Superconductors and the periodic penetration parameter: Defining and utilizing in diverse applications

There are various types of materials that have different levels of electrical conductivity, and one category is known as superconductors or superconducting materials. Superconducting materials are characterized by their complete lack of electrical resistivity. These materials are highly important due to their wide range of applications in electricity transmission, although they do have certain limitations. The Bardeen–Cooper–Schryver theory and the Ginzburg–Landau theory are two significant theories used to explain the nature of superconducting materials. Of particular interest in this study is the Ginzburg–Landau differential equation, which is considered a vital equation in this field. This equation belongs to a class of nonlinear differential equations. Our research focuses on simulating solutions to the Ginzburg–Landau equation under steady-state conditions. We conducted simulations for several superconducting materials, including aluminum, niobium, lead, tin, niobium germanide, niobium tin, vanadium silicate, lead hexa-molybdenum octa-sulfur, magnesium diboride, uranium triplatinum, potassium, barium copper oxide, yttrium, calcium copper oxide, and barium mercury. We define a new parameter of the superconductor conduction materials, which is the periodic parameter of the superconductor. By analyzing the periodic solutions obtained from the Ginzburg–Landau differential equation, we were able to determine the values of the periodic penetration parameters for each material. Notably, monatomic superconducting materials exhibited periodic penetration parameters in the range of tens of micrometers, while tetra- and penta-elements materials had values in the tens of nanometers. Superconducting materials of two or three different elements showed average values for these parameters. These findings provide valuable insights into the characteristics and behavior of various superconducting materials.