. Fourneau, L. A. Angurel, G. F. de la Fuente, J. Bonse, A. V. Silhanek, and A. Badía-Majós, “Laser engineered architectures for magnetic flux manipulation on superconducting Nb thin films,” Appl. Surf. Sci. 679, 161214 (2025). 10.1016/j.apsusc.2024.161214
A. G. Sivakov, O. G. Turutanov, A. E. Kolinko, and A. S. Pokhila, “Spatial characterization of the edge barrier in wide superconducting films,” Low Temp. Phys. 44, 226–232 (2018). 10.1063/1.5024540
X. Zhang, X. Zhang, J. Huang, C. Yang, L. You, X. Liu, P. Hu, Y. Xiao, W. Zhang, Y. Wang, L. Li, Z. Wang, and H. Li, “Geometric origin of intrinsic dark counts in superconducting nanowire single-photon detectors,” Superconductivity 1, 100006 (2022). 10.1016/j.supcon.2022.100006
F. B. Hagedorn and P. M. Hall, “Right‐angle bends in thin strip conductors,” J. Appl. Phys. 34, 128–133 (1963). 10.1063/1.1729052
J. R. Clem and K. K. Berggren, “Geometry-dependent critical currents in superconducting nanocircuits,” Phys. Rev. B 84, 174510 (2011). 10.1103/PhysRevB.84.174510
A. N. Zotova and D. Y. Vodolazov, “Intrinsic detection efficiency of superconducting nanowire single photon detector in the modified hot spot model,” Supercond. Sci. Technol. 27, 125001 (2014). 10.1088/0953-2048/27/12/125001
D. Y. Vodolazov, K. Ilin, M. Merker, and M. Siegel, “Defect-controlled vortex generation in current-carrying narrow superconducting strips,” Supercond. Sci. Technol. 29, 025002 (2016). 10.1088/0953-2048/29/2/025002
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, 1125–1388 (1994). 10.1103/RevModPhys.66.1125
A. Gurevich and M. Friesen, “Nonlinear transport current flow in superconductors with planar obstacles,” Phys. Rev. B 62, 4004–4025 (2000). 10.1103/PhysRevB.62.4004
J. Dular, C. Geuzaine, and B. Vanderheyden, “Finite-element formulations for systems with high-temperature superconductors,” IEEE Trans. Appl. Supercond. 30, 1–13 (2020). 10.1109/TASC.2019.2935429
M. P. Garfunkel and B. Serin, “The formation of a boundary between normal-conducting and superconducting metal,” Phys. Rev. 85, 834–840 (1952). 10.1103/PhysRev.85.834
V. L. Ginzburg, “On the destruction and the onset of superconductivity in a magnetic field,” Soviet Physics JETP 34, 78 (1958).
C. P. Bean and J. D. Livingston, “Surface barrier in type-II superconductors,” Phys. Rev. Lett. 12, 14–16 (1964). 10.1103/PhysRevLett.12.14
H. J. Fink and A. G. Presson, “Stability limit of the superheated Meissner state due to three-dimensional fluctuations of the order parameter and vector potential,” Phys. Rev. 182, 498–503 (1969). 10.1103/PhysRev.182.498
F. P.-J. Lin and A. Gurevich, “Effect of impurities on the superheating field of type-II superconductors,” Phys. Rev. B 85, 054513 (2012). 10.1103/PhysRevB.85.054513
L. Kramer, “Stability limits of the Meissner state and the mechanism of spontaneous vortex nucleation in superconductors,” Phys. Rev. 170, 475–480 (1968). 10.1103/PhysRev.170.475
J. Matricon and D. Saint-James, “Superheating fields in superconductors,” Phys. Lett. A 24, 241–242 (1967). 10.1016/0375-9601(67)90412-4
J. R. Clem, “Theory of ac losses in type‐II superconductors with a field‐dependent surface barrier,” J. Appl. Phys. 50, 3518–3530 (1979). 10.1063/1.326349
L. G. Aslamazov and S. V. Lemnitskii, “Resistive state in broad superconducting films,” Sov. J. Exp. Theor. Phys. 57, 1291 (1983).
D. Y. Vodolazov, I. L. Maksimov, and E. H. Brandt, “Modulation instability of the order parameter in thin-film superconductors with edge barrier,” Europhys. Lett. 48, 313 (1999). 10.1209/epl/i1999-00483-y
J. Gutierrez, B. Raes, J. Van de Vondel, A. V. Silhanek, R. B. G. Kramer, G. W. Ataklti, and V. V. Moshchalkov, “First vortex entry into a perpendicularly magnetized superconducting thin film,” Phys. Rev. B 88, 184504 (2013). 10.1103/PhysRevB.88.184504
V. P. Galaǐko, “Formation of vortex nuclei in superconductors of the second kind,” Sov. J. Exp. Theor. Phys. 23, 878 (1966).
S. J. Chapman, “Superheating field of type II superconductors,” SIAM J. Appl. Math. 55, 1233–1258 (1995). 10.1137/S0036139993254760
P. de Gennes, “Vortex nucleation in type II superconductors,” Solid State Commun. 3, 127–130 (1965). 10.1016/0038-1098(65)90387-X
G. Boato, G. Gallinaro, and C. Rizzuto, “Direct evidence for quantized flux threads in type-II superconductors,” Solid State Commun. 3, 173–176 (1965). 10.1016/0038-1098(65)90285-1
R. W. De Blois and W. De Sorbo, “Surface barrier in type-II superconductors,” Phys. Rev. Lett. 12, 499–501 (1964). 10.1103/PhysRevLett.12.499
T. Yogi, G. J. Dick, and J. E. Mercereau, “Critical rf magnetic fields for some type-I and type-II superconductors,” Phys. Rev. Lett. 39, 826–829 (1977). 10.1103/PhysRevLett.39.826
M. K. Transtrum, G. Catelani, and J. P. Sethna, “Superheating field of superconductors within Ginzburg-Landau theory,” Phys. Rev. B 83, 094505 (2011). 10.1103/PhysRevB.83.094505
G. Catelani and J. P. Sethna, “Temperature dependence of the superheating field for superconductors in the high-κ London limit,” Phys. Rev. B 78, 224509 (2008). 10.1103/PhysRevB.78.224509
H. J. Fink and A. G. Presson, “Superheating of the Meissner state and the giant vortex state of a cylinder of finite extent,” Phys. Rev. 168, 399–402 (1968). 10.1103/PhysRev.168.399
H. Fink and A. Presson, “Superheating of the Meissner state,” Phys. Lett. A 25, 378–379 (1967). 10.1016/0375-9601(67)90708-6
D. Vodolazov, I. Maksimov, and E. Brandt, “Vortex entry conditions in type-II superconductors: Effect of surface defects,” Phys. C 384, 211–226 (2003). 10.1016/S0921-4534(02)01877-4
E. Zeldov, A. I. Larkin, V. B. Geshkenbein, M. Konczykowski, D. Majer, B. Khaykovich, V. M. Vinokur, and H. Shtrikman, “Geometrical barriers in high-temperature superconductors,” Phys. Rev. Lett. 73, 1428–1431 (1994). 10.1103/PhysRevLett.73.1428
M. Benkraouda and J. R. Clem, “Magnetic hysteresis from the geometrical barrier in type-II superconducting strips,” Phys. Rev. B 53, 5716–5726 (1996). 10.1103/PhysRevB.53.5716
E. H. Brandt, G. P. Mikitik, and E. Zeldov, “Two regimes of vortex penetration into platelet-shaped type-II superconductors,” J. Exp. Theor. Phys. 117, 439–448 (2013). 10.1134/S1063776113110010
R. Liang, P. Dosanjh, D. A. Bonn, W. N. Hardy, and A. J. Berlinsky, “Lower critical fields in an ellipsoid-shaped YBa2Cu3O6.95 single crystal,” Phys. Rev. B 50, 4212–4215 (1994). 10.1103/PhysRevB.50.4212
R. Labusch and T. Doyle, “Macroscopic equations for the description of the quasi-static magnetic behaviour of a type II superconductor of arbitrary shape,” Phys. C 290, 143–147 (1997). 10.1016/S0921-4534(97)01617-1
D. Majer, E. Zeldov, and M. Konczykowski, “Separation of the irreversibility and melting lines in Bi2 Sr2 CaCu2O8 crystals,” Phys. Rev. Lett. 75, 1166–1169 (1995). 10.1103/PhysRevLett.75.1166
W. A. Jones, P. N. Barnes, M. J. Mullins, F. J. Baca, R. L. S. Emergo, J. Wu, T. J. Haugan, and J. R. Clem, “Impact of edge-barrier pinning in superconducting thin films,” Appl. Phys. Lett. 97, 262503 (2010). 10.1063/1.3529945
V. Rouco, C. Navau, N. Del-Valle, D. Massarotti, G. P. Papari, D. Stornaiuolo, X. Obradors, T. Puig, F. Tafuri, A. Sanchez, and A. Palau, “Depairing current at high magnetic fields in vortex-free high-temperature superconducting nanowires,” Nano Lett. 19, 4174–4179 (2019). 10.1021/acs.nanolett.9b01693
T. Schuster, M. V. Indenbom, H. Kuhn, E. H. Brandt, and M. Konczykowski, “Flux penetration and overcritical currents in flat superconductors with irradiation-enhanced edge pinning: Theory and experiment,” Phys. Rev. Lett. 73, 1424–1427 (1994). 10.1103/PhysRevLett.73.1424
R. P. Huebener, R. T. Kampwirth, and J. R. Clem, “Meissner shielding currents and magnetic flux penetration in thin-film superconductors,” J. Low Temp. Phys. 6, 275–285 (1972). 10.1007/BF00628313
A. Buzdin and D. Feinberg, “Parallel field penetration in a layered superconductor,” Phys. Lett. A 165, 281–284 (1992). 10.1016/0375-9601(92)90051-M
E. H. Brandt, “The flux-line lattice in superconductors,” Rep. Prog. Phys. 58, 1465 (1995). 10.1088/0034-4885/58/11/003
F. F. Ternovskii and L. N. Shekhata, “Structure of the mixed state near the boundary of a semi-infinite type II superconductor of the second kind,” Soviet Physics JETP 35, 1202 (1972).
