Specific Heat and Density of MgB2 Superconductor in Two Band Models: A Theoretical Study

Abstract

The goal of this work is to compare the results of theory qualitatively with the existing data from experiments while examining the fundamental properties of M_gB₂ superconductive properties, such as specific heat, density of states, and temperature. M_gB₂ with \(\mathit{T}\)_c \(\approx\) 40K, is a record-breaking compound among the s-p metals and alloys. This substance seems to be a unique illustration of dual band electrical frameworks that are only loosely coupled to one another. The superconductivity in this simple compound is mostly due to the boron sub-lattice conduction band, as demonstrated by experimental evidence. There are two superconductivity gaps, according to investigations like tunneling spectroscopy, specific heat measurements, and high resolution spectroscopy. Considering a canonical two band BCS Hamiltonian containing a Fermi Surface of \(\pi\) - and \(\sigma\)- bands and following Green's function technique and equation of motion method, we have shown that M_gB₂ possess two superconducting gaps. The system permits a precursor period for Cooper pair droplets, which transitions into a locked state at a threshold temperature below the mean field solution, it is also noted. Additionally, a study of specific heat and state densities is offered. For particular heat, the consistency between theory and experimental findings is quite convincing. Introduction, Model Hamiltonian, Physical Properties, Numerical Calculations, Discussion, and Conclusions are the five components that make up the study.