Electronic structure and phonon instabilities in the vicinity of the quantum phase transition and superconductivity of (Sr, Ca) ₃ Ir ₄ Sn ₁₃

The nature of the lattice instability connected to the structural transition and superconductivity of (Sr,Ca)₃ Ir ₄ Sn ₁₃ is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a function of chemical and hydrostatic pressure show that the primary lattice instabilities in Sr ₃ Ir ₄ Sn₁₃ lie at phonon modes of wave vectors q=(0.5,0,0) and q=(0.5,0.5,0). Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of -14.1 and -9.0 meV per formula unit, respectively. However, the application of chemical pressure to form Ca₃ Ir ₄ Sn ₁₃ reduces the energetic advantage of these instabilities, which is completely removed by the application of a hydrostatic pressure of 35 kbar to Ca₃ Ir ₄ Sn ₁₃. The evolution of these lattice instabilities is consistent with the experimental phase diagram. The structural distortion associated with the mode at q=(0.5,0.5,0) produces a distorted cell with the same space-group symmetry as the experimentally refined low-temperature structure. Furthermore, calculation of the deformation potential due to these modes quantitatively demonstrates a strong electron-phonon coupling. Therefore, these modes are likely to be implicated in the structural transition and superconductivity of this system.