Brief numerical analysis of (3+1) Ginzburg-Landau equations

Abstract

In this contribution, we show the implementation of the Link-variable method for solve the complete set of acopled non-linear time dependent Ginzburg-Landau differential equations in a three-dimensional homogeneous and isotropic mesoscopic superconducting system. In this case, the sample is immersed in an external magnetic d at zero applied current. The effects of demagnetization are taken in count and we show the order parameter and its phase in zero field cooling and field cooling process. This numerical analysis shows good results when this solution is applied to a superconducting cubic sample.

Proximity effects in a single- and two-band superconducting heterostructures: time-dependent Ginzburg-Landau approach.

“…Then, in this paper, we will study the vortex-state (Cooper pair density), magnetization as a proximity conditions function, via a new parameter λ ′ (see Fig. 1(b)) that consider the distance between these condensates, which depends on λ 0 , which is the penetration length, usually used in single-band condensates, which describes the entry of the magnetic field into the superconducting sample [1][2][3][4][5][6]15].…”

“…Thus, renewed interest has been generated in superconducting systems, especially during the year 2023, after the possibility of the existence of a superconductor at room temperature and pressure, denominated as LK.99, which has generated great controversy in the academic community [8][9][10]. The study of mesoscopic superconducting systems, in which the coherence length ξ in the superconducting sample, has been studied extensively in systems of a superconducting single-band condensates, described by a pseudo wave function, which can be studied through the dependence of the value of the Ginzburg-Landau parameter κ, being type I κ < 1/ √ 2 and type II κ > 1/ √ 2, for which the latter exhibit the well-known mixed state, in which the superconducting state and the normal state, forming the so-called Abrikosov vortex states in a triangular lattice, which generally depends on the geometry of the conductive sample and whose study contrasts with excellent accuracy with respect to the experimental measurements carried out, via magnetic measurements [11][12][13][14][15]. Thus, during the last decade several multi-gap superconductors were discovered, initiated with the discovery of MgB 2 [16].…”