The Investigation of an Anomalous Isotope Exponent of Superconductors Under High Pressure in Weak-Coupling Limit

Abstract

Effects of pressure and isotope exponent of superconductor on critical temperature were investigated within the weak-coupling limit. The dispersion relation of carriers in the superconducting state under high pressure was obtained, including the electron–phonon interaction and Coulomb potentials. The equations of the critical temperature and isotope effect were analytically derived and numerically calculated. The enhancement of the critical temperature depended on the external pressure upon the unit cell, resulting in the narrow fluctuation in density of state. It was noticed that the more the fluctuation height increased, the higher the critical temperature was performed. The range of the isotope effect exponent (α) was 0 < α< 0.5 in the normal behaviour, while α> 0.5 in the anomalous behaviour. Also, a negative isotope effect exponent was found in this work. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.