Charge density waves and the Coulomb correlation effects in Na2Ti2P2O ( P=Sb,As)

Abstract

To explore the origin of the phase transitions in ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}{P}_{2}\mathrm{O}$ ($P$ = Sb, As), we have investigated their band structures and phonon dispersions based on the $ab\phantom{\rule{4pt}{0ex}}initio$ density functional theory. We have found that the phonon softening instabilities occur for both compounds at q${}_{X}$ and q${}_{M}$, which lead to charge density wave (CDW) instabilities through the electron-phonon coupling. When the Coulomb correlation effect of Ti $d$ electrons is taken into account, the CDW transition to a $2\ifmmode\times\else\texttimes\fi{}1\ifmmode\times\else\texttimes\fi{}1$ supercell driven by the normal mode at q${}_{X}$ produces the most stable state for both compounds. In the CDW ground states, ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$ and ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}{\mathrm{As}}_{2}\mathrm{O}$ have the partial and full gap openings in the band structures, respectively, which are in good agreement with the observed transport and angle-resolved photoemission spectroscopy results. Our paper reveals that the Coulomb correlation effects of Ti $d$ electrons are essential to properly describe the CDW transitions in ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}{P}_{2}\mathrm{O}$.