Charge density wave in LuP2In ( P=Pt , Pd) induced by electron-phonon interaction

Abstract

We have explored the origin of charge density wave (CDW) instabilities in ${\mathrm{LuPd}}_{2}\mathrm{In}$ and ${\mathrm{LuPt}}_{2}\mathrm{In}$ cubic-Heusler compounds, employing band structure and phonon dispersion calculations based on the ab initio density functional theory. We have found that, despite quite enhanced electronic susceptibilities along $\mathbf{q}=M\ensuremath{-}R$ for both compounds, the phonon softening instability occurs only for ${\mathrm{LuPt}}_{2}\mathrm{In}$ at $\mathbf{q}=M$, as is consistent with experimental result. We have demonstrated that the key factor inducing the CDW in ${\mathrm{LuPt}}_{2}\mathrm{In}$ is neither the Fermi-surface nesting nor the spin-orbit coupling strength but the electron-phonon interaction with large deformation potential at $\mathbf{q}=M$. In the CDW ground state, the Pt cubes are rotated within the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}1$ Heusler structure, retaining the mirror symmetry through all Lu-In planes, which results in the suppression of density of states of Pt $d$ band near the Fermi level.