Theory of nonlinear phononics for coherent light control of solids

We present a microscopic theory for ultrafast control of solids with high-intensity terahertz frequency optical pulses. When resonant with selected infrared-active vibrations, these pulses transiently modify the crystal structure and lead to new collective electronic properties. The theory predicts the dynamical path taken by the crystal lattice using first-principles calculations of the energy surface and classical equations of motion, as well as symmetry considerations. Two classes of dynamics are identified. In the perturbative regime, displacements along the normal mode coordinate of symmetry-preserving Raman active modes can be achieved by cubic anharmonicities. This explains the light-induced insulator-to-metal transition reported experimentally in manganites. We predict a regime in which ultrafast instabilities that break crystal symmetry can be induced. This nonperturbative effect involves a quartic anharmonic coupling and occurs above a critical threshold, below which the nonlinear dynamics of the driven mode displays softening and dynamical stabilization.

Figure 1

Top: Sketch of the atomic displacements corresponding to the $A_g\left(9\right)$ Raman mode in ${\text{PrMnO}}_3$. A positive displacement drives the angle between octahedra (indicated by the arrow) closer to ${90}^{\circ }$, hence the structure closer to the cubic one. Middle: Total energy as a function of the $A_g\left(9\right)$ amplitude for several values of the $B_{1u}\left(54\right)$ amplitude. For visual clarity, we plot $V(Q_{\mathrm{R}},Q_{\mathrm{IR}})-V(0,Q_{\mathrm{IR}})$ so that all curves coincide at $Q_{\mathrm{R}}=0$. Bottom: $\text{LDA}+\text{DMFT}$ orbitally resolved density of states (spectral function) of Mn-$d$ states in PMO for the equilibrium orthorhombic crystal structure (insulator) and cubic crystal structure (metal).

Figure 2

Top: Sketch of the atomic displacements corresponding to the $B_{1g}\left(18\right)$ Raman mode in ${\text{La}}_2$${\text{CuO}}_4$, illustrating the symmetry between a negative and positive displacement. Bottom: Total energy as a function of the $B_{1g}\left(18\right)$ amplitude for several values of the $B_{3u}\left(41\right)$ amplitude. For visual clarity, we plot $V(Q_{\mathrm{R}},Q_{\mathrm{IR}})-V(0,Q_{\mathrm{IR}})$ so that all curves coincide at $Q_{\mathrm{R}}=0$.

Figure 3

Dynamics of the Raman mode in the case of a quartic coupling (as in LCO). Top panel: The four dynamical regimes in the undamped case [(a)–(d)]. Bottom panel: Dynamics below (e) and above threshold (f) in the presence of damping.