Control of electronic states by a nearly monocyclic terahertz electric-field pulse in organic correlated electron materials

In this sub-section, we show that the amplitude of the ferroelectric polarization in the I phase of TTF-CA can be rapidly modulated by a THz electric field [35]. As already mentioned, SHG is the most effective probe to detect the change of the ferroelectric polarization amplitude induced by a THz electric field pulse. The experimental configuration of the THz-pulse pump SHG probe measurement is shown in figure 7(a). The measurement was performed in the reflection configuration with the polarization directions of the fundamental probe pulse (1.3 eV) and the THz pump pulse both parallel to the molecular stacking axis (the a-axis). When TTF-CA was irradiated with a 1.3 eV fundamental pulse without THz electric fields at 65 K, 2.6 eV SH light was emitted. The SH light intensity I_SHG was measured as a function of the input probe-pulse intensity at 1.3 eV, and the former was proportional to the square of the latter (not shown). This confirmation is important to avoid the saturation of SH light intensity and to execute accurate measurements.

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Next, we discuss the results of the THz-pulse pump SHG probe experiment. A typical result is shown in figure 7(b). The red line shows the electric-field waveform of the THz pump pulse (E_THz(t)). The origin (t = 0) is set to the time when the electric field has its maximum amplitude. In this case, the maximum electric-field amplitude was E_THz(0) = 36 kV cm⁻¹. The open circles in figure 7(b) show the time evolution of the change in the SH light intensity, ΔI_SHG(t)/I_SHG, which is in good agreement with that of E_THz(t) (the red line). This shows that ΔI_SHG(t)/I_SHG ∝ E_THz(t) and the macroscopic polarization P was instantaneously modulated by the THz electric-field pulse. ΔI_SHG(0)/I_SHG is 1.5% at E_THz(0) = 36 kV cm⁻¹. When the electric-field amplitude E_THz(0) is increased up to 415 kV cm⁻¹, ΔI_SHG(0)/I_SHG reaches ∼13% as shown in figure 7(c). The magnitude of the polarization modulation will be discussed later.

We next discuss the results of the THz-pulse pump optical-reflectivity probe measurements, from which important information about the nature of the THz-electric-field-induced polarization modulation can be obtained. Figure 8(a) shows the polarized reflectivity spectra in the visible region of TTF-CA, which are measured with the electric field of light perpendicular to the molecular stacking axis a (E⊥a). As this light polarization is almost parallel to the molecular plane, intramolecular (IM) transitions can be detected. The peak at ∼2.2 eV was assigned to the IM transition of TTF molecules. It is known that the energy position of this band depends sensitively on the degree of CT ρ [63]. As seen in figure 8(a), the peak energy of this band was 2.38 eV at 90 K in the N phase, 2.25 eV at 77 K and 2.24 eV at 4 K in the I phase. Such a shift of the peak energy reflects the change in the degree of CT ρ—that is, ρ ∼ 0.3 (90 K) to ∼0.53 (77 K) and ∼0.58 (4 K) [65]. In other words, the peak photon energy decreased with increasing ρ. Therefore, by measuring the reflectivity change ΔR/R in this region, the electric-field-induced changes in ρ, Δρ, could be evaluated.

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Figure 9(a) shows a schematic of THz-pulse pump optical-reflectivity probe spectroscopy. First, probe photon energy was set at 2.2 eV, the peak energy of the IM transition band of TTF in the I phase. The polarization of the probe pulse was perpendicular to the a-axis (E⊥a) and that of the THz pump pulse was parallel to the a-axis (E//a). The electric field waveform E_THz(t) of the THz pulse and its Fourier power spectrum are shown in figures 9(b) and (c) respectively. The maximum amplitude of the electric field is 38 kV cm⁻¹. In figure 9(d), the time evolution of the transient reflectivity change ΔR(t)/R at 78 K is shown by the blue circles. E_THz(t) is also shown by a thin solid line in a normalized scale. The time evolution of ΔR(t)/R near the time origin is very similar to that of E_THz(t). By changing the probe energy, similar measurements were performed (not shown). In figure 8(b), the maximum values of the reflectivity changes at the time origin, ΔR(0)/R, are plotted by orange circles as a function of the probe energy. These data agree well with the first derivative of the reflectivity dR/dE shown by the broken line, indicating the reflectivity change by the red shift of the reflectivity peak. This agreement demonstrates that ρ was increased by the THz electric field.