J. R. Clem, “A model for flux pinning in superconductors,” in Low Temperature Physics-LT 13: Volume 3: Superconductivity, edited by K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel (Springer, Boston, MA, 1974), pp. 102–106.
L. Burlachkov, “Magnetic relaxation over the Bean-Livingston surface barrier,” Phys. Rev. B 47, 8056–8064 (1993). 10.1103/PhysRevB.47.8056
V. S. Gorbachev and S. E. Savel'ev, “Surface effects in a non-local critical state model,” JETP 82, 748 (1996).
A. V. Kuznetsov, D. V. Eremenko, and V. N. Trofimov, “Onset of flux penetration into a thin superconducting film strip,” Phys. Rev. B 59, 1507–1513 (1999). 10.1103/PhysRevB.59.1507
A. A. Elistratov, D. Y. Vodolazov, I. L. Maksimov, and J. R. Clem, “Field-dependent critical current in type-II superconducting strips: Combined effect of bulk pinning and geometrical edge barrier,” Phys. Rev. B 66, 220506 (2002). 10.1103/PhysRevB.66.220506
Å. Olsen, H. Hauglin, T. Johansen, P. Goa, and D. Shantsev, “Single vortices observed as they enter nbse2,” Phys. C 408–410, 537–538 (2004). 10.1016/j.physc.2004.03.070
L. Embon, Y. Anahory, Z. L. Jelic, E. O. Lachman, Y. Myasoedov, M. E. Huber, G. P. Mikitik, A. V. Silhanek, M. V. Milošević, A. Gurevich, and E. Zeldov, “Imaging of super-fast dynamics and flow instabilities of superconducting vortices,” Nat. Commun. 8, 85 (2017). 10.1038/s41467-017-00089-3
J. Pearl, “Current distribution in superconducting films carrying quantized fluxoids,” Appl. Phys. Lett. 5, 65–66 (1964). 10.1063/1.1754056
G. Carneiro and E. H. Brandt, “Vortex lines in films: Fields and interactions,” Phys. Rev. B 61, 6370–6376 (2000). 10.1103/PhysRevB.61.6370
E. H. Brandt, “Vortex-vortex interaction in thin superconducting films,” Phys. Rev. B 79, 134526 (2009). 10.1103/PhysRevB.79.134526
V. G. Kogan, “Pearl's vortex near the film edge,” Phys. Rev. B 49, 15874–15878 (1994). 10.1103/PhysRevB.49.15874
G. P. Mikitik, “Critical current in thin flat superconductors with Bean-Livingston and geometrical barriers,” Phys. Rev. B 104, 094526 (2021). 10.1103/PhysRevB.104.094526
G. P. Mikitik and Y. V. Sharlai, “Determination of the magnetic penetration depth with measurements of the vortex-penetration field for type-II superconductors,” Phys. Rev. B 110, 064507 (2024). 10.1103/PhysRevB.110.064507
M. Motta, F. Colauto, J. I. Vestgården, J. Fritzsche, M. Timmermans, J. Cuppens, C. Attanasio, C. Cirillo, V. V. Moshchalkov, J. Van de Vondel, T. H. Johansen, W. A. Ortiz, and A. V. Silhanek, “Controllable morphology of flux avalanches in microstructured superconductors,” Phys. Rev. B 89, 134508 (2014). 10.1103/PhysRevB.89.134508
I. L. Maksimov and A. A. Elistratov, “Edge barrier and structure of the critical state in superconducting thin films,” JETP Lett. 61, 204 (1995).
I. L. Maksimov, “Edge pinning and critical-state structure in thin superconducting films,” Europhys. Lett. 32, 753 (1995). 10.1209/0295-5075/32/9/009
A. A. Elistratov and I. L. Maksimov, “A generalized critical-state model for low-dimensional superconductors with an edge barrier,” Phys. Solid State 42, 201–206 (2000). 10.1134/1.1131147
B. L. T. Plourde, D. J. Van Harlingen, D. Y. Vodolazov, R. Besseling, M. B. S. Hesselberth, and P. H. Kes, “Influence of edge barriers on vortex dynamics in thin weak-pinning superconducting strips,” Phys. Rev. B 64, 014503 (2001). 10.1103/PhysRevB.64.014503
I. Aranson, M. Gitterman, and B. Y. Shapiro, “Onset of vortices in thin superconducting strips and wires,” Phys. Rev. B 51, 3092–3096 (1995). 10.1103/PhysRevB.51.3092
I. Aranson, B. Y. Shapiro, and V. Vinokur, “Nucleation and growth of the normal phase in thin superconducting strips,” Phys. Rev. Lett. 76, 142–145 (1996). 10.1103/PhysRevLett.76.142
A. V. Kuznetsov, D. V. Eremenko, and V. N. Trofimov, “Onset of flux penetration into a type-II superconductor disk,” Phys. Rev. B 56, 9064–9070 (1997). 10.1103/PhysRevB.56.9064
A. V. Kuznetsov, D. V. Eremenko, and V. N. Trofimov, “Onset of flux penetration into a type-I superconductor disk,” Phys. Rev. B 57, 5412–5418 (1998). 10.1103/PhysRevB.57.5412
H. Castro, B. Dutoit, A. Jacquier, M. Baharami, and L. Rinderer, “Experimental study of the geometrical barrier in type-I superconducting strips,” Phys. Rev. B 59, 596–602 (1999). 10.1103/PhysRevB.59.596
A. D. Hernández and D. Domínguez, “Surface barrier in mesoscopic type-I and type-II superconductors,” Phys. Rev. B 65, 144529 (2002). 10.1103/PhysRevB.65.144529
G. R. Berdiyorov, L. R. E. Cabral, and F. M. Peeters, “Surface barrier for flux entry and exit in mesoscopic superconducting systems,” J. Math. Phys. 46, 095105 (2005). 10.1063/1.2010351
K. K. Likharev, “The formation of a mixed state in planar semiconductor films,” Radiophys. Quantum Electron. 14, 722–727 (1971). 10.1007/BF01033185
G. M. Maksimova, “Mixed state and critical current in narrow semiconducting films,” Phys. Solid State 40, 1607–1610 (1998). 10.1134/1.1130618
J. R. Clem, “Vortex exclusion from superconducting strips and SQUIDs in weak perpendicular ambient magnetic fields,” in Proceedings of the APS March Meeting Abstracts (APS, 1998), p. K36.06.
