Structural instability and the Mott-Peierls transition in a half-metallic hollandite : K$_{2}$Cr$_{8}$O$_{16}$

In order to explore the driving mechanism of the concomitant metal-insulator and structural transitions in quasi-one-dimensional hollandite K$_{2}$Cr$_{8}$O$_{16}$, electronic structures and phonon properties are investigated by employing the {\it ab initio} density functional theory (DFT) calculations. We have found that the imaginary phonon frequency reflecting the structural instability appears only in the DFT+$U$ ($U$: Coulomb correlation) calculation, which indicates that the Coulomb correlation plays an essential role in the structural transition. The lattice displacements of the softened phonon at X explain the observed lattice distortions in K$_{2}$Cr$_{8}$O$_{16}$ perfectly well, suggesting the Peierls distortion vector {\bf Q} of X (0, 0, 1/2). The combined study of electronic and phonon properties reveals that half-metallic K$_{2}$Cr$_{8}$O$_{16}$, upon cooling, undergoes the correlation-assisted Peierls transition to become a Mott-Peierls ferromagnetic insulator at low temperature.