Ab-initio Calculations of Lattice Dynamics and Superconductivity in FCC Lithium and Iodine and BCC Tellurium

We present the calculations of the phonon frequency and its line width over the Brillouin zone for simple substances based on ab-initio linear response theory and the evaluation of superconducting transition temperature. The substances we report on are FCC iodine, FCC lithium, and BCC tellurium at high pressures. In iodine the phonon dispersion reveals a phonon softening along the Σ-line (Γ–K direction) near the lower pressure boundary of the FCC phase. In lithium, the frequency softening is striking along the entire Λ-line (Γ–L direction) and along the Σ-line (Γ–K direction) in the upper pressure boundary of the FCC phase. The FCC structure shows a phonon instability around 40 GPa and a turnover of the T c before reaching this pressure. Similar phonon anomaly has been observed in BCC tellurium under high pressure. We discuss the origins of the soft phonon modes. The soft modes have much bigger line width than the other modes and contribute more to the electron phonon coupling constants. We have discussed the superconducting transition temperature on the basis of the Allen–Dynes formula, assuming phonon mediated superconductivity in those materials. The increasing phonon anomalies strongly dictate the direction of increasing T c in these materials. Calculated values of T c themselves show good agreement with experiments.