G. Stan, S. B. Field, and J. M. Martinis, “Critical field for complete vortex expulsion from narrow superconducting strips,” Phys. Rev. Lett. 92, 097003 (2004). 10.1103/PhysRevLett.92.097003
E. Bronson, M. P. Gelfand, and S. B. Field, “Equilibrium configurations of pearl vortices in narrow strips,” Phys. Rev. B 73, 144501 (2006). 10.1103/PhysRevB.73.144501
K. H. Kuit, J. R. Kirtley, W. van der Veur, C. G. Molenaar, F. J. G. Roesthuis, A. G. P. Troeman, J. R. Clem, H. Hilgenkamp, H. Rogalla, and J. Flokstra, “Vortex trapping and expulsion in thin-film YBa2Cu3O7−δ strips,” Phys. Rev. B 77, 134504 (2008). 10.1103/PhysRevB.77.134504
R. B. G. Kramer, G. W. Ataklti, V. V. Moshchalkov, and A. V. Silhanek, “Direct visualization of the Campbell regime in superconducting stripes,” Phys. Rev. B 81, 144508 (2010). 10.1103/PhysRevB.81.144508
J.-Y. Ge, V. N. Gladilin, J. Van de Vondel, and V. V. Moshchalkov, “Vortex matter and critical magnetic fields in mesoscopic superconducting strips,” Supercond. Sci. Technol. 36, 085014 (2023). 10.1088/1361-6668/acdc5a
V. Kopylov, A. Koshelev, I. Schegolev, and T. Togonidze, “The role of surface effects in magnetization of high-Tc superconductors,” Phys. C 170, 291–297 (1990). 10.1016/0921-4534(90)90326-A
D. T. Fuchs, E. Zeldov, M. Rappaport, T. Tamegai, S. Ooi, and H. Shtrikman, “Transport properties governed by surface barriers in Bi2Sr2CaCu2O8,” Nature 391, 373–376 (1998). 10.1038/34879
Y. Segev, I. Gutman, S. Goldberg, Y. Myasoedov, E. Zeldov, E. H. Brandt, G. P. Mikitik, T. Katagiri, and T. Sasagawa, “Suppression of geometrical barrier in Bi2Sr2CaCu2O8+δ crystals by Josephson vortex stacks,” Phys. Rev. B 83, 104520 (2011). 10.1103/PhysRevB.83.104520
R. Willa, V. B. Geshkenbein, and G. Blatter, “Suppression of geometric barrier in type-II superconducting strips,” Phys. Rev. B 89, 104514 (2014). 10.1103/PhysRevB.89.104514
D. Y. Vodolazov, “Flux-flow instability in a strongly disordered superconducting strip with an edge barrier for vortex entry,” Supercond. Sci. Technol. 32, 115013 (2019). 10.1088/1361-6668/ab4168
O. V. Dobrovolskiy, D. Y. Vodolazov, F. Porrati, R. Sachser, V. M. Bevz, M. Y. Mikhailov, A. V. Chumak, and M. Huth, “Ultra-fast vortex motion in a direct-write Nb-C superconductor,” Nat. Commun. 11, 3291 (2020). 10.1038/s41467-020-16987-y
A. Maiani, A. Benfenati, and E. Babaev, “Vortex nucleation barriers and stable fractional vortices near boundaries in multicomponent superconductors,” Phys. Rev. B 105, 224507 (2022). 10.1103/PhysRevB.105.224507
M. Fogelström, D. Rainer, and J. A. Sauls, “Tunneling into current-carrying surface states of high- tc superconductors,” Phys. Rev. Lett. 79, 281–284 (1997). 10.1103/PhysRevLett.79.281
C.-R. Hu, “Midgap surface states as a novel signature for dxa2- xb2-wave superconductivity,” Phys. Rev. Lett. 72, 1526–1529 (1994). 10.1103/PhysRevLett.72.1526
C. Iniotakis, S. Graser, T. Dahm, and N. Schopohl, “Local density of states at polygonal boundaries of d-wave superconductors,” Phys. Rev. B 71, 214508 (2005). 10.1103/PhysRevB.71.214508
C. Iniotakis, T. Dahm, and N. Schopohl, “Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors,” Phys. Rev. Lett. 100, 037002 (2008). 10.1103/PhysRevLett.100.037002
M. I. Dolz, N. R. C. Bolecek, J. Puig, H. Pastoriza, G. Nieva, J. Guimpel, C. J. van der Beek, M. Konczykowski, and Y. Fasano, “Enhancement of penetration field in vortex matter in mesoscopic superconductors due to Andreev bound states,” Phys. Rev. B 100, 064508 (2019). 10.1103/PhysRevB.100.064508
L. Burlachkov, Y. Yeshurun, M. Konczykowski, and F. Holtzberg, “Explanation for the low-temperature behavior of hc1 in YBa2Cu3O7,” Phys. Rev. B 45, 8193–8196 (1992). 10.1103/PhysRevB.45.8193
L. Burlachkov, M. Konczykowski, Y. Yeshurun, and F. Holtzberg, “Bean–Livingston barriers and first field for flux penetration in high‐Tc crystals,” J. Appl. Phys. 70, 5759–5761 (1991). 10.1063/1.350152
M. Konczykowski, L. I. Burlachkov, Y. Yeshurun, and F. Holtzberg, “Evidence for surface barriers and their effect on irreversibility and lower-critical-field measurements in Y-Ba-Cu-O crystals,” Phys. Rev. B 43, 13707–13710 (1991). 10.1103/PhysRevB.43.13707
N. Chikumoto, M. Konczykowski, N. Motohira, K. Kishio, and K. Kitazawa, “The first magnetic penetration field in BSCCO single crystals, temperature dependence and electron irradiation effect,” Phys. C 185–189, 1835–1836 (1991). 10.1016/0921-4534(91)91043-4
F. Bass, V. Freilikher, B. Shapiro, and M. Shvartser, “Effect of the surface roughness on Bean-Livingston surface barrier,” Phys. C 260, 231–241 (1996). 10.1016/0921-4534(96)00134-7
A. Buzdin and M. Daumens, “Electromagnetic pinning of vortices on different types of defects,” Phys. C 294, 257–269 (1998). 10.1016/S0921-4534(97)01729-2
A. Aladyshkin, A. Mel'nikov, I. Shereshevsky, and I. Tokman, “What is the best gate for vortex entry into type-II superconductor?,” Phys. C 361, 67–72 (2001). 10.1016/S0921-4534(01)00288-X
T. Kubo, “Flux trapping in superconducting accelerating cavities during cooling down with a spatial temperature gradient,” Prog. Theor. Exp. Phys. 2016, 053G01. 10.1093/ptep/ptw049
T. Kubo, “Field limit and nano-scale surface topography of superconducting radio-frequency cavity made of extreme type II superconductor,” Prog. Theor. Exp. Phys. 2015, 63G01. 10.1093/ptep/ptv082
D. Y. Vodolazov, “Effect of surface defects on the first field for vortex entry in type-II superconductors,” Phys. Rev. B 62, 8691–8694 (2000). 10.1103/PhysRevB.62.8691
P. I. Soininen and N. B. Kopnin, “Stability of superflow,” Phys. Rev. B 49, 12087–12094 (1994). 10.1103/PhysRevB.49.12087
B. Baelus and F. Peeters, “The effect of surface defects on the vortex expulsion and penetration in mesoscopic superconducting disks,” Phys. C 408–410, 543–544 (2004). 10.1016/j.physc.2004.03.206
T. D. Vu, H. T. Huy, A. Ito, M. Toji, H. Shishido, M. Kato, M. Hayashi, and T. Ishida, “Confined vortices in de facto mesoscopic Mo80Ge20 disks with sector defects,” Supercond. Sci. Technol. 31, 125009 (2018). 10.1088/1361-6668/aae506
T. D. Vu, H. T. Huy, A. Ito, M. Toji, H. Shishido, M. Kato, M. Hayashi, and T. Ishida, “Erratum: Confined vortices in de facto mesoscopic Mo80Ge20 disks with sector defects (2018 Supercond. Sci. Technol. 31 125009),” Supercond. Sci. Technol. 32, 019601 (2019). 10.1088/1361-6668/aaf0af
T. S. Alstrøm, M. P. Sørensen, N. F. Pedersen, and S. Madsen, “Magnetic flux lines in complex geometry type-II superconductors studied by the time dependent Ginzburg-Landau equation,” Acta Appl. Math. 115, 63–74 (2011). 10.1007/s10440-010-9580-8
Y. Kuroda, S. Hatsumi, Y. Ootuka, and A. Kanda, “Effect of surface defects on vortex penetration in small superconducting squares,” Phys. C: Supercond. Appl. 470, 1145–1147 (2010). 10.1016/j.physc.2010.05.059
A. R. Pack, J. Carlson, S. Wadsworth, and M. K. Transtrum, “Vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in two and three dimensions: Role of surface defects and material inhomogeneities,” Phys. Rev. B 101, 144504 (2020). 10.1103/PhysRevB.101.144504
J. Carlson, A. Pack, M. K. Transtrum, J. Lee, D. N. Seidman, D. B. Liarte, N. S. Sitaraman, A. Senanian, M. M. Kelley, J. P. Sethna, T. Arias, and S. Posen, “Analysis of magnetic vortex dissipation in Sn-segregated boundaries in Nb3Sn superconducting RF cavities,” Phys. Rev. B 103, 024516 (2021). 10.1103/PhysRevB.103.024516
A. Benfenati, A. Maiani, F. N. Rybakov, and E. Babaev, “Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory,” Phys. Rev. B 101, 220505 (2020). 10.1103/PhysRevB.101.220505
D. Y. Vodolazov, F. M. Peeters, S. V. Dubonos, and A. K. Geim, “Multiple flux jumps and irreversible behavior of thin al superconducting rings,” Phys. Rev. B 67, 054506 (2003). 10.1103/PhysRevB.67.054506
D. Y. Vodolazov and F. M. Peeters, “Superconducting rectifier based on the asymmetric surface barrier effect,” Phys. Rev. B 72, 172508 (2005). 10.1103/PhysRevB.72.172508
G. J. Kimmel, A. Glatz, V. M. Vinokur, and I. A. Sadovskyy, “Edge effect pinning in mesoscopic superconducting strips with non-uniform distribution of defects,” Sci. Rep. 9, 211 (2019). 10.1038/s41598-018-36285-4
L. Burlachkov, A. E. Koshelev, and V. M. Vinokur, “Transport properties of high-temperature superconductors: Surface vs bulk effect,” Phys. Rev. B 54, 6750–6757 (1996). 10.1103/PhysRevB.54.6750
A. K. Geim, I. V. Grigorieva, S. V. Dubonos, J. G. S. Lok, J. C. Maan, A. E. Filippov, and F. M. Peeters, “Phase transitions in individual sub-micrometre superconductors,” Nature 390, 259–262 (1997). 10.1038/36797
P. Singha Deo, V. A. Schweigert, and F. M. Peeters, “Hysteresis in mesoscopic superconducting disks: The Bean-Livingston barrier,” Phys. Rev. B 59, 6039–6042 (1999). 10.1103/PhysRevB.59.6039
P. S. Swartz and H. R. Hart, “Asymmetries of the critical surface current in type-II superconductors,” Phys. Rev. 156, 412–420 (1967). 10.1103/PhysRev.156.412
P. J. Moll, “Geometrical design of 3D superconducting diodes,” Commun. Mater. 6, 73 (2025). 10.1038/s43246-025-00788-1
C. A. Aguirre, J. Barba-Ortega, A. S. de Arruda, and J. Faundez, “Superconducting diode effect in a meso-wedge geometry with Abrikosov vortice,” unpublished (2025).
