An Ab-Initio Study of Superconductivity in LiAlB4: an MgB2-related Compound

Superconductors have grown in importance within materials science, largely due to their applications in magnets. Despite this, the theoretical frameworks to describe most types of superconductor remain to be understood, with a key exception in BCS-type superconductors, governed by electron-phonon interactions. Here we conduct a first principles study of the BCS-type superconductor with the highest critical temperature (Tc) at ambient pressure at around 39 K, MgB2. In particular, we focus on crucial aspects of MgB2 which contribute to this Tc, including the importance of the E2g phonon mode involving in-plane vibrations of boron atoms. Through CASTEP, an analysis of the density of states at the Fermi energy is conducted, followed by a study of the vibrational properties of the material. Finally, the Eliashberg spectral function is used in tandem with the Allen-Dynes equation to calculate the Tc, demonstrated to be in good agreement with experimental studies at 39.16 K using μ∗ = 0.1. This thesis continues by introducing a new material, LiAlB4, chosen from a set of metal aluminium tetraborates and containing a similar layered structure to MgB2 with honeycomb-structured boron sheets. We find the structure to be both thermodynamically and dynamically stable, with a similar density of states at the Fermi energy as MgB2. Also displaying similar in-plane boron vibrations, LiAlB4 improves on the electron-phonon coupling strength of MgB2 to give Tc = 49.36 K at ambient pressure for μ∗ = 0.1. This is shown to largely be the result of lower frequency phonon modes related to Li vibrations, which give stronger electron-phonon coupling.