Directional Forces by Momentumless Excitation and Order-to-Order Transition in Peierls-Distorted Solids: The Case of GeTe

Time-dependent density-functional theory molecular dynamics reveals an unexpected effect of optical excitation in the experimentally observed rhombohedral-to-cubic transition of GeTe. The excitation induces coherent forces along [001], which may be attributed to the unique energy landscape of Peierls-distorted solids. The forces drive the $A_{1g}$ optical phonon mode in which Ge and Te move out of phase. Upon damping of the $A_{1g}$ mode, phase transition takes place, which involves no atomic diffusion, defect formation, or the nucleation and growth of the cubic phase.

Figure 1

Atomic motifs of (a) $c$-GeTe and (b) $r\text{−}\mathrm{GeTe}$. (c) The supercell used in simulation. The rhombohedral primitive cell is highlighted by larger balls.

Figure 2

(a) Partial density of states (PDOS). Shaded areas indicate a rough estimate on what would be the occupations of the states upon a 5% excitation. (b) Potential energy surfaces (PESs). Gray line is the ground state, whereas the purple line is the excited state. (c) Atomic forces (red arrows) due to excitation. Graded green color indicates the positions of the Ge atoms (solid is in front and faint is in the back). Charge density difference between ground and excitation states is also shown on a plane cutting through the center of the primitive unit cell, as shown by the solid blue line in (d) and (e). The unit of CDD is $e/a_0^3$, where $a_0$ is the Bohr radius.

Figure 3

Time evolution of average (a) force, (b) bond length, and (c) angle and (d) ionic temperature of GeTe with a 5% excitation. Red solid and black dashed lines in (d) indicate, respectively, the melting point ($T_m$) and Curie temperature ($T_{r-c}$) for ferroelectric transition taken from literature [30, 31].

Figure 4

Time evolution of bond-length probability density distribution after excitation. Time taken for the plot corresponds to peaks and valleys in Fig. 3 at which the differences in bond lengths are largest. Dashed lines are Gaussian fitting with peak positions at 2.84, 3.02, and 3.25 Å, respectively. It appears that the central green line will further grow at the expense of others for $t>1053\mathrm{fs}$.

Figure 5

Trajectories of atomic motion in the time frame from 0 to 1.2 ps in the TDDFT-MD simulation with a 5% excitation.