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To scrutinise the initial change of ΔR(t)/R, in figure 10(a) the ΔR(t)/R values reflecting the change in ρ are plotted as a function of E_THz(t) in the range of t_d = −1.5–1.5 ps. Clearly, ΔR/R are proportional to E_THz(t) and the change in ρ followed the change of the electric field with no time delay. These results suggest that the change in ρ induced by the electric field occurred via purely electronic processes without any structural change, and is attributable to the intermolecular fractional CTs within each dimeric DA pair.

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In the left part of figure 11, the possible CT processes by the THz electric field ((a) → (b) and (a) → (c)) are shown schematically. As seen in figure 9(d), ΔR(t)/R along the time origin is positive, indicating that Δρ and ΔP were positive. This means that the original polarization P is parallel to the THz electric field E_THz(0) at the time origin as shown in figure 11(b). Similar experiments were performed on several samples. In some samples, ΔR(t)/R was negative at the time origin, indicating that Δρ and P were negative. In those samples, P was antiparallel to E_THz(0), as shown in figure 11(c).

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Such a dependence of ΔR(0)/R on the relative directions of P and E_THz(0) can be ascertained more directly by rotating the direction of E_THz(0). By using two polarizers, the electric-field direction of E_THz(0) was rotated by ±90° as shown in figure 12(a). When the direction of E_THz(0) was reversed, the sign of ΔR/R, that is, the sign of Δρ was reversed. Thus, it was possible to increase or decrease the ferroelectric polarization by choosing the direction of the THz electric field relative to the polarization.

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Here, we discuss the evaluation of the magnitude of the polarization change ΔP and the change in the degree of CT ρ, Δρ, induced by the electric field at the time origin. These values can be calculated from the change of the SHG intensity or the reflectivity.

The SHG intensity change ΔI_SHG(0)/I_SHG due to a THz electric field with amplitude E_THz(0) = 36 kV cm⁻¹ was ∼1.5% (figure 7(b)) [35]. Assuming that the second-order nonlinear susceptibility χ⁽²⁾ is proportional to the magnitude of P, the relation of ΔI_SHG/I_SHG = 2 ΔP/P can be obtained from the relation, I_SHG ∝ P². From the value of ΔI_SHG(0)/I_SHG, ΔP(0)/P was estimated to be ∼0.75% at E_THz(0) = 36 kV cm⁻¹. When E_THz(0) is increased up to 415 kV cm⁻¹ (figure 7(c)), ΔP(0)/P reaches 6.5%. Thus, ultrafast and large polarization modulation was possible in TTF-CA using a strong THz electric-field pulse.

The reflectivity change in the steady state between 77 K and 4 K at 2.2 eV ((R_4K − R_77K)/R_77K = 6.2 × 10⁻²) corresponds to the change of the degree of CT Δρ ∼ 0.05. From this relation and the magnitude of the THz-electric-field-induced reflectivity change, ΔR(0)/R (∼3.1 × 10⁻³), Δρ was calculated to be ∼2.5 × 10⁻³ at E_THz(0) = 38 kV cm⁻¹. The original polarization P was produced by the collective CTs, δρ ∼ 0.2, from A to D molecules, which occurred across T_c. Therefore, the polarization change ΔP(0)/P from the magnitude of Δρ obtained by the THz-pulse pump optical-reflectivity probe measurements could be calculated. In this case, ΔP(0)/P was evaluated to be ∼1.25% at E_THz(0) = 38 kV cm⁻¹. Using the relation ΔP(0)/P ∝ E_THz(0), ΔP(0)/P was calculated to be ∼1.18% at E_THz(0) = 36 kV cm⁻¹, consistent with the value obtained from the SHG measurements (ΔP(0)/P ∼ 0.75%) at the same electric-field amplitude.

