**4. References**


[3] Agterberg, D. F. & Tsunetsugu, H. [2008]. Dislocations and vortices in pair-density-wave superconductors, *Nature Phys.* 4: 639.

[26] Khavkine, I., Kee, H.-Y. & Maki, K. [2004]. Supercurrent in nodal superconductors, *Phys.*

Flux-Periodicity Crossover from hc/e in Normal Metallic to hc/2e in Superconducting Loops 363

[27] Landauer, R. & Büttiker, M. [1985]. Resistance of small metallic loops, *Phys. Rev. Lett.*

[28] Lindström, T., Charlebois, S. A., Tzalenchuk, A. Y., Ivanov, Z., Amin, M. H. S. & Zagoskin, A. M. [2003]. Dynamical effects of an unconventional current-phase relation

[29] Little, W. A. [1964]. Long-range correlations in superconductivity, *Rev. Mod. Phys.* 36: 264. [30] Little, W. A. & Parks, R. D. [1962]. Observation of quantum periodicity in the transition

[31] Loder, F., Kampf, A. P. & Kopp, T. [2008]. Crossover from *hc*/*e* to *hc*/2*e* current

[32] Loder, F., Kampf, A. P. & Kopp, T. [2009]. Flux periodicities in loops of nodal

[33] Loder, F., Kampf, A. P. & Kopp, T. [2010]. Superconducting state with a finite-momentum pairing mechanism in zero external magnetic field, *Phys. Rev. B.* 81: 020511(R). [34] Loder, F., Kampf, A. P., Kopp, T., Mannhart, J., Schneider, C. & Barash, Y. [2008]. Magnetic

[36] Mineev, V. P. & Samokhin, K. V. [1999a]. *Introduction to Unconventional Superconductivity*,

[37] Mineev, V. P. & Samokhin, K. V. [1999b]. *Introduction to Unconventional Superconductivity*,

[38] Onsager, L. [1961]. Magnetic flux through a superconducting ring, *Phys. Rev. Lett.* 7: 50. [39] Parks, R. D. & Little, W. A. [1964]. Fluxoid quantization in a multiply-connected

[40] Peshkin, M. [1963]. Fluxoid quantization, pair symmetry, and the gap energy in the

[41] Schneider, C. [2007]. Conference on "*Superconductivity and Magnetism in the Perovskites*

[42] Schneider, C., Hammerl, G., Logvenov, G., Kopp, T., Kirtley, J. R., Hirschfeld, P. & Mannhart, J. [2004]. Half-*h*/2*e* critical current-oscillations of squids, *Europhys. Lett.*

[43] Schrieffer, J. R. [1964]. *Theory of Superconductivity*, Addison Wesley Publishing Company,

[44] Tinkham, M. [1963]. Effect of fluxoid quantization on transitions of superconducting

[45] Vakaryuk, V. [2008]. Universal mechanism for breaking the *hc*/2*e* periodicity of flux-induced oscillations in small superconducting rings, *Phys. Rev. Lett.* 101: 167002. [46] Vakaryuk, V. & Vinokur, V. [2011]. Effect of half-quantum vortices on magnetoresistance

[47] von Oppen, F. & Riedel, E. K. [1991]. Average persistent current in a mesoscopic ring,

[48] von Oppen, F. & Riedel, E. K. [1992]. Flux-periodic persistent current in mesoscopic

*Rev. B.* 70: 184521.

in YBCO dc SQUIDs, *Phys. Rev. Lett.* 90: 117002.

superconductors, *New J. Phys.* 11: 075005.

temperature of a superconducting cylinder, *Phys. Rev. Lett.* 9: 9.

oscillations in rings of *s*-wave superconductors, *Phys. Rev. B* 78: 174526.

SSux periodicity of *h*/*e* in superconducting loops, *Nature Phys.* 4: 112.

current carrying bardeen-cooper-schrieffer state, *Phys. Rev.* 132: 14.

of perforated superconducting films, *Phys. Rev. Lett.* 107: 037003.

superconducting rings close to *T*c, *Phys. Rev. B* 46: 3203.

[35] London, F. [1950]. *Superfluids*, John Wiley & Sons, New York.

Gordon and Breach science publishers, chapter 8.

Gordon and Breach science publishers, chapter 17.

*and Other Novel Materials*", Tel Aviv, unpublished.

superconductor, *Phys. Rev.* 133: A97.

54: 2049.

68: 86.

chapter 8.

films, *Phys. Rev.* 129: 2413.

*Phys. Rev. Lett.* 66: 84.


