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Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

A. E. Macias-Medri

Pós-Graduação em Física, UFPR, CP 19044, CEP 81531-980, Curitiba-PR, Brazil

E-mail Address: amacias3@fisica.ufpr.br

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and

J. J. Rodríguez-Núñez

Dpto. Física and SuperComp Laboratory, FaCyT-UC, Valencia 2001, Venezuela

E-mail Address: jjrn01@gmail.com

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https://doi.org/10.1142/S0217984918501567Cited by:1 (Source: Crossref)

Abstract

A two-band and quartic interaction order Ginzburg–Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter $γ$ $γ$ ) and fourth (quartic, with coupling parameter $\tilde{γ}$ $\tilde{γ}$ ) order between the two superconducting order parameters ( $f_{i}$ $f_{i}$ with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the $f_{i}$ $f_{i}$ -profiles, where our starting point was the calculation of the superconducting critical temperature $T_{c}$ $T_{c}$ . With this at hand, we evaluate $f_{i}$ $f_{i}$ and the magnetic field along the z-axis, $B_{0}$ $B_{0}$ , as function of $γ$ $γ$ , $\tilde{γ}$ $\tilde{γ}$ , the radial distance $r / λ_{1} (0)$ $r / λ_{1} (0)$ and the temperature $T$ $T$ , for $T \approx T_{c}$ $T \approx T_{c}$ . The self-consistent equations allow us to compute $λ$ $λ$ (penetration depth) and the healing lengths of $f_{i}$ $f_{i}$ ( $L_{h_{i}}$ $L_{h_{i}}$ with i = 1,2) as functions of T, $γ$ $γ$ and $\tilde{γ}$ $\tilde{γ}$ . At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

Keywords:

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