Mathematical modeling of current-voltage characteristics of high-temperature superconductors with fractal boundaries of normal phase clusters

M. A. Vasyutin ; N. D. Kuzmichev ; D. A. Shilkin

Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 4, pp. 507-519.

Résumé

The fractality effect of the normal phase clusters' boundaries of a high-temperature superconductor ${YBa}_{2}{Cu}_{3}{O}_{7-x}$ (YBCO) on the magnetic flux creep is investigated. Experimental current-voltage and magnetoresistive characteristics of YBCO at the boiling point of nitrogen are obtained. Based on the model of intergranular clusters with fractal boundaries, an approximation of the experimental data is obtained after geometric-probability analysis of the photomicrographs of the samples. A model of the magnetoresistive state caused by flux creep is proposed for various transport currents, and experimental and empirical dependences of the fractal dimension of the normal YBCO phase cluster boundaries on the constant magnetic field are found. The magnetic field intensity is determined for a given fractal dimension, at which the vortex penetration into the granules begins. It is shown that the state of the samples corresponds to the metastable phase of the vortex glass. The connectivity index of the stall paths of the vortex bundles at the percolation threshold is calculated.

Détail

Keywords: high-temperature superconductor, clusters of the normal phase, fractal boundaries, flux creep.

Bibliographie

[1] B. Mandelbrot, Fractal geometry of nature., Times Books, NY, 1982, 468 pp. | MR

[2] L. M. Zelenyi, A. V. Milovanov, “Fractal topology and strange kinetics: from percolation theory to problems of cosmic electrodynamics”, Uspekhi fizicheskikh nauk, 174:8 (2004), 809–852 (In Russ.) | DOI

[3] M. Prester, “Experimental evidence of a fractal dissipative regime in $high-{T}_{c}$ superconductors”, Phys. Rev. B., 60:5 (1999), 3100–3103 | DOI

[4] V. S. Flis, A. A. Kalenyuk, A. L. Kasatkin, V. O. Moskalyuk, A. I. Rebikov, V. L. Svechnikov, K. G. Tretyachenko, V. M. Pan, “HTS cuprate films doped with nanoparticles and their electrodynamics caused by Abrikosov vortices”, Fizika nizkikh temperatur, 36:1 (2010), 74–88 (In Russ.)

[5] Yu. N. Nozdrin, E. E. Pestov, V. V. Kurin, S. V. Baryshev, A. V. Bobyl, S. F. Karmanenko, D. A. Sakseev, R. A. Suris, “The influence of the microstructure of ${YBa}_{2}{Cu}_{3}{O}_{7-x}$ epitaxial films on their electrophysical and non-linear microwave properties”, Solid State Physics, 48:12 (2006), 2136–2145 (In Russ.)

[6] T. V. Suhareva, V. A. Finkel, “Contribution of superconducting granules and intergranular boundaries to the magnetoresistance of ceramic HTSC ${YBa}_{2}{Cu}_{3}{O}_{7-\delta}$ in weak magnetic fields”, Solid State Physics, 52:8 (2010), 1479–1485 (In Russ.)

[7] Yu. I. Kuzmin, “Resistive state of superconducting structures with fractal clusters of the normal phase”, Solid State Physics, 43:7 (2001), 1157–1164 (In Russ.)

[8] Yu. I. Kuzmin, “Fractal geometry of normal phase clusters and magnetic flux trapping in $high-{T}_{c}$ superconductors”, Phys. Lett. A., 267:1 (2000), 66–70 | DOI

[9] Yu. I. Kuzmin, “Dynamics of the magnetic flux trapped in fractal clusters of normal phase in a superconductor”, Phys. Rev. B., 64:9 (2001), 1–13 | DOI

[10] M. Ziese, “Percolative vortex motion in high-temperature superconductors”, Phys. Rev. B., 53:18 (1996), 12422–12429 | DOI

[11] J. E. Sonier, R. F. Kiefl, J. H. Brewer, D. A. Bonn, S. R. Dunsiger, W. N. Hardy, R. Liang, R. I. Miller, D. R. Noakes, C. E. Stronach, “Expansion of the vortex cores in ${YBa}_{2}{Cu}_{3}{O}_{6.95}$ at low magnetic fields”, Phys. Rev. B., 59:2 (1999), R729–R732 | DOI

[12] C. J. Olson, C. Reichhardt, F. Nori, “Fractal networks, braiding channels, and voltage noise in intermittently flowing rivers of quantized magnetic flux”, Phys. Rev. Lett., 80:10 (1998), 2197–2200 | DOI

[13] D. A. Balaev, I. L. Belozerova, D. M. Gohfeld, L. V. Kashkina, Yu. I. Kuzmin, K. R. Migel, M. I. Petrov, S. I. Popkov, K. A. Shuihutdinov, “Current-voltage characteristics of a high-temperature foam superconductor ${Bi}_{1.8}{Pb}_{0.3}{Sr}_{2}{Ca}_{2}{Cu}_{3}{O}_{x}$ with a fractal cluster structure”, Solid State Physics, 48:2 (2006), 193–198 (In Russ.) | MR

[14] Yu. I. Kuzmin, “Electric field induced by magnetic flux motion in superconductor containing fractal clusters of a normal phase”, Phys. Lett. A., 281:1 (2001), 39–43 | DOI

[15] Yu. I. Kuzmin, “Giant dispersion of critical currents in a superconductor with fractal clusters of the normal phase”, Technical Physics Letters, 28:13 (2002), 74–82 (In Russ.)

[16] M. A. Vasyutin, N. D. Kuzmichev, “Nonlinearity of the current-voltage characteristics of HTSC ${YBa}_{2}{Cu}_{3}{O}_{7-x}$, determined by modulation technique”, Technical physics letters, 18:23 (1992), 5–9 (In Russ.)

[17] Yu. I. Kuzmin, “The state of vortex glass in superconductors with fractal clusters of the normal phase”, Technical Physics Letters, 36:9 (2010), 17–25 (In Russ.)

[18] N. D. Kuzmichev, M. A. Vasyutin, “Differential equations for reconstructing the derivative of a hysteresis-free nonlinear current-voltage characteristic of a semiconductor structure”, Semiconductors, 53:1 (2019), 111–114 (In Russ.)

[19] S. V. Meriakri, “Dynamic phase transitions in moving vortex structures in type-2 superconductors”, Technical Physics, 75:5 (2005), 87–91 (In Russ.)

[20] R. H. Koch, V. Foglietti, W. J. Gallagher, G. Koren, A. Gupta, M. P. A. Fisher, “Experimental evidence for vortex-glass superconductivity in Y-Ba-Cu-O”, Phys. Rev. Lett., 63:14 (1989), 1511– 1514 | DOI

[21] P. L. Gammel, L. F. Schneemeyer, D. J. Bishop, “SQUID picovoltometry of ${YBa}_{2}{Cu}_{3}{O}_{7-x}$ single crystals: Evidence for a finite-temperature phase transition in the high-field vortex state”, Phys. Rev. Lett., 66:7 (1991), 953–956 | DOI

[22] N. D. Kuzmichev, “Penetration of a magnetic field into the system of weak bonds of a granular superconductor ${YBa}_{2}{Cu}_{3}{O}_{7-x}$”, Solid State Physics, 43:11 (2001), 1934–1938 (In Russ.)

[23] Yu. I. Kuzmin, I. V. Pleshakov, “Electric field induced by collective creep of vortices in superconductors with fractal clusters of the normal phase”, Technical Physics Letters, 42:3 (2016), 76–83 (In Russ.)