Advancing superconductivity research: Insights from numerical simulations of potassium fullerenide-60 and gold and with Ginzburg-Landau theory

There are many types of superconductors, including gold ormus and some fullerene derivatives. Gold can become a superconductor at extremely low temperatures (<1 K), allowing it to conduct electricity without resistance. While not as commonly used as materials like niobium or lead, gold superconductors are valuable for research and development in superconductivity. Fullerene derivatives like potassium fullerenide-60 also exhibit high superconductivity. Limited studies have been conducted on both gold ormus and superconducting fullerene derivatives. Our study of numerical simulations of the Ginzburg-Landau theory in superconductors for gold ormus and potassium fullerenide-60 has yielded important results. We have successfully simulated class-I and class-II superconducting gold ormus, as well as potassium fullerenide-60, using the Runge-Kutta fourth order method. Our analysis demonstrates the convergence of our simulation outcomes and highlights the importance of considering truncation error and selecting appropriate step sizes for accurate results. The periodic factor of penetration (PFP) for each superconductor has been determined, with class-I superconducting gold having a PFP of 250 nm, class-II superconducting gold having a PFP of 566.2 nm, and potassium fullerenide-60 having a PFP of 1.374 nm. Additionally, our study reveals the relationship between the periodic penetration factor and the length of the penetration depth, showing that the PFP reaches a minimum value at a penetration depth length of 130 nm. Overall, our findings contribute to a better understanding of superconductivity in gold ormus and potassium fullerenide-60, emphasizing the importance of accurate numerical simulations for studying complex physical phenomena. Our study confirmed the accuracy of the Runge-Kutta fourth-order method in simulating superconductors. By examining the PFP for various superconducting materials, we identified trends in penetration depth, shedding light on superconductivity. Our simulations give valuable insights for advancing research in this field, with the Runge-Kutta fourth-order method striking a balance between accuracy and efficiency. Careful parameter adjustment ensures reliable simulations and contributes to progress in superconductivity research.