D. Y. Vodolazov, B. A. Gribkov, A. Y. Klimov, V. V. Rogov, and S. N. Vdovichev, “Strong influence of a magnetic layer on the critical current of Nb bridge in finite magnetic fields due to surface barrier effect,” Appl. Phys. Lett. 94, 012508 (2009). 10.1063/1.3030983
D. Cerbu, V. N. Gladilin, J. Cuppens, J. Fritzsche, J. Tempere, J. T. Devreese, V. V. Moshchalkov, A. V. Silhanek, and J. Van de Vondel, “Vortex ratchet induced by controlled edge roughness,” New J. Phys. 15, 063022 (2013). 10.1088/1367-2630/15/6/063022
S. S. Ustavschikov, M. Y. Levichev, I. Y. Pashenkin, N. S. Gusev, S. A. Gusev, and D. Y. Vodolazov, “Diode effect in a superconducting hybrid Cu/MoN strip with a lateral cut,” J. Exp. Theor. Phys. 135, 226–230 (2022). 10.1134/S1063776122080064
B. Budinská, B. Aichner, D. Y. Vodolazov, M. Y. Mikhailov, F. Porrati, M. Huth, A. Chumak, W. Lang, and O. Dobrovolskiy, “Rising speed limits for fluxons via edge-quality improvement in wide MoSi thin films,” Phys. Rev. Appl. 17, 034072 (2022). 10.1103/PhysRevApplied.17.034072
A. I. Bezuglyj, V. A. Shklovskij, B. Budinská, B. Aichner, V. M. Bevz, M. Y. Mikhailov, D. Y. Vodolazov, W. Lang, and O. V. Dobrovolskiy, “Vortex jets generated by edge defects in current-carrying superconductor thin strips,” Phys. Rev. B 105, 214507 (2022). 10.1103/PhysRevB.105.214507
V. Bevz, M. Mikhailov, B. Budinská, S. Lamb-Camarena, S. Shpilinska, A. Chumak, M. Urbánek, M. Arndt, W. Lang, and O. Dobrovolskiy, “Vortex counting and velocimetry for slitted superconducting thin strips,” Phys. Rev. Appl. 19, 034098 (2023). 10.1103/PhysRevApplied.19.034098
V. M. Bevz, B. Budinska, S. Lamb-Camarena, S. O. Shpilinska, C. Schmid, M. Y. Mikhailov, W. Lang, and O. V. Dobrovolskiy, “Vortex chains and vortex jets in MoSi microbridges,” Phys. Rapid Res. Lett. 17, 2200513 (2023). 10.1002/pssr.202200513
S. S. Ustavschikov, M. Y. Levichev, I. Y. Pashen'kin, N. S. Gusev, S. A. Gusev, and D. Y. Vodolazov, “Vortex dynamics in superconducting MoN strip with a side cut,” J. Exp. Theor. Phys. 137, 372–383 (2023). 10.1134/S1063776123090169
L. G. Aslamazov and A. I. Larkin, “Josephson effect in wide superconducting bridges,” Sov. J. Exp. Theor. Phys. 41, 381–386 (1975).
S. S. Ustavschikov, M. Y. Levichev, I. Y. Pashen'kin, N. S. Gusev, S. A. Gusev, and D. Y. Vodolazov, “Negative differential resistance and Shapiro steps in a superconducting MoN strip with a cut,” JETP Lett. 115, 626–633 (2022). 10.1134/S0021364022600641
C. Reichhardt, C. J. Olson, and F. Nori, “Dynamic phases of vortices in superconductors with periodic pinning,” Phys. Rev. Lett. 78, 2648–2651 (1997). 10.1103/PhysRevLett.78.2648
J. Gutierrez, A. V. Silhanek, J. Van de Vondel, W. Gillijns, and V. V. Moshchalkov, “Transition from turbulent to nearly laminar vortex flow in superconductors with periodic pinning,” Phys. Rev. B 80, 140514 (2009). 10.1103/PhysRevB.80.140514
J. Barba-Ortega, M. R. Joya, and E. Sardella, “Resistive state of a thin superconducting strip with an engineered central defect,” Eur. Phys. J. B 92, 143 (2019). 10.1140/epjb/e2019-100082-y
Y. Hou, F. Nichele, H. Chi, A. Lodesani, Y. Wu, M. F. Ritter, D. Z. Haxell, M. Davydova, S. Ilić, O. Glezakou-Elbert, A. Varambally, F. S. Bergeret, A. Kamra, L. Fu, P. A. Lee, and J. S. Moodera, “Ubiquitous superconducting diode effect in superconductor thin films,” Phys. Rev. Lett. 131, 027001 (2023). 10.1103/PhysRevLett.131.027001
L. R. Cadorim, E. Sardella, and C. C. d. S. Silva, “Harnessing the superconducting diode effect through inhomogeneous magnetic fields,” Phys. Rev. Appl. 21, 054040 (2024). 10.1103/PhysRevApplied.21.054040
M. Castellani, O. Medeiros, A. Buzzi, R. A. Foster, M. Colangelo, and K. K. Berggren, “A superconducting full-wave bridge rectifier,” arXiv:2406.12175 (2025).
J. Ingla-Aynés, Y. Hou, S. Wang, E.-D. Chu, O. A. Mukhanov, P. Wei, and J. S. Moodera, “Efficient superconducting diodes and rectifiers for quantum circuitry,” Nat. Electron. 8, 411 (2025). 10.1038/s41928-025-01375-5
V. Rouco, A. Palau, C. Monton, N. Del-Valle, C. Navau, A. Sanchez, X. Obradors, and T. Puig, “Geometrically controlled ratchet effect with collective vortex motion,” New J. Phys. 17, 073022 (2015). 10.1088/1367-2630/17/7/073022
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). 10.1038/s41467-021-23077-0
A. V. Silhanek, J. Van de Vondel, and V. V. Moshchalkov, “Guided vortex motion and vortex ratchets in nanostructured superconductors,” in Nanoscience and Engineering in Superconductivity, edited by V. Moshchalkov, R. Woerdenweber, and W. Lang (Springer, Berlin, Heidelberg, 2010), pp. 1–24.
Linear Collider Collaboration, “Progress report for the ILC” (2015), see https://newsline.linearcollider.org/2015/10/29/linear-collider-collaboration-published-progress-report-for-the-ilc/.
J.-M. Vogt, O. Kugeler, and J. Knobloch, “Impact of cool-down conditions at Tc on the superconducting rf cavity quality factor,” Phys. Rev. ST Accel. Beams 16, 102002 (2013). 10.1103/PhysRevSTAB.16.102002
J.-M. Vogt, O. Kugeler, and J. Knobloch, “High-q operation of superconducting rf cavities: Potential impact of thermocurrents on the rf surface resistance,” Phys. Rev. ST. Accel. Beams 18, 042001 (2015). 10.1103/PhysRevSTAB.18.042001
A. Romanenko, A. Grassellino, O. Melnychuk, and D. A. Sergatskov, “Dependence of the residual surface resistance of superconducting radio frequency cavities on the cooling dynamics around Tc,” J. Appl. Phys. 115, 184903 (2014). 10.1063/1.4875655
S. Posen, M. Checchin, A. C. Crawford, A. Grassellino, M. Martinello, O. S. Melnychuk, A. Romanenko, D. A. Sergatskov, and Y. Trenikhina, “Efficient expulsion of magnetic flux in superconducting radiofrequency cavities for high Q applications,” J. Appl. Phys. 119, 213903 (2016). 10.1063/1.4953087
N.-N. Li and A. He, “Effect of defects on flux expulsion of pure niobium superconducting radio frequency cavities via spatial temperature gradient,” Phys. C: Supercond. Appl. 615, 1354391 (2023). 10.1016/j.physc.2023.1354391
A. He and X.-N. Hu, “Achieving optimal magnetic flux expulsion of a Nb3Sn superconducting radio-frequency cavity via spatial temperature gradient,” Phys. Lett. A 487, 129129 (2023). 10.1016/j.physleta.2023.129129
D. Gonnella, J. Kaufman, and M. Liepe, “Impact of nitrogen doping of niobium superconducting cavities on the sensitivity of surface resistance to trapped magnetic flux,” J. Appl. Phys. 119, 073904 (2016). 10.1063/1.4941944
P. Dhakal, G. Ciovati, and A. Gurevich, “Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity,” Phys. Rev. Accel. Beams 23, 023102 (2020). 10.1103/PhysRevAccelBeams.23.023102
T. Kubo, Y. Iwashita, and T. Saeki, “Radio-frequency electromagnetic field and vortex penetration in multilayered superconductors,” Appl. Phys. Lett. 104, 032603 (2014). 10.1063/1.4862892
S. Posen, M. K. Transtrum, G. Catelani, M. U. Liepe, and J. P. Sethna, “Shielding superconductors with thin films as applied to rf cavities for particle accelerators,” Phys. Rev. Appl. 4, 044019 (2015). 10.1103/PhysRevApplied.4.044019
A. Gurevich, “Maximum screening fields of superconducting multilayer structures,” AIP Adv. 5, 017112 (2015). 10.1063/1.4905711
D. B. Liarte, M. K. Transtrum, and J. P. Sethna, “Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors,” Phys. Rev. B 94, 144504 (2016). 10.1103/PhysRevB.94.144504
D. B. Liarte, S. Posen, M. K. Transtrum, G. Catelani, M. Liepe, and J. P. Sethna, “Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: Stability theory, disorder, and laminates,” Supercond. Sci. Technol. 30, 033002 (2017). 10.1088/1361-6668/30/3/033002
T. Kubo, “Multilayer coating for higher accelerating fields in superconducting radio-frequency cavities: A review of theoretical aspects,” Supercond. Sci. Technol. 30, 023001 (2017). 10.1088/1361-6668/30/2/023001
V. Ngampruetikorn and J. A. Sauls, “Effect of inhomogeneous surface disorder on the superheating field of superconducting rf cavities,” Phys. Rev. Res. 1, 012015 (2019). 10.1103/PhysRevResearch.1.012015
Q.-Y. Wang, C. Xue, C. Dong, and Y.-H. Zhou, “Effects of defects and surface roughness on the vortex penetration and vortex dynamics in superconductor–insulator–superconductor multilayer structures exposed to rf magnetic fields: Numerical simulations within TDGL theory,” Supercond. Sci. Technol. 35, 045004 (2022). 10.1088/1361-6668/ac4ad1
A. Gurevich, T. Kubo, and J. A. Sauls, “Challenges and opportunities of SRF theory for next generation particle accelerators,” arXiv:2203.08315 (2022)
C. Xue, Q.-Y. Wang, H.-X. Ren, A. He, and A. V. Silhanek, “Case studies on time-dependent Ginzburg-Landau simulations for superconducting applications,” Electromag. Sci. 2, 1–20 (2024). 10.23919/emsci.2024.0012
A. Gurevich, “Enhancement of rf breakdown field of superconductors by multilayer coating,” Appl. Phys. Lett. 88, 012511 (2006). 10.1063/1.2162264
W. P. M. R. Pathirana and A. Gurevich, “Superheating field in superconductors with nanostructured surfaces,” Front. Electron. Mater. 3, 1246016 (2023). 10.3389/femat.2023.1246016
M. Asaduzzaman, R. M. L. McFadden, E. Thoeng, R. E. Laxdal, and T. Junginger, “Measurements of the first-flux-penetration field in surface-treated and coated Nb: Distinguishing between near-surface pinning and an interface energy barrier,” Supercond. Sci. Technol. 37, 085006 (2024). 10.1088/1361-6668/ad54f3
R. Porter, D. Hall, M. Liepe, and J. Maniscalco, “Surface roughness effect on the performance of Nb3Sn cavities,” in Proceedings of the Linear Accelerator Conference (LINAC'16), East Lansing, MI, USA, 25–30 September 2016, Linear Accelerator Conference No. 28 (JACoW, Geneva, Switzerland, 2017), pp. 129–132,.
