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Uniting the order and disorder dynamics in photoexcited VO2

Photoinduced phase transition (PIPT) is always treated as a coherent process, but ultrafast disordering in PIPT is observed in recent experiments. Utilizing the real-time time-dependent density functional theory (rt-TDDFT) method, here, we track the motion of individual vanadium (V) ions during PIPT in VO2 and uncover that their coherent or disordered dynamics can be manipulated by tuning the laser fluence. We find that the photoexcited holes generate a force on each V-V dimer to drive their collective coherent motion, in competing with the thermal-induced vibrations. If the laser fluence is so weak that the photoexcited hole density is too low to drive the phase transition alone, the PIPT is a disordered process due to the interference of thermal phonons. We also reveal that the photoexcited holes populated by the V-V dimerized bonding states will become saturated if the laser fluence is too strong, limiting the timescale of photoinduced phase transition.

time-dependent density functional theory (rt-TDDFT) method, here, we track the motion of individual vanadium (V) ions during PIPT in VO2 and uncover that their coherent or disordered dynamics can be manipulated by tuning the laser fluence. We find that the photoexcited holes generate a force on each V-V dimer to drive their collective coherent motion, in competing with the thermal-induced vibrations. If the laser fluence is so weak that the photoexcited hole density is too low to drive the phase transition alone, the PIPT is a disordered process due to the interference of thermal phonons. We also reveal that the photoexcited holes populated by the V-V dimerized bonding states will become saturated if the laser fluence is too strong, limiting the timescale of photoinduced phase transition. 2

Introduction:
Photoexcitation using ultrafast laser pulses provides a powerful approach to manipulate the material properties with a timescale in the limit of atomic motion 1-9 . It was believed that the atomic motion in the photoinduced phase transitions (PIPTs) is in collective coherent dynamics [10][11][12][13] . But, recent experiments show an ultrafast disordering of atomic motions in PIPTs of VO2 14 and Rb0.3MoO3 15 , challenging the conventional view of phase transitions. As an archetypical 3d-correlated oxide 16,17 , manipulating the transition from the monoclinic (M1) insulator phase to rutile (R) metallic phase in VO2, as shown in Fig. 1a and 1d, is a popular topic with numerous efforts that have focused on elucidating the evolution of both the electronic and lattice degrees of freedom. Photoinduced insulatorto-metal transition (IMT) is ultrafast with sub-femtosecond timescales 18,19 . Using a fourdimensional (4D) femtosecond electron diffraction to measure the evolution of the V-V dimers following the photoexcitation, P. Baum et al. 20 discovered that the motion of the V atoms is first along the direction of the V-V bond (a axis) with femtosecond timescales, then along the b and c axis within picosecond timescales, thus claiming a coherent structural transition from M1 to R phase. Besides, some experimental groups have reported that the PIPT in VO2 originates from a coherent motion of V-V dimers at 6 THz phonon mode 10,[21][22][23] . However, in a recent experiment, S. Wall et al. 14 used a femtosecond total xray scattering method beyond the general x-ray or electron diffraction 2,12,20,[24][25][26] to measure averages over many unit cells and they discovered the motion of V-V dimers is disordered in PIPT rather than a collective motion along the coherent phonon coordinate.
Besides the debate of atomic ordering or disordering in the phase transition, the timescale of M1-to-R phase transition in VO2 also has a major controversy. Early experiments reported the timescale of PIPT being gradually reduced from 100 fs to 40 fs 18 with increasing laser fluence 10,18,19 . However, M. R. Otto et al. 25  This has been attributed to disordered movements of the atoms, and M. R. Otto et al.
supported that the PIPT in VO2 should be viewed as a disordering or even melting transition 25 . How to consolidate these different experimental claims, both in order and disorder phase transition and in their corresponding timescales, is thus a major challenge in this field.
In this work, to investigate the coherent or disordered manner of atomic motion, we have utilized our newly developed rt-TDDFT algorithm 6,27,28 to simulate the PIPT in VO2.
We show that the phase transition is in atomic disordering with a timescale of about 200 fs 3 at low laser fluence and, at high laser fluence, becomes a coherent manner with a fluencedependent timescale below 100 fs. The disordering phase transition is driven by a combination of the atomic driving forces caused by photoexcitation and thermal phonon vibration. On the other hand, the coherent phase transition is only controlled by the photoexcited atomic driving forces, and the thermal phonon is only a small perturbation.
We also demonstrate that, with increasing the laser fluence, the smallest timescale of phase transition is indeed saturated to a minimum value of ~ 55 fs, which is due to the saturation of the population of the V-V bonding states by the photoexcited holes. Our findings provide a unified theory for understanding the atomic coherent and disordering motion in PIPT, uniting different experimental results.  Coherence and disordering of atomic motion. To simulate the photoinduced M1-to-R ultrafast phase transition, we utilize an 800 nm laser to pump electrons from valence bands to conduction bands of VO2 in our rt-TDDFT simulations. The initial lattice temperature is set to 50 K. In photoexcited simulations, we use an external electric field with a Gaussian shape ( Supplementary Fig. 1a), to simulate the laser pulse. Here, t0 = 17.5 fs, the pulse width √2 = 7 fs, and the photon energy  = 1.55 eV, which are consistent with experimental parameters 14,25 (see Method).
Besides, we use E0 to tune the laser fluence. With increasing E0 from 0.1 to 0.5, the photoexcited electrons from the valence band to conduction band gradually increase from 1.0% to 6.3% of valence electrons ( Supplementary Fig. 1b).
We show the evolution of V-V bonds to track the M1-to-R phase transition in To describe the degree of disorder in atomic motion, we define a disorder parameter The summation runs over V atoms, and n represents the number of V-V bonds. The xi, yi, and zi represent V-V bond length in x, y, z directions. The xave, yave and zave represent the average V-V bond length in x, y, z directions. Fig. 2b and Supplementary Fig. 2b shows the change within the timescale of phase transition in different electronic excitations.
At 1.0% electronic excitation, the disordered degree has rapidly reached 0.2 Å before the M1-to-R phase transition. However, the disorder degrees are less than 0.1 Å in other higher excitations. Remarkably, the higher electronic excitation does not increase the disorder at the phase transition point, it decreases it a little bit. We can thus conclude that the electron excitation does not induce disorder. We next proceed with the fast Fourier transform (FFT) for V-V bonds to obtain phonon modes of V atomic motion. Three low-frequency phonon modes from atomic vibrations are discovered at 0.7, 1.8, and 2.9 THz at 1.0% excitation (Fig. 2c). The chaotic phonon modes with three peaks further confirm the disordered process of phase transition at the 1.0% excitation. We only find a single peak between 4-5.5 THz at all higher excitations ( Fig. 2c and Supplementary Fig. 2c). These highfrequency modes are generally called coherent phonons in experimental literature 10,21,22 , and they are attributed as the cause for the coherent PIPT.   Fig. 4). Overall, we discover that the photoexcited holes result in a driving force acting on V-V dimers ( Fig. 4c and 4d), which The driving force induced by photoexcitation can create a coherent atomic motion.
However, we observe a disordering behavior in M1-to-R phase transition in 1.0% excitations. To distinct the different factors, we re-done the rt-TDDFT calculations with the same excitation but at the lattice temperature (T = 1 K) to exclude the interference of thermal phonons. In 1.0% excitations, the long bonds (dI) and short bonds (dII) scarcely change (no M1-to-R phase transition) within 1.0 ps because the coherent driving forces induced by the lower excitation are not enough to create the phase transition by themselves ( Supplementary Fig. 5a). This illustrates that the structural transformation needs the assistance of thermal phonons at a low excitation level. In 2.3% excitations at T = 1 K, the long bonds (dI) and short bonds (dII) gradually become the same value at 850 fs ( Supplementary Fig. 5b), demonstrating that, in this case, the phase transition is dominated by the coherent driving force, instead of the thermal phonon. We thus have two different cases: at lower fluence, the phase transition needs the help of thermal phonon, and the atomic movement appears to be disorder; at higher fluence, the phase transition can be driven by the coherent atomic movement alone, thus the atomic movement appears to be order and coherent.  (Fig. 4a). As a result of this, the driving force acting on the V-V dimers is bounded by an upper limit, which determinates the fastest dissociation speed of V-V dimers.