It is valuable to compare the observed response to the THz electric field with the polarization−electric field (P − E) characteristic previously reported. The P − E characteristic is schematically shown by the orange line in figure 10(b). The coercive field E_C is about 5 kV cm⁻¹ at 50 K [59]. By applying a static electric field larger than E_C, the polarization was reversed via movement of the domain wall. The response to the THz electric field was essentially different from that of the static electric field. The ΔR/R − E_THz curve shown in figure 10(a) can be regarded as the Δρ − E_THz curve as the right vertical axis was scaled by Δρ. Considering that the magnitude of the CT, δρ ∼ 0.2, across the NI transition determined the magnitude of the original polarization P, P + ΔP was proportional to (δρ + Δρ). Alternatively, the (δρ + Δρ) − E_THz curve corresponds to the P − E_THz curve. This P − E_THz curve is schematically shown by the blue line in figure 10(b). Since the motion of a ferroelectric domain wall is slow and its time scale is in the millisecond range [59], it did not move during a sub-picosecond change in the electric field within a THz pulse. This means that we can apply a large electric field only to the electronic system without inducing any motions of ferroelectric domain walls. Thus, we can conclude that a large and ultrafast polarization modulation is caused by electronic-state changes. Such a feature has also been theoretically demonstrated by H Gomi and collaborators [76].

In the time evolution of the reflectivity change ΔR(t)/R due to a THz electric field for t_d > 5 ps, a coherent oscillation was observed. As seen in figure 9(d), ΔR(t)/R in this time domain could not be reproduced by E_THz(t) alone. By subtracting the normalized THz waveform E_THz(t) from ΔR(t)/R, the oscillatory component ΔR_OSC(t)/R was extracted, and is shown by green circles in figure 9(e). A clear oscillation with a period of about 0.6 ps is shown. By means of wavelet analysis, the time dependence of the Fourier power spectra of the THz waveform E_THz(t), the reflectivity change ΔR(t)/R, and the oscillatory component ΔR_OSC(t)/R were obtained, and are shown as the contour maps in figure 9(f), (g), and (h) respectively. E_THz(t) ranged from 5–60 cm⁻¹ and was localised around the time origin. On the other hand, ΔR_OSC(t)/R had a monochromatic component at 54 cm⁻¹, which was observed even at t_d > 10 ps. The same component was also clearly observed in ΔR(t)/R. The oscillation mode with the same frequency was activated in the steady-state polarized Raman spectrum only in the I phase and assigned to the mode corresponding to the dimerization—that is, the stretching mode of DA dimers [35]. The coherent oscillation with the same frequency was also observed in the photoinduced N-to-I transition and is interpreted as the transient oscillation associated with dimerization of the photoinduced I states [69–71, 73, 75]. Therefore, it is reasonable to ascribe the coherent oscillation observed in figures 9(d), (e), (g) and (h) to the dimeric lattice mode or equivalently the optical mode. Since the reflectivity of the IM transition band of TTF molecules was used as a probe in this pump−probe experiment, the result indicates that coherent oscillation strongly modulated the degree of CT, ρ.

Taking into account the experimental results mentioned above, we discuss the origin of the coherent oscillation generated by the THz electric field. A possible mechanism is the direct excitation of the dimeric lattice mode by the THz electric field, since the THz pulse had a finite intensity at 54 cm⁻¹ (∼1.6 THz) as shown in figure 9(c). However, this possibility must be excluded, because the directions of the observed electric-field-induced displacements of the D and A molecules were opposite to those expected for displacement-type ferroelectricity. Figure 11 explains this in more detail. When the polarization P was directed left (figure 11(a)) and the THz electric field E_THz(0) was parallel to P, the direct excitation of the IR active lattice mode consists of the displacements of D (A) molecules in the left (right) direction as shown by the green arrows in figure 11(f). These molecular displacements led to an increase of the molecular distance between D and A molecules in each dimer. This decreased the Coulomb attractive interaction in each dimer, resulting in decreased ρ. Here, the first cycle of the oscillatory change in ρ in figure 9(e) was in good agreement with the initial rapid change in ρ (figure 9(d)) directly driven by the THz electric field. This result clearly shows that when E_THz(0) was parallel to P (figure 11(b)), the D (A) molecules moved antiparallel (parallel) to the original polarization P, as shown in figure 11(d). These results demonstrate that the dimeric lattice mode was not directly excited by the THz electric field.