20 Superconductors

[3] Agterberg, D. F. & Tsunetsugu, H. [2008]. Dislocations and vortices in pair-density-wave

[4] Aharonov, Y. & Bohm, D. [1959]. Significance of electromagnetic potentials in the

[5] Ambegaokar, V. & Eckern, U. [1991]. Diamagnetic response of mesoscopic

[6] Barash, Y. S. [2008]. Low-energy subgap states and the magnetic flux periodicity in

[7] Bardeen, J. [1962]. Critical fields and currents in superconductors, *Rev. Mod. Phys.* 34: 667. [8] Bardeen, J., Cooper, L. N. & Schrieffer, J. R. [1957]. Theory of superconductivity, *Phys.*

[9] Bogachek, E. N., Gogadze, G. A. & Kulik, I. O. [1975]. Doubling of the period of flux quantization in hollow superconducting cylinders due to quantum effects in the normal

[10] Brenig, W. [1961]. Remark concerning quantized magnetic flux in superconductors, *Phys.*

[11] Büttiker, M., Imry, Y. & Landauer, R. [1983]. Josephson behavior in small normal

[12] Büttiker, M. & Klapwijk, T. M. [1986]. Flux sensitivity of a piecewise normal and

[13] Byers, N. & Yang, C. N. [1961]. Theoretical considerations concerning quantized

[14] Cayssol, J., Kontos, T. & Montambaux, G. [2003]. Isolated hybrid normal/superconducting ring in a magnetic flux: From persistent current to josephson

[15] Cheung, H., Gefen, Y., Riedel, E. K. & Shih, W. [1988]. Persistent currents in small

[16] de Gennes, P. G. [1966]. *Superconductivity of Metals and Alloys*, Addison Wesley Publishing

[17] Deaver, B. S. & Fairbank, W. M. [1961]. Experimental evidence for quantized flux in

[18] Doll, R. & Näbauer, M. [1961]. Experimental proof of magnetic flux quantization in a

[19] Douglass, D. H. [1963]. Properties of a thin hollow superconducting cylinder, *Rev. Rev.*

[23] Gough, C. H., Colclough, M. S., Forgan, E. M., Jordan, R. g. & Keene, M. [1987]. Flux

[24] Jang, J., Ferguson, D. G., Vakaryuk, V., Budakian, R., Chung, S. B., Goldbart, P. M. & Maeno, Y. [2011]. Observation of half-height magnetization steps in Sr2RuO4, *Science*

[25] Juriˇci´c, V., Herbut, I. F. & Tešanovi´c, Z. [2008]. Restoration of the magnetic *hc*/*e*-periodicity in unconventional superconductors, *Phys. Rev. Lett.* 100: 187006.

[20] Eckern, U. [1994]. Superconductivity in restricted geometries, *Physica B* 203: 448. [21] Eckern, U. & Schwab, P. [1995]. Normal persistent currents, *Adv. in Physics* 44: 387. [22] Essmann, U. & Träuble, H. [1967]. The direct observation of individual flux lines in type

superconductors, *Nature Phys.* 4: 639.

quantum theory, *Phys. Rev.* 115: 485.

state, *Phys. Stat. Sol. (b)* 67: 287.

current, *Phys. Rev. B* 67: 184508.

Company, chapter 5.

132: 513.

331: 186.

one-dimensional rings, *Phys. Lett. A* 96: 365.

superconducting metal loop, *Phys. Rev. B* 33: 5114.

one-dimensional metal rings, *Phys. Rev. B* 37: 6050.

superconducting cylinders, *Phys. Rev. Lett.* 7: 43.

superconducting ring, *Phys. Rev. Lett.* 7: 51.

ii superconductors, *Phys. Lett. A* 24: 526.

quantization in a high-*Tc* superconductor, *Nature* 326: 855.

magnetic flux in superconducting cylinders, *Phys. Rev. Lett.* 7: 46.

*Rev.* 108: 1175.

*Rev. Lett.* 7: 337.

superconducting rings above *T*c, *Phys. Rev. B* 44: 10358.

*d*-wave superconducting rings, *Phys. Rev. Lett.* 100: 177003.


**1. Introduction**

http://dx.doi.org/10.5772/50429

under the applied magnetic field.

superconductor is related to complex Josephson medium.

cited.

Since their discovery in 1986 the high-T*c* superconductors (HTSC) have been employed in several applications.The expectation with the discover of new devices sparked the beginning of an intense research to understand the parameters which control the physical properties of these materials. With the goal to the practical applications, the critical current density (J*c*) is one of the crucial parameters that must be optimized for HTSC [1]. Thus the aim of this chapter is to describe he transport critical current behavior of polycrystalline superconductors

**A Description of the Transport Critical Current** 

**Chapter 15**

**Behavior of Polycrystalline Superconductors** 

**Under the Applied Magnetic Field** 

C.A.C. Passos, M. S. Bolzan, M.T.D. Orlando, H. Belich Jr,

J.L. Passamai Jr., J. A. Ferreira and E. V. L. de Mello

Additional information is available at the end of the chapter

According to Gabovich and Mosieev [2], there is a dependence of the superconducting properties on the macrostructure of ceramic. They studied the BaPb1−*x*Bi*x*O3 metal oxide superconductor properties which are a consequence of the granularity of the ceramic macrostructure and the existence of weak Josephson links between the grains. In this case, the superconductivity depends strongly on the presence of grain boundaries and on the properties of the electronic states at the grain boundaries. This determines the kinetic characteristics of the material. For instance, the temperature dependence of the electrical conductivity of oxide

Nowadays it is well known that the J*c* in polycrystalline superconductors is determined by two factors: the first is related to the defects within the grains (intragrain regions) such as point defects, dislocations, stacking faults, cracks, film thickness, and others [3, 4]. When polycrystalline samples are submitted to magnetic field, the intragranular critical current can be limited by the thermally activated flux flow at high magnetic fields. Secondly the critical current depends on the grain connectivity, that is, intergrain regions. Rosenblatt *et*

> ©2012 Passos et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

©2012 Passos et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