H. Padamsee and V. Shemelin, DESY, “Magnetic field enhancement at pits and bumps on the surface of superconducting cavities,” TTC-Reports, TESLA 2008 SRF 080903-04, 2008.
T. Kubo, “Magnetic field enhancement at a pit on the surface of a superconducting accelerating cavity,” Prog. Theor. Exp. Phys. 2015, 073G01. 10.1093/ptep/ptv088
M. L. Y. Xie and G. H. Hoffstaetter, “Quench and high field Q-SLOP studies using a single cell cavity with artificial pits,” in Proceedings of the IPAC2013, Shanghai, China (JACoW, 2013) pp. 2465–2467.
Y. A. Genenko, H. Rauh, and S. V. Yampolskii, “The Bean–Livingston barrier at a superconductor/magnet interface,” J. Phys.: Condens. Matter 17, L93 (2005). 10.1088/0953-8984/17/10/L02
B. Oripov, T. Bieler, G. Ciovati, S. Calatroni, P. Dhakal, T. Junginger, O. B. Malyshev, G. Terenziani, A.-M. Valente-Feliciano, R. Valizadeh, S. Wilde, and S. M. Anlage, “High-frequency nonlinear response of superconducting cavity-grade Nb surfaces,” Phys. Rev. Appl. 11, 064030 (2019). 10.1103/PhysRevApplied.11.064030
S. Posen and D. L. Hall, “Nb3Sn superconducting radiofrequency cavities: Fabrication, results, properties, and prospects,” Supercond. Sci. Technol. 30, 033004 (2017). 10.1088/1361-6668/30/3/033004
T. Behnke, J. E. Brau, P. N. Burrows, J. Fuster, M. Peskin, M. Stanitzki, Y. Sugimoto, S. Yamada, and H. Yamamoto, “The international linear collider technical design report—Volume 4: Detectors,” arXiv:1306.6329 (2013).
A. Sheikhzada and A. Gurevich, “Dynamic pair-breaking current, critical superfluid velocity, and nonlinear electromagnetic response of nonequilibrium superconductors,” Phys. Rev. B 102, 104507 (2020). 10.1103/PhysRevB.102.104507
S. Posen, N. Valles, and M. Liepe, “Radio frequency magnetic field limits of Nb and Nb3Sn,” Phys. Rev. Lett. 115, 047001 (2015). 10.1103/PhysRevLett.115.047001
C. P. Bean, “Magnetization of hard superconductors,” Phys. Rev. Lett. 8, 250–253 (1962). 10.1103/PhysRevLett.8.250
A. M. Campbell and J. E. Evetts, “Flux vortices and transport currents in type II superconductors,” Adv. Phys. 21, 199–428 (1972). 10.1080/00018737200101288
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, 3443–3452 (1994). 10.1103/PhysRevB.49.3443
L. Prigozhin, “Solution of thin film magnetization problems in type-II superconductivity,” J. Comput. Phys. 144, 180–193 (1998). 10.1006/jcph.1998.5978
J. Brisbois, O.-A. Adami, J. I. Avila, M. Motta, W. A. Ortiz, N. D. Nguyen, P. Vanderbemden, B. Vanderheyden, R. B. G. Kramer, and A. V. Silhanek, “Magnetic flux penetration in Nb superconducting films with lithographically defined microindentations,” Phys. Rev. B 93, 054521 (2016). 10.1103/PhysRevB.93.054521
T. Schuster, H. Kuhn, and E. H. Brandt, “Flux penetration into flat superconductors of arbitrary shape: Patterns of magnetic and electric fields and current,” Phys. Rev. B 54, 3514–3524 (1996). 10.1103/PhysRevB.54.3514
C. Jooss, R. Warthmann, A. Forkl, and H. Kronmüller, “High-resolution magneto-optical imaging of critical currents in YBa2Cu3O7 thin films,” Phys. C 299, 215–230 (1998). 10.1016/S0921-4534(97)01887-X
S. B. Alvarez, “Thermally and dynamically driven magnetic flux penetration in type-II superconductors,” Ph.D. thesis, Université de Liège, 2020. https://www.epnm.uliege.be/cms/c_13456803/en/epnm-theses
G. P. Lousberg, M. Ausloos, P. Vanderbemden, and B. Vanderheyden, “Bulk high-Tc superconductors with drilled holes: How to arrange the holes to maximize the trapped magnetic flux?,” Supercond. Sci. Technol. 21, 025010 (2008). 10.1088/0953-2048/21/02/025010
T. Schuster, H. Kuhn, E. H. Brandt, M. V. Indenbom, M. Kläser, G. Müller-Vogt, H.-U. Habermeier, H. Kronmüller, and A. Forkl, “Current and field pattern in rectangular and inhomogeneous superconductors,” Phys. Rev. B 52, 10375–10389 (1995). 10.1103/PhysRevB.52.10375
M. Welling, C. Aegerter, R. Westerwaal, S. Enache, R. Wijngaarden, and R. Griessen, “Effect of hydrogen uptake and substrate orientation on the flux penetration in NbHx thin films,” Phys. C 406, 100–106 (2004). 10.1016/j.physc.2004.03.236
M. Solovyov, E. Pardo, J. Šouc, F. Gömöry, M. Skarba, P. Konopka, M. Pekarčíková, and J. Janovec, “Non-uniformity of coated conductor tapes,” Supercond. Sci. Technol. 26, 115013 (2013). 10.1088/0953-2048/26/11/115013
J. Albrecht, A. T. Matveev, J. Strempfer, H.-U. Habermeier, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Dramatic role of critical current anisotropy on flux avalanches in MgB2 films,” Phys. Rev. Lett. 98, 117001 (2007). 10.1103/PhysRevLett.98.117001
S. Treiber and J. Albrecht, “The formation and propagation of flux avalanches in tailored MgB2 films,” New J. Phys. 12, 093043 (2010). 10.1088/1367-2630/12/9/093043
S. Treiber, C. Stahl, G. Schütz, and J. Albrecht, “Stability of the current-carrying state in nonhomogeneous MgB2 films,” Phys. Rev. B 84, 094533 (2011). 10.1103/PhysRevB.84.094533
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). 10.1088/0953-2048/29/10/105001
Y. Lu, Z. Jing, H. Yong, and Y. Zhou, “Flux avalanche in a superconducting film with non-uniform critical current density,” Proc. R. Soc. A 472, 20160469 (2016). 10.1098/rspa.2016.0469
L. B. L. G. Pinheiro, L. Jiang, E. A. Abbey, D. A. D. Chaves, A. J. Chiquito, T. H. Johansen, J. Van de Vondel, C. Xue, Y.-H. Zhou, A. V. Silhanek, W. A. Ortiz, and M. Motta, “Magnetic flux penetration in nanoscale wedge-shaped superconducting thin films,” Phys. Rev. B 106, 224520 (2022). 10.1103/PhysRevB.106.224520
I. S. Aranson, A. Gurevich, M. S. Welling, R. J. Wijngaarden, V. K. Vlasko-Vlasov, V. M. Vinokur, and U. Welp, “Dendritic flux avalanches and nonlocal electrodynamics in thin superconducting films,” Phys. Rev. Lett. 94, 037002 (2005). 10.1103/PhysRevLett.94.037002
A. Gurevich and J. McDonald, “Nonlinear current flow around defects in superconductors,” Phys. Rev. Lett. 81, 2546–2549 (1998). 10.1103/PhysRevLett.81.2546
A. Gurevich, “Electromagnetic instabilities and current structures in anisotropic superconductors,” Phys. Rev. B 46, 3638–3656 (1992). 10.1103/PhysRevB.46.3638
M. Friesen and A. Gurevich, “Nonlinear current flow in superconductors with restricted geometries,” Phys. Rev. B 63, 064521 (2001). 10.1103/PhysRevB.63.064521
J. I. Vestgården, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Flux penetration in a superconducting strip with an edge indentation,” Phys. Rev. B 76, 174509 (2007). 10.1103/PhysRevB.76.174509
J. Eisenmenger, P. Leiderer, M. Wallenhorst, and H. Dötsch, “Influence of microscopic defects in type-II superconducting thin films on the magnetic flux penetration,” Phys. Rev. B 64, 104503 (2001). 10.1103/PhysRevB.64.104503
J. I. Vestgården, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Flux distribution in superconducting films with holes,” Phys. Rev. B 77, 014521 (2008). 10.1103/PhysRevB.77.014521
M. Geahel, I. Jouanny, D. Gorse-Pomonti, M. Poirier-Quinot, J. Briatico, and C. J. Van der Beek, “Edge contamination, bulk disorder, flux front roughening, and multiscaling in type II superconducting thin films,” Condens. Matter 2, 27 (2017). 10.3390/condmat2030027
J. Duron, F. Grilli, B. Dutoit, and S. Stavrev, “Modelling the e–j relation of high-Tc superconductors in an arbitrary current range,” Phys. C 401, 231–235 (2004). 10.1016/j.physc.2003.09.044