The most plausible mechanism for the generation of the coherent oscillation is the modulation of the spin-Peierls dimerization via the rapid modulation of ρ. When the direction of E_THz(0) was parallel to P (figure 11(b)), ρ increased first to ρ + Δρ(t) via electronic processes, such that P increased as mentioned above. The increased ρ induced an increase of the spin moment in each molecule. Then, the spin-Peierls mechanism was more effective, and molecular dimerization was strengthened as shown in figure 11(d). The resultant increase of the molecular displacements further increased the degree of CT from ρ + Δρ to ρ + Δρ + Δρ' by the increase in the Coulomb attractive interaction within each dimer. Thus, the THz electric field gave rise to a forced molecular oscillation of the spin-Peierls mode via the change in ρ. Then, an additional oscillation in the degree of CT with amplitude Δρ' and in the polarization with amplitude ΔP' occurred, synchronised with the molecular oscillation, denoted as (d) ↔ (e) in figure 11. When the direction of E_THz(0) was antiparallel to the original polarization P as the case of figure 11(c), ρ first decreased and then oscillated coherently as denoted by (e) ↔ (d) in the same figure, triggered by the decrease in the dimeric molecular displacements (figure 11(e)).

In this mechanism, the time evolution of the oscillatory component ΔR_OSC(t)/R can be expressed by the following formula:

$$\begin{eqnarray}&&{\rm{\Delta }}{R}_{\mathrm{OSC}}(t)/R\propto {\int }_{-{\rm{\infty }}}^{t}{E}_{\mathrm{THz}}(\tau ){e}^{-(t-\tau )/{\tau }_{0}}\,\sin [{\rm{\Omega }}(t-\tau )]{\rm{d}}\tau .\end{eqnarray} \tag{ 2 }$$

Here, τ₀ and Ω are the decay time and the frequency of the oscillation, respectively. In this formula, we calculate the convolution integral of a damped sinusoidal oscillator with E_THz(t). This formula may be regarded as the forced oscillation of the optical mode driven directly by the THz electric field. However, we can show that the oscillation driven by the electric-field-induced modulation of ρ can also be expressed by the same formula [35]. By using this formula, we can precisely simulate the response to the electric field across the whole time region including the time domain around t = 0 ps. Using equation (2), the time evolution of ΔR_OSC(t)/R was almost reproduced with τ₀ ∼ 8.7 ps and Ω ∼ 54 cm⁻¹, as shown by the solid line in figure 9(e). Around t = 0 ps, a finite discrepancy exists between ΔR_OSC(t)/R and the fitting curve. This is probably caused by the errors in ΔR_OSC(t)/R around t = 0 ps. At t = 0 ps, the amplitude of the direct charge-modulation component is larger by about one order than that of the oscillatory component. As mentioned above, the oscillatory component ΔR_OSC(t)/R is extracted by subtracting the normalized THz waveform E_THz(t) reflecting the direct charge-modulation component from ΔR(t)/R, so that some errors are likely to appear in ΔR_OSC(t)/R around t = 0 ps.

Since the overall fitting is satisfactory, we can conclude that the coherent oscillation of the degree of CT ρ originates from the modulation of the spin-Peierls dimerizations due to the rapid change in ρ induced by the THz electric field.