Discussion
In the work, we have observed the coherent and disordered phase transition for the M1-to-R phase transition which strongly depends on the number of photoexcited carriers.
The disordered process happens within 190 fs in a lower photoexcited density where the thermal phonons are an important factor to make the phase transition possible. During the disordered process, the force direction on vanadium atoms has changed with time due to the effect of thermal phonons (Fig. 4e). The disordered phase transition mechanism and the transition timescale are consistent with the experimental 14,25 and AIMD results within 0.9% electronic excitations 14 . In a higher photoexcitation, the phase transition tends to a coherent dynamic with the coherent phonon mode, and the thermal phonons are only a small perturbation. This is caused by the increase of photoexcited electrons, which produces a larger driving force (Fig. 4f). The timescale of phase transition is also reduced to 100 fs, corresponding to the coherent dynamics reported by the previous experiments of VO2 10 . With the further increase of photoinduced carriers, the coherent phonon mode gradually arrives at a saturation (~ 5.5 THz) which limits the atomic speed and the timescale of the phase transition (~ 55 fs). Such saturation has been reported experimentally for VO2 10,18 . Here, we have theoretically illustrated that the phenomenon is from the saturation of hole number on V-V dimers bond states. We believe these phenomena should also exist in other phase-transition materials, such as TiSe2, TaS2, and In atomic wires on Si surfaces [34][35][36] . Our simulations not only solve the experimental controversies but also provide a powerful view to understand the pathway of ultrafast phase transition by laserpulse excitations.

12
Method: Computational details. We do the static calculations and rt-TDDFT simulations by the ab-initio package (PWmat) 37 Here, ( ) represents the nuclear positions and ( ) represents the charge density.
In equation (4), the evolution of the wave functions ( ) is changed to the evolution of the coefficient , ( ) . In equation (5), a linear-time-dependent Hamiltonian (LTDH) is applied to represent the time dependence of the Hamiltonian within a time step. Thus, our rt-TDDFT simulation has a much larger time step (0.1 fs) than the conventional rt-TDDFT (sub-attosecond).
To mimic the photoexcitation, we introduce a uniform A field in reciprocal space 40 ,