A. Morandi, “2D electromagnetic modelling of superconductors,” Supercond. Sci. Technol. 25, 104003 (2012). 10.1088/0953-2048/25/10/104003
F. Sirois, F. Grilli, and A. Morandi, “Comparison of constitutive laws for modeling high-temperature superconductors,” IEEE Trans. Appl. Supercond. 29, 1–10 (2019). 10.1109/TASC.2018.2848219
H. Ruiz, J. Hänisch, M. Polichetti, A. Galluzzi, L. Gozzelino, D. Torsello, S. Milošević-Govedarović, J. Grbović-Novaković, O. Dobrovolskiy, W. Lang, G. Grimaldi, A. Crisan, P. Badica, A. Ionescu, P. Cayado, R. Willa, B. Barbiellini, S. Eley, and A. Badía–Majós, “Critical current density in advanced superconductors,” Prog. Mater. Sci. 155, 101492 (2026). 10.1016/j.pmatsci.2025.101492
Z. W. Zhao, S. L. Li, Y. M. Ni, H. P. Yang, Z. Y. Liu, H. H. Wen, W. N. Kang, H. J. Kim, E. M. Choi, and S. I. Lee, “Suppression of superconducting critical current density by small flux jumps in MgB2 thin films,” Phys. Rev. B 65, 064512 (2002). 10.1103/PhysRevB.65.064512
A. A. F. Olsen, T. H. Johansen, D. Shantsev, E.-M. Choi, H.-S. Lee, H. J. Kim, and S.-I. Lee, “Avalanches injecting flux into the central hole of a superconducting MgB2 ring,” Phys. Rev. B 76, 024510 (2007). 10.1103/PhysRevB.76.024510
V. Chabanenko, A. Nabiałek, and R. Puźniak, “Multi-steps magnetic flux entrance/exit at thermomagnetic avalanches in the plates of hard superconductors,” Materials 15, 2037 (2022). 10.3390/ma15062037
E.-M. Choi, H.-S. Lee, J. Y. Lee, S.-I. Lee, A. A. F. Olsen, V. V. Yurchenko, D. V. Shantsev, T. H. Johansen, H.-J. Kim, and M.-H. Cho, “Width-dependent upper threshold field for flux noise in MgB2 strips,” Appl. Phys. Lett. 91, 042507 (2007). 10.1063/1.2760141
Z. Jing, H. Yong, and Y.-H. Zhou, “Dendritic flux avalanches and the accompanied thermal strain in type-II superconducting films: Effect of magnetic field ramp rate,” Supercond. Sci. Technol. 28, 075012 (2015). 10.1088/0953-2048/28/7/075012
M. Baziljevich, E. Baruch-El, T. H. Johansen, and Y. Yeshurun, “Dendritic instability in YBa2Cu3O7 films triggered by transient magnetic fields,” Appl. Phys. Lett. 105, 012602 (2014). 10.1063/1.4887374
M. Shinden, H. Fujishiro, K. Takahashi, and M. D. Ainslie, “Possibility of mechanical fracture of superconducting ring bulks due to thermal stress induced by local heat generation during pulsed-field magnetization,” Supercond. Sci. Technol. 35, 045015 (2022). 10.1088/1361-6668/ac5785
H. Mochizuki, H. Fujishiro, T. Naito, Y. Itoh, Y. Yanagi, and T. Nakamura, “Trapped field characteristics and fracture behavior of REBaCuO bulk ring during pulsed field magnetization,” IEEE Trans. Appl. Supercond. 26, 1–5 (2016). 10.1109/TASC.2015.2513415
S. L. Wipf, “Magnetic instabilities in type-II superconductors,” Phys. Rev. 161, 404–416 (1967). 10.1103/PhysRev.161.404
R. G. Mints and A. L. Rakhmanov, “Critical state stability in type-II superconductors and superconducting-normal-metal composites,” Rev. Mod. Phys. 53, 551–592 (1981). 10.1103/RevModPhys.53.551
V. V. Chabanenko, A. I. D'yachenko, M. V. Zalutskii, V. F. Rusakov, H. Szymczak, S. Piechota, and A. Nabialek, “Magnetothermal instabilities in type II superconductors: The influence of magnetic irreversibility,” J. Appl. Phys. 88, 5875–5883 (2000). 10.1063/1.1314611
E. Altshuler and T. H. Johansen, “Colloquium: Experiments in vortex avalanches,” Rev. Mod. Phys. 76, 471–487 (2004). 10.1103/RevModPhys.76.471
K. Chen, S. W. Hsu, T. L. Chen, S. D. Lan, W. H. Lee, and P. T. Wu, “High transport critical currents and flux jumps in bulk YBa2Cu3Ox superconductors,” Appl. Phys. Lett. 56, 2675–2677 (1990). 10.1063/1.103267
S. Wipf, “Review of stability in high temperature superconductors with emphasis on flux jumping,” Cryogenics 31, 936–948 (1991). 10.1016/0011-2275(91)90217-K
A. L. Rakhmanov, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Finger patterns produced by thermomagnetic instability in superconductors,” Phys. Rev. B 70, 224502 (2004). 10.1103/PhysRevB.70.224502
Y. Kimishima, S. Takami, T. Okuda, M. Uehara, T. Kuramoto, and Y. Sugiyama, “Complete flux jump in bulk MgB2 sintered under high pressure,” Phys. C: Supercond. Appl. 463–465, 281–285 (2007). 10.1016/j.physc.2007.03.492
C. Xue, H.-X. Ren, P. Jia, Q.-Y. Wang, W. Liu, X.-J. Ou, L.-T. Sun, and A. V. Silhanek, “Holistic numerical simulation of a quenching process on a real-size multifilamentary superconducting coil,” Nat. Commun. 15, 10454 (2024). 10.1038/s41467-024-54406-8
J. I. Vestgården, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Lightning in superconductors,” Sci. Rep. 2, 886 (2012). 10.1038/srep00886
C. A. Durán, P. L. Gammel, R. E. Miller, and D. J. Bishop, “Observation of magnetic-field penetration via dendritic growth in superconducting niobium films,” Phys. Rev. B 52, 75–78 (1995). 10.1103/PhysRevB.52.75
S. Blanco Alvarez, J. Brisbois, S. Melinte, R. B. G. Kramer, and A. V. Silhanek, “Statistics of thermomagnetic breakdown in Nb superconducting films,” Sci. Rep. 9, 3659 (2019). 10.1038/s41598-019-39337-5
J. Albrecht, A. T. Matveev, M. Djupmyr, G. Schütz, B. Stuhlhofer, and H.-U. Habermeier, “Bending of magnetic avalanches in MgB2 thin films,” Appl. Phys. Lett. 87, 182501 (2005). 10.1063/1.2123395
T. H. Johansen, M. Baziljevich, D. V. Shantsev, P. E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M.-S. Kim, and S. I. Lee, “Dendritic flux patterns in MgB2 films,” Supercond. Sci. Technol. 14, 726 (2001). 10.1088/0953-2048/14/9/319
I. A. Rudnev, D. V. Shantsev, T. H. Johansen, and A. E. Primenko, “Avalanche-driven fractal flux distributions in NbN superconducting films,” Appl. Phys. Lett. 87, 042502 (2005). 10.1063/1.1992673
F. Colauto, M. Motta, A. Palau, M. G. Blamire, T. H. Johansen, and W. A. Ortiz, “First observation of flux avalanches in a-MoSi superconducting thin films,” IEEE Trans. Appl. Supercond. 25, 1–4 (2015). 10.1109/TASC.2014.2376183
P. Leiderer, J. Boneberg, P. Brüll, V. Bujok, and S. Herminghaus, “Nucleation and growth of a flux instability in superconducting YBa2Cu3O7−x films,” Phys. Rev. Lett. 71, 2646–2649 (1993). 10.1103/PhysRevLett.71.2646
U. Bolz, J. Eisenmenger, J. Schiessling, B.-U. Runge, and P. Leiderer, “Magnetic instability in YBa2Cu3O7 films,” Phys. B 284–288, 757–758 (2000). 10.1016/S0921-4526(99)02060-8
I. Rudnev, S. Antonenko, D. Shantsev, T. Johansen, and A. Primenko, “Dendritic flux avalanches in superconducting nb3sn films,” Cryogenics 43, 663–666 (2003). 10.1016/S0011-2275(03)00157-7
L. B. L. G. Pinheiro, M. Motta, F. Colauto, T. H. Johansen, E. Bellingeri, C. Bernini, C. Ferdeghini, and W. A. Ortiz, “Imaging flux avalanches in V3Si superconducting thin films,” IEEE Trans. Appl. Supercond. 29, 1–4 (2019). 10.1109/TASC.2019.2902788
G. J. Dolan, “Direct observations of the magnetic structure in thin films of Pb, Sn, and In,” J. Low Temp. Phys. 15, 111–132 (1974). 10.1007/BF00655630
M. Menghini, R. J. Wijngaarden, A. V. Silhanek, S. Raedts, and V. V. Moshchalkov, “Dendritic flux penetration in Pb films with a periodic array of antidots,” Phys. Rev. B 71, 104506 (2005). 10.1103/PhysRevB.71.104506
M. Motta, A. Silhanek, and W. Ortiz, “Magnetic flux avalanches in superconducting films with mesoscopic artificial patterns,” in The Oxford Handbook of Small Superconductors (Oxford University Press, 2017), see https://academic.oup.com/book/0/chapter/355851520/chapter-ag-pdf/44416276/book_42055_section_355851520.ag.pdf.