In order to detect polarization generated by a THz pulse, the use of the THz-pulse pump SHG probe method is very effective. Since TTF-CA has no spontaneous polarization in the N phase, no SHG can be observed as schematically illustrated in the upper panel of figure 13(a). To evaluate the intensity of electric-field-induced SHG signals in the N phase, the following experimental procedure was performed. First, the intensity of the SHG signal was measured in the I phase at 65 K with no THz pulse irradiation. The photon energy of the incident probe pulse (the emitted SH pulse) is 1.3 eV (2.6 eV). The incident and emitted pulses are both polarized parallel to the a-axis. Those experimental conditions were the same as those used in the experiments described in the previous sub-section. Next, the temperature of the sample was increased up to 90 K in the N phase. The THz-pulse pump SHG probe measurement was then performed with the same intensity of the incident probe pulse (the lower panel of figure 13(a)). In this experimental procedure, the intensity of the THz-electric-field-induced SHG in the N phase was compared to that of the steady-state SHG signal in the I phase.

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Figure 13(c) shows the THz-pulse pump SHG probe measurements taken at 90 K. When the maximum amplitude of the THz pulse was less than 40 kV cm⁻¹, no electric-field-induced SHG signals were detected in the N phase [35]. As the electric field amplitude increased to 400 kV cm⁻¹ (figure 13(b)), the SHG signal was clearly observed as shown in figure 13(c). This indicates that a macroscopic polarization can be generated in the sub-picosecond time scale by a THz pulse. The intensity of the SH light at t_d = 0 ps, ΔI_SHG−90K(0), was 2.9% of the intensity of the steady-state SH light at 65 K in the I phase, I_SHG−65K. If it is assumed that the intensity of the SH light was proportional to the square of the polarization amplitude, the magnitude of the polarization induced by the THz pulse was ∼17% of the original polarization in the I phase (6.3 μC/cm²), since ΔI_SHG−90K(0)/I_SHG−65K ∼ (ΔP_SHG−90K(0)/P_SHG−65K)² ∼ 2.9%.

Next, we discuss the time evolution of the electric-field-induced SHG signal, ΔI_SHG−90K(t) shown in figure 13(c). The initial SHG signal from t_d = −0.3–0.3 ps is very similar to the square of the THz-electric-field waveform, (E_THz(t))², shown by the shaded area in the same figure. The observed relation of ΔI_SHG−90K(t)/I_SHG−65K ∝ (E_THz(t))² is reasonable, since TTF-CA has inversion symmetry in the N phase. The SHG signal follows (E_THz(t))² without delay, suggesting that CT processes between DA molecules would cause polarization generation similar to the polarization modulation by a THz pulse in the I phase. On the other hand, the time evolution of the SHG signal, ΔI_SHG−90K(t)/I_SHG−65K, for t_d > 0.3 ps was considerably different from (E_THz(t))²; an oscillatory structure is evident. Such a difference contrasts with the I phase, in which the change of SHG intensity, ΔI_SHG(t)/I_SHG, by a THz pulse was proportional to the THz electric field waveform except for a small contribution of the coherent oscillation associated with the lattice mode.

To interpret the response in the N phase, we performed THz-pulse pump optical-reflectivity probe spectroscopy focusing on the CT band in the near-IR region. The spectral shape of the CT band was sensitive to ρ, similarly to the IM transition band of TTF; the reflectivity from 0.6 eV to 1.35 eV increased with increasing ρ [77]. The time evolution of the reflectivity change ΔR(t)/R at 1.3 eV is shown in figure 13(d) as a typical example. Using the same probe photon energy (1.3 eV) is appropriate in comparing the time evolution of ΔR(t)/R and ΔI_SHG(t). The positive ΔR(t)/R signal indicates the increased ρ by the THz pulse. The shaded area in figure 13(d) also shows the square of the THz electric field, (E_THz(t))². The observed ΔR(t)/R near the time origin closely follows (E_THz(t))², as well as ΔI_SHG(t). This indicates that the electric-field-induced change in ρ occurred without delay and that the fractional CTs Δρ(t) from A to D molecules were responsible for the polarization generation ΔP(t). Such polarization generation by the THz electric field is similar to that of the spontaneous polarization generation across the NI transition. Figure 13(e) shows the temperature dependence of ΔR(0)/R reflecting the magnitude of the electric-field-induced increase of ρ and P. ΔR(0)/R increases with decrease of temperature down to T_c, showing a critical behaviour. For t_d > 0.3 ps, the time evolution of ΔR(t)/R deviates from the waveform of (E_THz(t))² and an oscillatory structure appeared, similarly to ΔI_SHG(t).

