Simulating Terahertz Field-Induced Ferroelectricity in Quantum Paraelectric ${\mathrm{SrTiO}}_3$

Recent experiments have demonstrated that light can induce a transition from the quantum paraelectric to the ferroelectric phase of ${\mathrm{SrTiO}}_3$. Here, we investigate this terahertz field-induced ferroelectric phase transition by solving the time-dependent lattice Schrödinger equation based on first-principles calculations. We find that ferroelectricity originates from a light-induced mixing between ground and first excited lattice states in the quantum paraelectric phase. In agreement with the experimental findings, our study shows that the nonoscillatory second harmonic generation signal can be evidence of ferroelectricity in ${\mathrm{SrTiO}}_3$. We reveal the microscopic details of this exotic phase transition and highlight that this phenomenon is a unique behavior of the quantum paraelectric phase.

Figure 1

THz field-induced ferroelectricity in ${\mathrm{SrTiO}}_3$. (a) Schematic image of the THz pulse applied to ${\mathrm{SrTiO}}_3$. (b) Schematic image of the atomic displacements involved in the FES mode ($Q_f$), lattice strain ($Q_c$), and AFD mode ($Q_a$). (c) Two-dimensional potential energy surface of ${\mathrm{SrTiO}}_3$ along with the FES mode and lattice coordinates. (d) Time profile of single-cycle THz pulse with 0.5 THz frequency. (e) Time profiles of the expectation value of the FES, AFD modes, and $c$-axis perturbed by the THz pulse. (f) Variation of the time-averaged lattice density perturbed by the THz pulse.

Figure 2

Mechanism of the THz field-induced phase transition from the quantum paraelectric state. (a) Time-averaged value of the FES displacement ($Q_f^{\mathrm{avg}}$) perturbed by a THz pulse in a wide range of intensities (top panel) and time profile of $Q_f$, $Q_c$, and $Q_a$ with a $650\mathrm{kV}/\mathrm{cm}$ pulse (bottom panel). (b) Schematic image of the phase transition from the quantum paraelectric state. (c) Ground and (d) first excited states of the quantum paraelectric phase in ${\mathrm{SrTiO}}_3$. Time profile of the SHG signal induced by a THz pulse with (e) $400\mathrm{kV}/\mathrm{cm}$ and (f) $650\mathrm{kV}/\mathrm{cm}$. In (a), the pink arrow indicates the result with $650\mathrm{kV}/\mathrm{cm}$ pulse. In (b), the red arrows reveal the THz field pulse-induced excitations of lattice wave function. In (e), the data of THz field-induced second harmonic signal with field strength $400\mathrm{kV}/\mathrm{cm}$ are obtained from Ref. [3] and their intensities are scaled for a qualitative comparison. The inset of (f) shows the relation between the SHG signal and the FES mode distortion evaluated by TDDFT calculations.

Figure 3

Effects of frequency and dissipation on THz-induced dynamics in ${\mathrm{SrTiO}}_3$. (a) Time-averaged value of FES displacement and (b) time profiles of $Q_f$, $Q_c$, and $Q_a$ at various THz frequencies $\omega$ and $\gamma =1.2\mathrm{THz}$. (c) Time-averaged value of FES displacement and (d) time profiles of $Q_f$, $Q_c$, and $Q_a$ at various dissipation rates $\gamma$ and $\omega =0.5\mathrm{THz}$. In (a) and (c), the pink arrows indicate the specific points for the time profiles in (b) and (d).