F. Colauto, M. Motta, and W. A. Ortiz, “Controlling magnetic flux penetration in low-TC superconducting films and hybrids,” Supercond. Sci. Technol. 34, 013002 (2021). 10.1088/1361-6668/abac1e
H. Lee, S. Jeon, B. Friedman, and K. Lee, “Simultaneous imaging of magnetic field and temperature distributions by magneto optical indicator microscopy,” Sci. Rep. 7, 43804 (2017). 10.1038/srep43804
U. Bolz, B. Biehler, D. Schmidt, B.-U. Runge, and P. Leiderer, “Dynamics of the dendritic flux instability in YBa2Cu3O7 films,” Europhys. Lett. 64, 517 (2003). 10.1209/epl/i2003-00261-y
G. Ghigo, F. Laviano, L. Gozzelino, R. Gerbaldo, E. Mezzetti, E. Monticone, and C. Portesi, “Evidence of rf-driven dendritic vortex avalanches in MgB2 microwave resonators,” J. Appl. Phys. 102, 113901 (2007). 10.1063/1.2816257
A. A. Awad, F. G. Aliev, G. W. Ataklti, A. Silhanek, V. V. Moshchalkov, Y. M. Galperin, and V. Vinokur, “Flux avalanches triggered by microwave depinning of magnetic vortices in Pb superconducting films,” Phys. Rev. B 84, 224511 (2011). 10.1103/PhysRevB.84.224511
A. Lara, F. G. Aliev, V. V. Moshchalkov, and Y. M. Galperin, “Thermally driven inhibition of superconducting vortex avalanches,” Phys. Rev. Appl. 8, 034027 (2017). 10.1103/PhysRevApplied.8.034027
Y.-H. Zhou, C. Wang, C. Liu, H. Yong, and X. Zhang, “Optically triggered chaotic vortex avalanches in superconducting YBa2Cu3O7−x films,” Phys. Rev. Appl. 13, 024036 (2020). 10.1103/PhysRevApplied.13.024036
M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83, 083707 (2012). 10.1063/1.4746255
P. Mikheenko, A. J. Qviller, J. I. Vestgården, S. Chaudhuri, I. J. Maasilta, Y. M. Galperin, and T. H. Johansen, “Nanosecond voltage pulses from dendritic flux avalanches in superconducting NbN films,” Appl. Phys. Lett. 102, 022601 (2013). 10.1063/1.4775693
J. I. Vestgården, Y. M. Galperin, and T. H. Johansen, “The thermomagnetic instability in superconducting films with adjacent metal layer,” J. Low Temp. Phys. 173, 303–326 (2013). 10.1007/s10909-013-0899-1
D. V. Denisov, D. V. Shantsev, Y. M. Galperin, E.-M. Choi, H.-S. Lee, S.-I. Lee, A. V. Bobyl, P. E. Goa, A. A. F. Olsen, and T. H. Johansen, “Onset of dendritic flux avalanches in superconducting films,” Phys. Rev. Lett. 97, 077002 (2006). 10.1103/PhysRevLett.97.077002
D. V. Denisov, A. L. Rakhmanov, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, “Dendritic and uniform flux jumps in superconducting films,” Phys. Rev. B 73, 014512 (2006). 10.1103/PhysRevB.73.014512
J. I. Vestgården, T. H. Johansen, and Y. M. Galperin, “Nucleation and propagation of thermomagnetic avalanches in thin-film superconductors (review article),” Low Temp. Phys. 44, 460–476 (2018). 10.1063/1.5037549
M. Baziljevich, A. Bobyl, D. Shantsev, E. Altshuler, T. Johansen, and S. Lee, “Origin of dendritic flux patterns in MgB2 films,” Phys. C 369, 93–96 (2002). 10.1016/S0921-4534(01)01226-6
F. Colauto, E. Choi, J. Y. Lee, S. I. Lee, E. J. Patiño, M. G. Blamire, T. H. Johansen, and W. A. Ortiz, “Suppression of flux avalanches in superconducting films by electromagnetic braking,” Appl. Phys. Lett. 96, 092512 (2010). 10.1063/1.3350681
C. Stahl, S. Treiber, G. Schütz, and J. Albrecht, “The avalanche process in gold covered MgB2 films,” Supercond. Sci. Technol. 26, 015007 (2013). 10.1088/0953-2048/26/1/015007
J. Brisbois, V. N. Gladilin, J. Tempere, J. T. Devreese, V. V. Moshchalkov, F. Colauto, M. Motta, T. H. Johansen, J. Fritzsche, O.-A. Adami, N. D. Nguyen, W. A. Ortiz, R. B. G. Kramer, and A. V. Silhanek, “Flux penetration in a superconducting film partially capped with a conducting layer,” Phys. Rev. B 95, 094506 (2017). 10.1103/PhysRevB.95.094506
D. G. Gheorghe, M. Menghini, R. J. Wijngaarden, S. Raedts, A. V. Silhanek, and V. V. Moshchalkov, “Anisotropic avalanches and flux penetration in patterned superconductors,” Phys. C: Supercond. Appl. 437–438, 69–72 (2006). 10.1016/j.physc.2005.12.021
F. Colauto, J. I. Vestgården, A. M. H. d. Andrade, A. A. M. Oliveira, W. A. Ortiz, and T. H. Johansen, “Limiting thermomagnetic avalanches in superconducting films by stop-holes,” Appl. Phys. Lett. 103, 032604 (2013). 10.1063/1.4813908
V. K. Vlasko-Vlasov, F. Colauto, T. Benseman, D. Rosenmann, and W.-K. Kwok, “Guiding thermomagnetic avalanches with soft magnetic stripes,” Phys. Rev. B 96, 214510 (2017). 10.1103/PhysRevB.96.214510
V. K. Vlasko-Vlasov, F. Colauto, A. A. Buzdin, D. Carmo, A. M. H. Andrade, A. A. M. Oliveira, W. A. Ortiz, D. Rosenmann, and W.-K. Kwok, “Crossing fields in thin films of isotropic superconductors,” Phys. Rev. B 94, 184502 (2016). 10.1103/PhysRevB.94.184502
F. Colauto, D. Carmo, A. M. H. de Andrade, A. A. M. Oliveira, W. A. Ortiz, and T. H. Johansen, “Anisotropic thermomagnetic avalanche activity in field-cooled superconducting films,” Phys. Rev. B 96, 060506 (2017). 10.1103/PhysRevB.96.060506
D. Carmo, F. Colauto, A. M. H. d. Andrade, A. A. M. Oliveira, W. A. Ortiz, Y. M. Galperin, and T. H. Johansen, “Active control of thermomagnetic avalanches in superconducting Nb films with tunable anisotropy,” Supercond. Sci. Technol. 31, 115009 (2018). 10.1088/1361-6668/aadffa
G. Ghigo, R. Gerbaldo, L. Gozzelino, F. Laviano, G. Lopardo, E. Monticone, C. Portesi, and E. Mezzetti, “Local thermal bistability in MgB2 microwave coplanar resonators: Opposite jumpwise response to weak-link switching and to vortex avalanches,” Appl. Phys. Lett. 94, 052505 (2009). 10.1063/1.3079335
P. d J. Cuadra-Solís, J. M. Hernández, A. García-Santiago, J. Tejada, J. Noskovic, A. Pidik, and M. Grajcar, “Vortex avalanches induced by single high-frequency pulses in MgB2 films,” J. Supercond. Novel Magn. 24, 395–400 (2011). 10.1007/s10948-010-0946-y
E. H. Brandt, “Electric field in superconductors with rectangular cross section,” Phys. Rev. B 52, 15442–15457 (1995). 10.1103/PhysRevB.52.15442
C. Jooss, J. Albrecht, H. Kuhn, S. Leonhardt, and H. Kronmüller, “Magneto-optical studies of current distributions in high-Tc superconductors,” Rep. Prog. Phys. 65, 651 (2002). 10.1088/0034-4885/65/5/202
A. Gurevich, “Thermal instability near planar defects in superconductors,” Appl. Phys. Lett. 78, 1891–1893 (2001). 10.1063/1.1358361
R. G. Mints and E. H. Brandt, “Flux jumping in thin films,” Phys. Rev. B 54, 12421–12426 (1996). 10.1103/PhysRevB.54.12421
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). 10.1103/PhysRevB.101.224505
Z. Jing, “Effects of edge cracks on the thermomagnetic instabilities of type-II superconducting thin films,” Natl. Sci. Rev. 10, nwad052 (2023). 10.1093/nsr/nwad052
M. Timmermans, T. Samuely, B. Raes, J. Van de Vondel, and V. V. Moshchalkov, “Dynamic visualization of nanoscale vortex orbits,” ACS Nano 8, 2782–2787 (2014). 10.1021/nn4065007
L. Embon, Y. Anahory, A. Suhov, D. Halbertal, J. Cuppens, A. Yakovenko, A. Uri, Y. Myasoedov, M. L. Rappaport, M. E. Huber, A. Gurevich, and E. Zeldov, “Probing dynamics and pinning of single vortices in superconductors at nanometer scales,” Sci. Rep. 5, 7598 (2015). 10.1038/srep07598
