Articles
Analytical development of Ginzburg-Landau equations for superconducting thin film in presence of currents
Published 2019-02-28
Keywords
- Ginzburg-Landau,
- current; Poisson,
- magnetization,
- susceptibility
How to Cite
Aguirre, C. A., Martins, Q. da S., & Barba Ortega, J. J. (2019). Analytical development of Ginzburg-Landau equations for superconducting thin film in presence of currents. Revista UIS Ingenierías, 18(2), 213–220. https://doi.org/10.18273/revuin.v18n2-2019020
Abstract
An analytical analysis to obtain the time dependent Ginzburg- Landau equations in presence of a current J and magnetic field H in a mesoscopic superconducting thin film is shown. The transport current is applied in a little contact in the boundary of the sample. This contacts are included through to the deGennes extrapolation parameter b in the boundary conditions. Finally, we show a useful tool that can be used to found the evolution of ψ(A,t) in this formalism. We found the dependence of the magnetization M(H) and magnetic susceptibility χ m (H) with b for such sample.
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References
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J. Barba-Ortega, E. D. Valbuena-Niño, M. Rincón Joya, “Transport phenomena in superconductors: kinematic vortex”, Iteckne, vol. 14, no. 1, pp. 11-16, 2017.
F. Duran-Flórez, M. Rincón-Joya, J. Barba-Ortega, “Perfil de súper-corrientes en una lámina de Ala campo magnético cero”, Respuestas, vol. 21, no. 2, pp. 6-12, 2016.
M. Tinkham, Introduction to Superconductivity. New York: McGraw-Hill, 1996.
P. G. de Gennes, Superconductivity of Metals and Alloys Addison- New York: Wesley, 1994.
A. D. Hernández and D. Domínguez, “Surface barrier in mesoscopic type-I and type-II superconductors”,
Phys. Rev. B, vol. 65, no. 14, 2002. doi: 10.1103/PhysRevB.65.144529
J. D. González, J. Barón-Jaimez and J. Barba- Ortega, “Complex Vortex Configuration in a Disk with a Higher/Lower Critical Temperature Superconducting Geometrical Central Defect”, J. Low Temp. Phys., vol. 179, no. 3-4, pp. 264-275, 2015. doi: 10.1007/s10909-015-1279-9
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A. L. Fetter and Hohenberg P. C., Superconductivity. New York: Marcel Dekker, 1969.
J. D. Patterson and B. C. Bailey, Solid-State Physics. New York: Springer Berlin Heidelberg, 2007. doi: 10.1007/978-3-540-34933-4
B. Xu, M. V. Milosevic and F. M. Peeters, “Calorimetric properties of mesoscopic superconducting disks, rings and cylinders”, Phys. Rev. B, vol. 81, no. 6, 2010. doi: 10.1103/PhysRevB.81.064501
K. Watanabe, T. Kita, and M. Arai, “Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors,” Phys. Rev. B, vol. 71, no. 14, p. 144515, 2005.
A. Shokri, M. Dehghan, “Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors”, CMES, vol.84, no.4, pp.333-358, 2012.
C. Aguirre, J. Barba-Ortega, “Efect of Anti-dots on the Magnetic Susceptibility in a Superconducting Long Prism”, J. Low Temp Phys, vol. 185, no. 5/6, pp. 186, 250, 2017. Doi: 10.1007/s10909-016-1695-5
C. Aguirre, H. Blas, J. Barba-Ortega, “Mesoscale vortex pinning landscapes in a two component superconductor”, Physica C, 2018. doi: 10.1007/s10909-016-1695-5
P. G. de Gennes and J. Matricon, “Collective Modes of Vortex Lines in Superconductors of the Second Kind”, Rev. Mod. Phys., pp. 45-49, 1964. doi: 10.1103/RevModPhys.36.45
L. Komendova, M. V. Miloševi´c, A. A. Shanenko, and F. M. Peeters, “Dierent length scales for order parameters in two-gap superconductors: Extended Ginzburg-Landau theory”, Phys. Rev.B, vol. 84, no. 6, 2011. doi: 10.1103/PhysRevB.84.06452
Y. Imry, Introduction to Mesoscopic Physics. Oxford Univ., 2002.
R. Fazio, V. F. Gantmakher and Y. Imry, New Directionsin Mesoscopic Physics. Berlin: Springer-
Verlag, 2003.
P. Singha-Deo, J. P. Pekola and Manninen M. “Heat capacity of mesoscopic superconducting disks, Europhys”, Europhys. Lett., vol. 50 no. 5, pp. 649-655, 2000. doi: 10.1209/epl/i2000-00319-x
A. Bezryadin, A. Buzdin and B. Pannetier, “Nucleation of vortices inside open and blind microholes”, Phys Rev B Condens Matter., vol. 53, no. 13, pp. 8553-8560, 1996.
