Analysis of superconducting critical temperature using numerical method

Abstract

Currently, many studies have shown that the critical temperature (Tc) of a superconductor can be predicted by using the BCS theory. In this work, we analyse Tc of superconductors, which is determined by the spectral function (α2F(ω)) derived from the interaction between electrons and phonons. The equation that we used for the calculation is T c strong = f 1 f 2 T c weak . In this equation, T c weak refers to the Allen-Dynes formula and f is the correction factor. We compare the Tc obtained from this equation with our method. Many important parameters are given and analysed, such as average coupling strength (λ), the square root of the average frequency square (ω2), and average logarithm frequency (ωln). We use numerical methods and expect to improve the equation to calculate Tc to be user-friendly. Normally, the calculation of Tc can be challenging and time-consuming. The most successful theory explaining the general properties of superconductors is the BCS theory. It explains the mechanism in which normal conductors become superconductors, and the pairing of electrons known as the Cooper pairing is formed by the electron-phonon interactions. In the past, the BCS theory predicted the limit of the critical temperature of superconductors to be around 30-40 kelvin. Recently, several researchers have been discovered a higher Tc value than the limited value from experiments under high pressure. Our method could provide a better analysis of appropriate Tc of superconductors to support new discoveries in the future.