L. Thiel, D. Rohner, M. Ganzhorn, P. Appel, E. Neu, B. Müller, R. Kleiner, D. Koelle, and P. Maletinsky, “Quantitative nanoscale vortex imaging using a cryogenic quantum magnetometer,” Nat. Nanotechnol. 11, 677–681 (2016). 10.1038/nnano.2016.63
I. S. Veshchunov, W. Magrini, S. V. Mironov, A. G. Godin, J.-B. Trebbia, A. I. Buzdin, P. Tamarat, and B. Lounis, “Optical manipulation of single flux quanta,” Nat. Commun. 7, 12801 (2016). 10.1038/ncomms12801
R. A. Hovhannisyan, S. Y. Grebenchuk, S. A. Larionov, A. G. Shishkin, A. K. Grebenko, N. E. Kupchinskaya, E. A. Dobrovolskaya, O. V. Skryabina, A. Y. Aladyshkin, V. V. Dremov, I. A. Golovchanskiy, A. V. Samokhvalov, A. S. Mel'nikov, D. Roditchev, and V. S. Stolyarov, “Scanning vortex microscopy reveals thickness-dependent pinning nano-network in superconducting niobium films,” Commun. Mater. 6, 42 (2025). 10.1038/s43246-025-00759-6
J. Parisi, B. Mühlemeier, R. P. Huebener, and W. Buck, “Combined time-resolved magnetooptical and electrical flux detection in thin-film superconductors,” J. Low Temp. Phys. 60, 45–56 (1985). 10.1007/BF00681652
G. De Simoni, F. Paolucci, P. Solinas, E. Strambini, and F. Giazotto, “Metallic supercurrent field-effect transistor,” Nat. Nanotechnol. 13, 802–805 (2018). 10.1038/s41565-018-0190-3
I. Golokolenov, A. Guthrie, S. Kafanov, Y. A. Pashkin, and V. Tsepelin, “On the origin of the controversial electrostatic field effect in superconductors,” Nat. Commun. 12, 2747 (2021). 10.1038/s41467-021-22998-0
C. H. Ahn, A. Bhattacharya, M. Di Ventra, J. N. Eckstein, C. D. Frisbie, M. E. Gershenson, A. M. Goldman, I. H. Inoue, J. Mannhart, A. J. Millis, A. F. Morpurgo, D. Natelson, and J.-M. Triscone, “Electrostatic modification of novel materials,” Rev. Mod. Phys. 78, 1185–1212 (2006). 10.1103/RevModPhys.78.1185
A. Palau, A. Fernandez-Rodriguez, J. C. Gonzalez-Rosillo, X. Granados, M. Coll, B. Bozzo, R. Ortega-Hernandez, J. Suñé, N. Mestres, X. Obradors, and T. Puig, “Electrochemical tuning of metal insulator transition and nonvolatile resistive switching in superconducting films,” ACS Appl. Mater. Interfaces 10, 30522–30531 (2018). 10.1021/acsami.8b08042
A. Patel, K. Filar, V. I. Nizhankovskii, S. C. Hopkins, and B. A. Glowacki, “Trapped fields greater than 7 t in a 12mm square stack of commercial high-temperature superconducting tape,” Appl. Phys. Lett. 102, 102601 (2013). 10.1063/1.4795016
M. Pekarčíková, L. Frolek, M. Necpal, E. Cuninková, M. Skarba, S. Hulačová, F. Ferenčík, and B. Bočáková, “Optimization of REBCO tapes through division and striation for use in superconducting cables with low ac losses,” Materials 16, 7333 (2023). 10.3390/ma16237333
M. Marchevsky, E. Zhang, Y. Xie, V. Selvamanickam, and P. G. Ganesan, “AC losses and magnetic coupling in multifilamentary 2G HTS conductors and tape arrays,” IEEE Trans. Appl. Supercond. 19, 3094–3097 (2009). 10.1109/TASC.2009.2017724
R. Nast, M. Vojenčiak, E. Demencik, A. Kario, B. Ringsdorf, A. Jung, B. Runtsch, F. Grilli, and W. Goldacker, “Influence of laser striations on the properties of coated conductors,” J. Phys.: Conf. Ser. 507, 022023 (2014). 10.1088/1742-6596/507/2/022023
S. Terzieva, M. Vojenčiak, F. Grilli, R. Nast, J. Šouc, W. Goldacker, A. Jung, A. Kudymow, and A. Kling, “Investigation of the effect of striated strands on the ac losses of 2G Roebel cables,” Supercond. Sci. Technol. 24, 045001 (2011). 10.1088/0953-2048/24/4/045001
M. D. Sumption, E. W. Collings, and P. N. Barnes, “AC loss in striped (filamentary) YBCO coated conductors leading to designs for high frequencies and field-sweep amplitudes,” Supercond. Sci. Technol. 18, 122 (2005). 10.1088/0953-2048/18/1/020
T. Machi, K. Nakao, T. Kato, T. Hirayama, and K. Tanabe, “Reliable fabrication process for long-length multi-filamentary coated conductors by a laser scribing method for reduction of ac loss,” Supercond. Sci. Technol. 26, 105016 (2013). 10.1088/0953-2048/26/10/105016
K. Suzuki, M. Yoshizumi, T. Izumi, Y. Shiohara, M. Iwakuma, A. Ibi, S. Miyata, and Y. Yamada, “Development of scribing process of coated conductors for reduction of ac losses,” Phys. C: Supercond. 468 468, 1579–1582 (2008). 10.1016/j.physc.2008.05.076
W. N. Hartnett, J. Ramirez, T. E. R. Olson, C. T. Hopp, M. C. Jewell, A. R. Knoll, D. W. Hazelton, and Y. Zhang, “Characterization of edge damage induced on REBCO superconducting tape by mechanical slitting,” Eng. Res. Express 3, 035007 (2021). 10.1088/2631-8695/ac0fc3
H. Song, F. Hunte, and J. Schwartz, “On the role of pre-existing defects and magnetic flux avalanches in the degradation of YBa2Cu3O7–x coated conductors by quenching,” Acta Mater. 60, 6991–7000 (2012). 10.1016/j.actamat.2012.09.003
P. Gao, Y. Zhang, X. Wang, and Y. Zhou, “Interface properties and failures of REBCO coated conductor tapes: Research progress and challenges,” Superconductivity 8, 100068 (2023). 10.1016/j.supcon.2023.100068
E. Pehlivan and G. A. Niklasson, “Fractal dimensions of niobium oxide films probed by protons and lithium ions,” J. Appl. Phys. 100, 053506 (2006). 10.1063/1.2337164
C. Xu, H. Tian, C. E. Reece, and M. J. Kelley, “Enhanced characterization of niobium surface topography,” Phys. Rev. Spec. Top. Accel. Beams 14, 123501 (2011). 10.1103/PhysRevSTAB.14.123501
W. M. Roach, J. R. Skuza, D. B. Beringer, Z. Li, C. Clavero, and R. A. Lukaszew, “NbN thin films for superconducting radio frequency cavities,” Supercond. Sci. Technol. 25, 125016 (2012). 10.1088/0953-2048/25/12/125016
D. Carmo, F. Colauto, A. M. H. de Andrade, A. A. M. Oliveira, W. A. Ortiz, and T. H. Johansen, “Controllable injector for local flux entry into superconducting films,” Supercond. Sci. Technol. 29, 095003 (2016). 10.1088/0953-2048/29/9/095003
A. Y. Aladyshkin, G. W. Ataklti, W. Gillijns, I. M. Nefedov, I. A. Shereshevsky, A. V. Silhanek, J. Van de Vondel, M. Kemmler, R. Kleiner, D. Koelle, and V. V. Moshchalkov, “Mesoscopic cross-film cryotrons: Vortex trapping and dc-Josephson-like oscillations of the critical current,” Phys. Rev. B 83, 144509 (2011). 10.1103/PhysRevB.83.144509
G. W. Ataklti, A. Y. Aladyshkin, W. Gillijns, I. M. Nefedov, J. Van de Vondel, A. V. Silhanek, M. Kemmler, R. Kleiner, D. Koelle, and V. V. Moshchalkov, “Localization of superconductivity in superconductor–electromagnet hybrids,” Supercond. Sci. Technol. 25, 065015 (2012). 10.1088/0953-2048/25/6/065015
A. Aladyshkin, I. Nefedov, A. Aladyshkina, and I. Shereshevskii, “Formation of bound vortex–antivortex pairs and their depinning in mesoscopic cross-film cryotrons,” Phys. C 479, 98–101 (2012). 10.1016/j.physc.2011.12.020
R. T. Ibekwe, N. Riva, D. G. Whyte, and Z. S. Hartwig, “On the use of intentionally-designed defect distributions in REBCO superconducting cables and magnets,” Supercond. Sci. Technol. 38, 075011 (2025). 10.1088/1361-6668/ade7b9
C. Song, M. P. DeFeo, K. Yu, and B. L. T. Plourde, “Reducing microwave loss in superconducting resonators due to trapped vortices,” Appl. Phys. Lett. 95, 232501 (2009). 10.1063/1.3271523