Investigating superconductivity in body centered tetragonal structures using density functional theory

The inversion symmetry of a crystal structure plays a central role in the formation of Cooper pairs in conventional super- conductors. Therefore, with the occurrence of superconductivity in BaNiSn3 type materials, which lacks inversion symmetry along the c-axis, noncentrosymmetric superconductors have considered as a hot topic of current research from both experimental and theoretical points of view. Thus, considerable experimental works have been made for the discovery of new noncentrosymmetric superconductors which crystallize in the body-centred tetragonal BaNiSn3 structure. Then, superconductivity has been discovered for SrAuSi3 material. Although superconductivity has been found experimentally, their electronic and phonon structures have not been studied in detail. Phonons and electrons are essential in the phenomenon of superconductivity because phonons play the role of bringing about the coupling between electrons to form Cooper pairs which are amenable for superconductivity, as explained in the Bardeen, Cooper, and Schrieffer (BCS) theory. Thus, we strongly believe that electronic and vibrational properties of SrAuSi3 material must be studied in order to understand the origin of superconductivity in this material. Recent years show that first-principles calculations offer an invaluable tool for carrying out theoretical studies of an important number of physical and chemical properties of the condensed matter with great accuracy. Therefore, we think that it is worthwhile to perform first-principles calculations for the structural and electronic properties the SrAuSi3 and SrAu2Si2. With the availability of these results, a linear response method will be applied to study phonons in these materials. Phonon dispersion curves and phonon density of states for these BaNiSn3 compounds will be presented and discussed in detail. In particular, the zone-centre phonon modes are of special interest in the lattice dynamics of solids since they can be obtained by various experimental methods. Thus, the eigendisplacement of zone-centre phonon modes in these materials will be analysed. Finally, we will carry out ab initio calculations of electron-phonon interaction for this material in order to calculate their superconducting parameters such as the density of states at the Fermi level (N(EF )), the Eliashberg spectral function (α2F(ω)), the electron-phonon coupling parameter (λ), and superconducting transition temperature (Tc). Using the calculated superconducting parameters, we will explain the origin of superconductivity in these materials