The analyses of the time evolution of ΔI_SHG(t) and ΔR(t)/R including the oscillatory components and their interpretations are complicated, thus we report here only the conclusion. Polarization generation by the THz pulse in the N phase can be ascribed to the coherent dynamics of tiny one-dimensional I domains fluctuating in the host N state, schematically shown in figures 14(a) and (b). Previous optical, dielectric, x-ray diffuse scattering, and transport measurements suggested that such I domains are generated even in the N phase because of the valence instability or the instability to the NI transition, and fluctuate in time and space [78–82]. To accurately estimate the amount of microscopic I domains, detailed IR molecular vibrational spectroscopy was performed (not shown). This revealed that ∼20% of molecules were ionised and existed as microscopic I domains at 90 K, just above T_c. Previous optical pump optical-reflectivity probe spectroscopy suggested that each I domain consisted of approximately ten DA pairs or 20 molecules at 90 K [71]. Such formation of microscopic I domains originated from the collective nature of I states due to long-range Coulomb attractive interaction.

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To explain the observed response to a THz electric field, consider two kinds of 1D microscopic I domains, I₊ and I₋, with opposite dipole moments, +μ and −μ respectively, shown in figure 14(b). The moment μ is large, since an I domain consists of approximately 10 DA pairs as mentioned above. In the absence of electric field, +μ and −μ cancel with each other and no polarization exists. When a THz pulse polarized along the a-axis is introduced to TTF-CA, not only does a fractional CT occur in each DA pair, increasing (decreasing) ρ by Δρ within the I₊ (I₋) domain, but also the I₊ domain, polarized parallel to E_THz(0), expands and the I₋ domain, polarized antiparallel to E_THz(0), shrinks as shown in figures 14(c) and (d), the total values of ρ and μ increase. Such expansion and shrinkage of an I domain occur via the motion of domain walls between microscopic N and I domains, called neutral-ionic domain walls (NIDWs) [83]. Thus, microscopic changes in μ in a number of I domains generate a large macroscopic polarization as illustrated in figure 14(e). This interpretation is consistent with the increase of ΔR(0)/R with decrease of temperature down to T_c shown in figure 13(e). Approaching T_c, the valence instability is enhanced and the electric-field-induced response is increased. The oscillatory response observed in ΔI_SHG(t) for t_d > 0.5 ps can be attributed to the subsequent breathing oscillation of NIDW pairs. The analyses revealed that the characteristic frequency of the breathing oscillation is changed from 32 cm⁻¹ at 170 K to 19 cm⁻¹ at 82 K. Such a softening can be explained by the fact that the energy difference between the N and I states decreases as the temperature approaches T_c. The details of the data and their analyses were reported in [37].

We first review the results of the THz-pulse pump SHG probe measurement to investigate the change of ferroelectric polarization P due to the THz electric field (E_THz(t)). As discussed in section 3.2, in general, the second-order nonlinear susceptibility χ⁽²⁾ determining the SHG process is proportional to the amplitude of the polarization P and, therefore, the intensity of SH light, I_SHG, is proportional to the square of P (I_SHG ∝ P²). From this relation, the electric-field-induced change of P, ΔP, can be derived from the change in I_SHG by the THz pulse.

Figure 16(a) shows the schematics of the THz-pulse pump SHG probe measurements; all the measurements were performed on the ab plane of α-(ET)₂I₃ and at 10 K in the CO phase. In the CO phase, two structures are possible, which are characterised as the right-handed structure or the left-handed structure as shown in the lower part of figure 16(a) [54]. Those structures in the CO phase cannot be discriminated without detailed structural analyses at low temperatures. The electric field (E) of incident (0.89 eV) and SH (1.78 eV) pulses are parallel to the a- and b-axis, respectively. In this combination of light polarizations, the intensity of SHG, I_SHG, is the highest [55].

