Investigation of the phonon dispersion associated with superlattice reflections in the BiS2 -based superconductor LaBiS2O0.5F0.5

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The phonon dispersion of a $\mathrm{Bi}{\mathrm{S}}_{2}$-based superconductor $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$ is investigated by first-principles calculations and inelastic x-ray scattering experiments. The origin of superlattice (SL) reflections arising from transverse-type lattice modulation, which were recently reported in [J. Kajitani et al., J. Phys. Soc. Jpn. 90, 103601 (2021)], is discussed in terms of lattice dynamics. Our first-principles calculations of phonon dispersion and the Fermi surfaces (FSs) demonstrate that the phonon mode corresponding to the transverse-type lattice modulation is unstable, and the propagation vector corresponding to the SL reflections is close to the FS nesting vector, which suggests that the phonon softening originates from the FS nesting. Against these calculated expectations, measured phonon dispersion in $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$ along the Z-A direction, where the SL point is located, shows no remarkable temperature dependence, and there are no steeply declining branches accompanied with a softening around the SL point. Based on these results, we discuss the two possibilities for the transverse lattice modulation in $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$: the order-disorder-type structural transition and the displacive structural transition with an overdamped mode, for both of which the local structure distortion or the short-range correlation within the $\mathrm{Bi}{\mathrm{S}}_{2}$ plane would be essential.