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.
Categories: cond-mat.str-el cond-mat.mtrl-sci