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Figure 16(b) shows the time evolutions of the changes of the SH intensity, ΔI_SHG(t)/I_SHG. The upper and lower panels of figure 16(b) show the results for E_THz//a and E_THz//b respectively. The maximum electric field of the THz pulse, E_THz(0), is 60 kV cm⁻¹. The time characteristics of ΔI_SHG(t)/I_SHG are almost in agreement with the electric-field waveform of the THz pulse shown in the red lines in figure 16(b). In the initial change of SH light, no delay is observed. Thus, we can consider that the ferroelectric polarization completely follows the THz electric field and this feature originates from the electronic-type ferroelectricity of this compound. The electric-field-induced change ΔP of the polarization P can be evaluated from the value of ΔI_SHG/I_SHG via ΔI_SHG/I_SHG ∼ 2ΔP/P as mentioned in section 3.2. When the THz electric field is parallel to the b-axis, ΔI_SHG(0)/I_SHG is estimated to be 2.6% at E_THz(0) = 60 kV cm⁻¹. This gives ΔP(0)/P = 1.3%. This magnitude of the polarization modulation corresponds to ∼8.5% at E_THz(0) = 415 kV cm⁻¹, which is comparable to ∼6.5% at the same electric-field amplitude in TTF-CA.

To investigate the dynamical aspect of the polarization modulation by a THz electric field in more detail, THz-pulse pump optical-reflectivity probe measurements were performed. Figure 17(a) shows the polarized reflectivity spectra of α-(ET)₂I₃ [36]. The electric field of the light (E) is parallel to the b-axis (E//b). The red line and the black line represent the spectra in the metallic phase (136 K) and the CO phase (5 K) respectively. A broad band below 0.6 eV observed in the CO phase is assigned to the charge-transfer transition of localised electrons between ET molecules [96]. The green line in figure 17(b) is the differential reflectivity spectrum (R_136K − R_5K)/R_5K, which shows the spectral change when the CO is melted or weakened. Thus, the reflectivity in the near-IR to mid-IR region is sensitive to the molecular valence, so that it reflects the amplitude of the CO.

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Figures 18(a) and (d) show the schematics of the THz-pulse pump optical-reflectivity probe measurements and the electric field waveform of a THz pump pulse, respectively. The time evolutions of ΔR(t)/R at 0.65 eV for E_THz//a and E_THz//b are shown by yellow circles in figures 18(b), (e) and (c), (f) respectively. The time evolutions of ΔR(t)/R at around the time origin −0.5 ps < t_d < 0.5 ps are in good agreement with the THz electric-field waveform (the red lines) in figures 18(b), (c). Subsequently, the prominent oscillatory components appears at t_d > 0.5 ps (figures 18(e), (f)), although no THz electric field exists in this time domain.

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First, we discuss the initial response at −0.5 ps < t_d < 0.5 ps. The yellow circles in figure 17(b) show the probe energy dependence of ΔR(0)/R for E_THz//b. This spectral shape is in good agreement with the differential reflectivity spectrum, (R_136K − R_5K)/R_5K shown by the green line in the same figure. This suggests that the CO is weakened by the THz electric field at t_d = 0 ps. As mentioned above, the initial ΔR(t)/R signals at −0.5 ps < t_d < 0.5 ps completely follow the electric-field change (figures 18(b), (c)). This indicates that the molecular valence is rapidly modulated by the THz electric field via the intermolecular CTs and that the modulation of SHG or the polarization P shown in figure 16(b) occurs also via the same intermolecular CTs. These results also suggest that the ferroelectricity in α-(ET)₂I₃ is electronic in nature.