O. Bourgeois, S. E. Skipetrov, F. Ong and J. Chaussy, “Calorimetry of Mesoscopic Superconducting Loops”, Phys. Rev. Lett., vol. 94, 2004. doi: 10.1103/PhysRevLett.94.057007
F. R. Ong, O. Bourgeois, S. E. Skipetrov and J. Chaussy, “Doping-dependent nonlinear Meissner effect and spontaneous currents in high-Tc superconductors”, Phys. Rev. Lett., vol. 97, 2004. doi: 10.1103/PhysRevB.71.014507
G. C. Buscaglia, C. Bolech and A. Lopez, Connectivity and Superconductivity. Springer, 2000.
W. C. Fon, K. C. Schwab, J. M.Worlock, and M. L. Roukes, “Nanoscale, Phonon-Coupled Calorimetry with Sub-Attojoule/Kelvin Resolution”, Nano Lett., vol. 5, no. 10, pp. 1968-171, 2005. doi: 10.1021/nl051345o
F. R. Ong and O. Bourgeois, “Topology eects on the heat capacity of mesoscopic”, European Phys. Lett. vol. 79, no. 6, 2007. doi: 10.1209/0295-5075/79/67003
L. Cabral, J. Albino Aguiar, “Vortex configurations in superconducting thin disks with finite,” Physica C Superconductivity, vol. 460, pp. 1295-1296, 2007. doi: 10.1016/j.physc.2007.03.330
S. Okumaa, Y. Yamazakia, N. Kokubob, “Novel vortex dynamics in Corbino-disk superconductors”, Physica C Superconductivity, vol. 470, 2010. doi: 10.1016/j.physc.2009.10.110
M. Miguel, S. Zapperi, “Tearing transition and plastic flow in superconducting thin films”, Nat Mater., vol. 2, no. 7, pp. 477-481, 2003. doi: 10.1038/nmat909
E. A. Andrushin, V. L. Ginzburg, and A. P. Silin, “On the giant thermoelectric efect in a hollow superconducting Cylinder”, Phys. Usp., vol. 40, pp. 435–438, 1997. doi: 10.1070/PU1997v040n04ABEH001559
R. O. Zaitsev, “Current-voltage characteristics of nanodimensional normal metal-superconductor point
difusion junctions”, Tech. Phys. Lett., vol. 29, no. 11, pp 913–916, 2003. doi: 10.1134/1.1631362
J. Barba-Ortega, E. Sardella, J. Albino Aguiar, “Superconducting properties of a parallelepiped mesoscopic superconductor: A comparative study between the 2D and 3D Ginzburg Landau models”, Phys. Lett. A, vol. 379, no. 7, pp. 732-737, 2015. doi: 10.1016/j.physleta.2014.12.030
J. Barba-Ortega, and M. Rincón Joya, “Configuración de vórtices en películas finas: Teoría Ginzburg-Landau no lineal,” TecnoLogicas, vol. 27, pp. 89-102, 2011.
J. Barba-Ortega, E. D. Valbuena-Niño, M. Rincón Joya, “Transport phenomena in superconductors: kinematic vortex”, Iteckne, vol. 14, no. 1, pp. 11-16, 2017.
F. Duran-Flórez, M. Rincón-Joya, J. Barba-Ortega, “Perfil de súper-corrientes en una lámina de Ala campo magnético cero”, Respuestas, vol. 21, no. 2, pp. 6-12, 2016.
M. Tinkham, Introduction to Superconductivity. New York: McGraw-Hill, 1996.
P. G. de Gennes, Superconductivity of Metals and Alloys Addison- New York: Wesley, 1994.
A. D. Hernández and D. Domínguez, “Surface barrier in mesoscopic type-I and type-II superconductors”,
Phys. Rev. B, vol. 65, no. 14, 2002. doi: 10.1103/PhysRevB.65.144529
J. D. González, J. Barón-Jaimez and J. Barba- Ortega, “Complex Vortex Configuration in a Disk with a Higher/Lower Critical Temperature Superconducting Geometrical Central Defect”, J. Low Temp. Phys., vol. 179, no. 3-4, pp. 264-275, 2015. doi: 10.1007/s10909-015-1279-9
J. Barba-Ortega, J. D. González and E. Sardella, “Tower as magnetic antipinning core in a small superconducting sample”, Physica C: Superconductivity and its Applications., vol. 506, pp. 146-150, 2014. doi: 10.1016/j.physc.2014.06.007
A. L. Fetter and Hohenberg P. C., Superconductivity. New York: Marcel Dekker, 1969.
J. D. Patterson and B. C. Bailey, Solid-State Physics. New York: Springer Berlin Heidelberg, 2007. doi: 10.1007/978-3-540-34933-4
B. Xu, M. V. Milosevic and F. M. Peeters, “Calorimetric properties of mesoscopic superconducting disks, rings and cylinders”, Phys. Rev. B, vol. 81, no. 6, 2010. doi: 10.1103/PhysRevB.81.064501
K. Watanabe, T. Kita, and M. Arai, “Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors,” Phys. Rev. B, vol. 71, no. 14, p. 144515, 2005.
A. Shokri, M. Dehghan, “Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors”, CMES, vol.84, no.4, pp.333-358, 2012.