Paving the way for future advancements in superconductivity research through gold ormus studies

Abstract Background Gold ormus is a type of superconductor that can exhibit superconductivity at temperatures below 1 Kelvin, allowing it to conduct electricity without resistance. While not as widely used as other materials like niobium or lead, gold ormus is valuable for research in superconductivity. Limited studies have been conducted on gold ormus. Numerical simulations of the Ginzburg–Landau theory have yielded important results for both gold ormus. Results Class-I and class-II superconducting gold ormus, have been successfully simulated using the Runge–Kutta fourth-order method. Our analysis shows the convergence of our simulation outcomes and emphasizes 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 ormus having a PFP of 250 nm, class-II superconducting gold ormus having a PFP of 566.2 nm. The relationship between the PFP and the length of the penetration depth has also been revealed. Conclusions Our study confirms the accuracy of the Runge–Kutta fourth-order method in simulating superconductors. By analyzing the PFP for different superconducting materials, we have identified trends in penetration depth that contribute to understanding superconductivity. Our simulations provide valuable insights for further research in the field of superconductivity. Adjusting parameters carefully ensures reliable simulations and advances progress in superconductivity research.