Electronic structure and phonon instabilities in the vicinity of the quantum phase transition and superconductivity of(Sr,Ca)3Ir4Sn13

Abstract

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$_4$Sn$_{13}$ lie at phonon modes of wavevectors $\mathbf{q}=(0.5,0,0)$ and $\mathbf{q}=(0.5,0.5,0)$. Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of -14.1 meV and -9.0 meV per formula unit respectively. However, the application of chemical pressure to form Ca$_3$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 Ca$_3$Ir$_4$Sn$_{13}$. The evolution of these lattice instabilities is consistent with experimental phase diagram. The structural distortion associated with the mode at $\mathbf{q}=(0.5,0.5,0)$ 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.