Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors

There has been a puzzle between experiments and theoretical predictions on the charge ordering of layered titanium-oxypnictides superconductors. Unconventional mechanisms to explain this discrepancy have been argued so far, even affecting the understanding of superconductivity on the compound. We provide a new theoretical prediction, by which the discrepancy itself is resolved without any complicated unconventional explanation. Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic $2 \times 2 \times 1$ one for BaTi$_2$As$_2$O, which has not yet been explained successfully so far, being different from tetragonal $\sqrt{2} \times \sqrt{2} \times 1$ for BaTi$_2$Sb$_2$O and BaTi$_2$Bi$_2$O. The electronic structure analysis can naturally explain experimental observations about CDW including most latest ones without any cramped unconventional mechanisms.