Simple theoretical proposal of the dependence of the deGennes extrapolation parameter with the surface temperature of a superconducting sample

Keywords: Time-dependent Ginzburg–Landau equations, deGennes parameter, Superconductor, Mesoscopic, Magnetization


The Time-dependent Ginzburg–Landau model (TDGLM) is a robust tool widely used to analyze the magnetization of the single-vortex state of a mesoscopic superconducting sample in presence of a magnetic field. The algorithm implemented in this work is applied to a square geometry surrounded by different kinds of materials simulated by deGennes extrapolation length . The inside of the sample remains at constant temperature , while its boundary remains at temperature . This temperature variation in the sample can be generated by a continuous laser wave injected into all the internal points, except for a thin surface layer in the boundary of the material. We found that the b value at , which mimics the magnetization curve for a corresponding , presents a linear dependence with the temperature. Therefore, although within the domain of validity TDGLM the parameter  is to be considered temperature-independent in the vicinity of the bulk critical temperature and that  depends on the density of states near the surface, we propose a simple dependence of using a TDGLM.


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Author Biographies

José José Barba-Ortega, *, Universidad Nacional de Colombia, Colombia

PhD en Física, Departamento de Física, Universidad Nacional de Colombia, Bogotá-Colombia,
*Corresponding author

Jesús D. González, Universidad del Magdalena, Colombia

PhD en Física, Grupo en Teoría de la Materia Condensada, Universidad del Magdalena, Santa Marta-Colombia,

Miryam Rincón-Joya, Universidad Nacional de Colombia, Colombia

PhD en Física, Departamento de Física, Universidad Nacional de Colombia, Bogotá-Colombia,


P. G. De Gennes, Superconductivity of Metals and Alloys, 1st ed. New York: Advanced Books Classics, 1966.

M. Tinkham, Introduction to Superconductivity, 2nd ed. New York: McGraw-Hill Book Co., 1996.

J. Barba-Ortega, E. Sardella, and R. Zadorosny, “Influence of the deGennes extrapolation parameter on the resistive state of a superconducting strip,” Phys. Lett. A, vol. 382, no. 4, pp. 215–219, Jan. 2018.

J. Barba-Ortega, C. C. de S. Silva, and J. A. Aguiar, “Superconducting slab in contact with thin superconducting layer at higher critical temperature,” Phys. C Supercond., vol. 469, no. 14, pp. 852–856, Jul. 2009.

J. Barba-Ortega, E. Sardella, and J. A. Aguiar, “Superconducting boundary conditions for mesoscopic circular samples,” Supercond. Sci. Technol., vol. 24, no. 1, p. 015001, Jan. 2010.

B. J. Baelus, B. Partoens, and F. M. Peeters, “One-dimensional modulation of the superconducting boundary condition for thin superconducting films,” Phys. Rev. B, vol. 73, no. 21, p. 212503, Jun. 2006.

M. M. Doria, A. R. de C. Romaguera, and F. M. Peeters, “Effect of the boundary condition on the vortex patterns in mesoscopic three-dimensional superconductors: Disk and sphere,” Phys. Rev. B, vol. 75, no. 6, p. 064505, Feb. 2007.

H. J. Fink, S. B. Haley, C. V. Giuraniuc, V. F. Kozhevnikov, and J. O. Indekeu, “Boundary conditions, dimensionality, topology and size dependence of the superconducting transition temperature,” Mol. Phys., vol. 103, no. 21–23, pp. 2969–2978, Nov. 2005.

M. Salluzzo et al., “Indirect Electric Field Doping of the CuO2 Planes of the Cuprate NdBa2 Cu3 O7 Superconductor,” Phys. Rev. Lett., vol. 100, no. 5, p. 056810, Feb. 2008.

A. S. Dhoot, S. C. Wimbush, T. Benseman, J. L. MacManus-Driscoll, J. R. Cooper, and R. H. Friend, “Increased Tc in Electrolyte-Gated Cuprates,” Adv. Mater., vol. 22, no. 23, pp. 2529–2533, May. 2010.

X. Leng, J. Garcia-Barriocanal, S. Bose, Y. Lee, and A. M. Goldman, “Electrostatic Control of the Evolution from a Superconducting Phase to an Insulating Phase in Ultrathin YBa2 Cu3 O7-x Films,” Phys. Rev. Lett., vol. 107, no. 2, p. 027001, Jul. 2011.

W. D. Gropp, H. G. Kaper, G. K. Leaf, D. M. Levine, M. Palumbo, and V. M. Vinokur, “Numerical Simulation of Vortex Dynamics in Type-II Superconductors,” J. Comput. Phys., vol. 123, no. 2, pp. 254–266, Feb. 1996.

G. C. Buscaglia, C. Bolech, and A. Lpez, Connectivity and Superconductivity, vol. 62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

J. Berger, “Time-dependent Ginzburg–Landau equations with charged boundaries,” J. Math. Phys., vol. 46, no. 9, p. 095106, Sep. 2005.

A. Crassous et al., “Nanoscale Electrostatic Manipulation of Magnetic Flux Quanta in Ferroelectric/Superconductor BiFeO3/YBa2Cu3 O7−δ Heterostructures,” Phys. Rev. Lett., vol. 107, no. 24, p. 247002, Dec. 2011.

M. V. Milošević and R. Geurts, “The Ginzburg–Landau theory in application,” Phys. C Supercond., vol. 470, no. 19, pp. 791–795, Oct. 2010.

V. Moshchalkov, R. Woerdenweber, and W. Lang, Nanoscience and Engineering in Superconductivity. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010.

C. Poole, H. Farach, and R. Creswick, Handbook of Superconductivity, 1st ed. New York: Academic Press, 2000.

J. Barba-Ortega and M. R. Joya, “Configuración de vórtices en películas finas: Teoría Ginzburg-Landau no lineal,” TecnoLógicas, no. 27, pp. 89–102, July 2011. Dec. 2011.

J. Barba-Ortega, E. D. Valbuena-Nino, and M. Rincón-Joya, “Transport phenomena in superconductors: kinematic vortex,” Iteckne, vol. 14, no. 1, pp. 11–16, Mar. 2017.

F. Durán-Florez, M. Rincón-Joya, and J. Barba-Ortega, “Perfil de súper-corrientes en una lámina de Al a campo magnético cero,” Respuestas, vol. 21, no. 2, pp. 6–12, Jan. 2016.

J. Barba-Ortega and M. Rincón-Joya, “Nucleación de vórtices y antivórtices en películas superconductoras con nanoestructuras magnéticas,” Respuestas, vol. 16, no. 1, pp. 45–49, Jan. 2011.

E. C. S. Duarte, E. Sardella, W. A. Ortiz, and R. Zadorosny, “Dynamics and heat diffusion of Abrikosov’s vortex-antivortex pairs during an annihilation process,” Journak Phys. Condens. Matter, vol. 29, no. 40, p. 405605, 2017.

How to Cite
Barba-Ortega, J. J., González, J. D., & Rincón-Joya, M. (2019). Simple theoretical proposal of the dependence of the deGennes extrapolation parameter with the surface temperature of a superconducting sample. TecnoLógicas, 22(45), 1-7.
Research Papers