Phase diagram of the ultrafast photoinduced insulator-metal transition in vanadium dioxide

We use time-resolved terahertz spectroscopy to probe the ultrafast dynamics of the insulator-metal phase transition induced by femtosecond laser pulses in a nanogranular vanadium dioxide (VO${}_2$) film. Based on the observed thresholds for characteristic transient terahertz dynamics, a phase diagram of critical pump fluence versus temperature for the insulator-metal phase transition in VO${}_2$ is established for the first time over a broad range of temperatures down to 17 K. We find that both Mott and Peierls mechanisms are present in the insulating state and that the photoinduced transition is nonthermal. We propose a critical-threshold model for the ultrafast photoinduced transition based on a critical density of electrons and a critical density of coherently excited phonons necessary for the structural transition to the metallic state. As a result, evidence is found at low temperatures for an intermediate metallic state wherein the Mott state is melted but the Peierls distortion remains intact, consistent with recent theoretical predictions. Finally, the observed terahertz conductivity dynamics above the photoinduced transition threshold reveal nucleation and growth of metallic nanodomains over picosecond time scales.

Figure 1

Photoinduced insulator-metal phase transition in VO${}_2$. (a) Low-temperature, monoclinic lattice associated with vanadium dimerization and insulating band structure. (b) High-temperature, rutile lattice with metallic band structure. Orange (gray)-filled regions of the band structure denote occupied states. Only vanadium ions are shown in the lattice structures. In the metallic state, each V is centered in an oxygen octahedron, which remains stationary across the transition. (c) Photoexcitation with 800-nm (1.55 eV) pump pulses results in the excitation of conduction electrons and the selective excitation of 6 THz phonons, which map the insulating lattice onto the metallic lattice. (d) Nucleated metallic nanodomains grow over time if sufficient structural relaxation in the form of a critical density of 6 THz phonons has been achieved in the surrounding region.

Figure 2

(a) Scanning electron microscope image of the nanogranular VO${}_2$ film. (b) DC conductivity of the film heated through the insulator-metal phase transition measured by four-point probe.

Figure 3

(a) Experimental setup for time-resolved THz spectroscopy of the VO${}_2$ film. The sample is mounted behind an aperture on a cold finger that can be cooled to 17 K. The insulator-metal phase transition is photoinduced in the VO${}_2$ film by an 800-nm, 100-fs optical pump pulse and then probed by a picosecond-duration THz probe pulse. (The 800-nm pump pulse, which is colinear with the THz probe pulse in the experiment, is displaced in the figure for clarity.) (b) The electric field of the transmitted THz probe pulse is modulated by free carrier absorption in the photoinduced metallic state. Reference and pumped waveforms indicate THz probe pulse transmission through the insulating state and photoinduced metallic state, respectively. The inset shows the THz pulse bandwidth.

Figure 4

Optical-pump/THz-probe dynamics of the ultrafast photoinduced metallic state in the VO${}_2$ film. The negative differential modulation of the THz pulse transmission, −Δ$T$/$T$, represents the photoinduced conductivity dynamics in the VO${}_2$ sample. THz conductivity dynamics at (a) 54.6 K and (b) 288.3 K illustrate the differences in onset and evolution of the metallic state at low and high temperatures, respectively, as a function of optical pump fluence. The THz conductivity dynamics at fluences of (c) 7.3 mJ/cm${}^2$ and (d) 11.0 mJ/cm${}^2$ illustrate the progression of the conductivity response as a function of temperature at constant fluence. The fast initial rise of the THz modulation signal is limited by the 0.5-ps time resolution of the time-resolved THz spectroscopy setup. After 0.5 ps, a slow rise in THz conductivity is observed at high temperatures and fluences. At low temperatures and fluences, an intermediate response emerges with no slow-rise behavior. The horizontal dashed line indicates the THz modulation observed for the fully metallic state at 350 K relative to the low-temperature, insulating state (Ref. 32). (e) Log-log plot of the slow rise THz conductivity dynamics at 295 K and 5.9 mJ/cm${}^2$ showing a crossover between two characteristic time scales at 20 ps following excitation. Black solid lines are guides for the eye. (f) The fluence dependence of the THz pulse-peak modulation at 5 ps pump-probe delay time reveals an increasing pump fluence threshold for the onset of the metallic state with decreasing temperature. (g) The difference between the THz pulse-peak modulation at 25 ps and 5 ps following optical excitation is used to estimate the magnitude of the slow-rise component. Above 180 K, the onset of the slow rise coincides with the metallic onset, but below 180 K the emergence of the slow rise occurs at larger fluences than the metallic threshold, indicative of intermediate metallic-state dynamics with no slow-rise character.

Figure 5

(a) Phase diagram of the ultrafast photoinduced insulator-metal transition of VO${}_2$. Regions A, B, C, and D are defined by their characteristic THz dynamics. Orange squares and black triangles indicate the thresholds for the appearance of the metallic state 5 ps and 25 ps after photoexcitation, respectively. Blue circles indicate thresholds for the onset of slow-rise dynamics. Filled navy blue diamonds denote the achievement of the fully metallic THz pulse modulation (−Δ$T$/$T$ ≥ 33.5$\%$) 5 ps following photoexcitation, while hollow brown diamonds indicate the fully metallic state is formed at 25 ps. Line 1 corresponds to the incident pump fluence needed to excite the metallic electron density at the front surface of the film (see text), while line 2 is the incident fluence required to raise the front surface 6 THz phonon population to the critical density. Line 3 indicates the incident fluence required to excite the critical 6 THz phonon density and supply the latent heat for the structural transition at the back surface of the film. Line 4 denotes the incident fluence required to directly photoexcite the critical electron density at the back surface of the film. As a result, region A represents the insulating state, region B represents the ultrafast photoinduced formation of the intermediate metallic state (Mott melting), region C represents the photoinduced nucleation and growth of the metallic state, and region D represents the ultrafast (<0.5 ps) photoinduced nucleation of the full metallic state throughout the film. The steady-state insulator-metal transition region is denoted by the hatched pattern. The incident fluences required to heat the front surface of the sample to 330 K (the start of the thermal transition), to raise the average temperature of the film to 350 K (including latent heat), and to raise the back surface temperature to 350 K (including latent heat) are indicated by the long-dashed line, short-dashed line, and dotted line, respectively. (b) Examples of THz conductivity dynamics taken along vertical cuts through the phase diagram at 80 K and 225 K.

Figure 6

Time-resolved terahertz spectroscopy of metallic nanodomain formation and expansion. (a) Examples of the real (squares) and imaginary (circles) photoinduced THz conductivity at 295 K for an incident fluence of 5.9 mJ/cm${}^2$ at various pump-probe delay times. Solid line are fits to the Drude-Smith model. (b) Pump-probe delay time dependence of the effective metallic nanodomain size, $d$, and (c) macroscopic electron density, $n$, extracted from the Drude-Smith fits at various pump fluences at 295 K. The average nanograin size in the film (94 nm) is denoted by a horizontal dashed line in (b) and the vertical dashed line marks a pump-probe delay time of 20 ps. Since the electron density is an average value for the film, a density less than the full metallic density [solid horizontal line in (c)] indicates that only a fraction of the film has undergone the transition to the metallic state.