Transient translation symmetry breaking via quartic-order negative light-phonon coupling at the Brillouin zone boundary in KTaO3

${\mathrm{KTaO}}_{3}$ presents a rich hyper-Raman spectrum originating from two-phonon processes at the Brillouin zone boundary, indicating the possibility of driving these phonon modes using intense midinfrared laser sources. We obtained the coupling of light to the highest-frequency longitudinal optic phonon mode ${Q}_{\text{HY}}$ at the $X\phantom{\rule{4pt}{0ex}}(0,0,\frac{1}{2})$ point by first principles calculations of the total energy as a function of the phonon coordinate ${Q}_{\text{HY}}$ and electric field $E$. We find that the energy curve as a function of ${Q}_{\text{HY}}$ softens for finite values of electric field, indicating the presence of ${Q}_{\text{HY}}^{2}{E}^{2}$ nonlinearity with negative coupling coefficient. We studied the feasibility of utilizing this nonlinearity to transiently break the translation symmetry of the material by making the ${Q}_{\text{HY}}$ mode unstable with an intense midinfrared pump pulse. We also considered the possibility that nonlinear phonon-phonon couplings can excite the lowest-frequency phonon coordinates ${Q}_{\text{LZ}}$ and ${Q}_{\text{LX}}$ at $X$ when the ${Q}_{\text{HY}}$ mode is externally driven. The nonlinear phonon-phonon couplings were also obtained from first principles via total-energy calculations as a function of the phonon coordinates, and these were used to construct the coupled classical equations of motion for the phonon coordinates in the presence of an external pump term on ${Q}_{\text{HY}}$. We numerically solved them for a range of pump frequencies and amplitudes and found three regimes where the translation symmetry is broken: (i) rectification of the lowest-frequency coordinates due to large amplitude oscillation of the ${Q}_{\text{HY}}$ coordinate about its equilibrium position, (ii) rectification of only the ${Q}_{\text{HY}}$ coordinate without displaced oscillations of the lowest-frequency coordinates, and (iii) rectification of all three coordinates. Due to the small magnitude of the coupling constant between the ${Q}_{\text{HY}}$ mode and the electric field, the smallest value of the pump amplitude that manages to transiently break the the translation symmetry of ${\mathrm{KTaO}}_{3}$ is 270 MV/cm. Such a large value of electric field will likely cause a dielectric breakdown of the material. However, our paper shows that light-phonon coupling with negative sign can exist in real materials and motivates the search of other materials with a larger magnitude of the coupling.