The modulation amplitude of the CO by the THz electric field can be evaluated by comparing ΔR(0)/R with the differential reflectivity (R_136K − R_5K)/R_5K. The difference in the charge, δρ, between charge-rich molecule A and charge-poor molecule A' is ∼0.4 in the CO phase at 20 K [54]. (R_136K − R_5K)/R_5K at 0.65 eV is almost equal to 53%. When the THz electric field with 31 kV cm⁻¹ is applied parallel to the b-axis, ΔR(0)/R at 0.65 eV is 0.46%. Therefore, the THz electric-field-induced change of the CO, Δρ/δρ, for E_THz(0) = 31 kV cm⁻¹ is calculated to be 0.46/53, that is, 0.87%. For E_THz(0) = 60 kV cm⁻¹, Δρ/δρ is estimated to be 1.68%, which is comparable to the change of the polarization ΔP(0)/P = 1.3% at 60 kV cm⁻¹ evaluated from the results of the SHG probe measurements.

As seen in figures 18(b), (c), the magnitude of the reflectivity change ΔR/R at t_d = 0 ps and at 0.65 eV for E_THz//b is twice as large as that for E_THz//a. This result seems to contradict with the simple prediction that the ferroelectric polarization is parallel to the a-axis mentioned above and suggests the possibility that the direction of ferroelectric polarization is diagonal in the two-dimensional ET layers on the ab plane.

To determine the direction of the ferroelectric polarization P, the dependence of the ΔR/R signals on the direction of the THz electric field was investigated. Figures 19(a) and (b) show the schematics of two possible CO patterns at low temperature [54]. They cannot be discriminated without detailed structural analyses on that crystal itself. Therefore, we must consider two possibilities. In figure 19(c), ΔR(0)/R at 0.65 eV is plotted as a function of the angle θ of the THz electric field measured from the b-axis. The experimental results are reproduced well by −cos(θ − 27°), shown by the red line. As shown in the inset of figure 19(c), ΔR(0)/R shows its minimum at θ = +27°. These results indicate that the polarization directs to the angle of +27° or −153° from b (−b)-axis. Since the amplitude of the polarization is decreased at θ = +27°, the polarization directs along −153° from b (−b)-axis.

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As mentioned above, the observed polarization modulation is attributable to the intermolecular CTs by the THz electric field. Therefore, it is natural to consider that the ferroelectric polarization itself would also be caused by collective CTs when the metal to CO transition occurs. This is similar to the formation of the ferroelectric polarization in the ionic phase of TTF-CA.

We next discuss the reason for the formation of the diagonal polarization. It is reasonable to consider that a fractional CT between two neighbouring molecules strongly interacting with each other is responsible for the ferroelectric polarization. In figure 19(a), the magnitude of the intermolecular transfer energy t is shown in the unit of eV [54]. t is relatively large along the diagonal directions, as shown by the solid green lines connecting A'−B−A and A'−C−A, which are inclined +157° and +27° from the b-axis, respectively. The direction of the polarization is considered to be −153° from the b (−b)-axis, so that the fractional CTs between A'−B and B−A are responsible for the polarization. Since the polarization is decreased at θ = +27° (figure 19(c)), we can conclude that the experimental condition is shown in figure 19(b) and the polarization is inclined −153° from the b (−b)-axis as shown by the white arrow in figure 19(b).

Here, we discuss the oscillatory components observed in the time evolutions of ΔR(t)/R at t_d > 0.5 ps in figures 18(e) and (f). They are considered to be the lattice modes driven by the THz electric field [35, 96]. To analyse the time evolutions of those oscillatory components, we adopted the following formula:

$$\begin{eqnarray}&&\frac{{\rm{\Delta }}R(t)}{R}=A\cdot {E}_{\mathrm{THz}}+\sum _{i=1}^{n}{B}_{i}\cdot {\int }_{-{\rm{\infty }}}^{t}{E}_{\mathrm{THz}}(\tau ){e}^{-\tfrac{(t-\tau )}{{\tau }_{i}}}\\ &&\,\,\times \,\sin ({\omega }_{i}(t-\tau )+{\phi }_{i}){\rm{d}}\tau .\end{eqnarray} \tag{ 3 }$$

Here, τ_i, ω_i and ϕ_i are the decay time, frequency and initial phase, respectively, of the oscillation denoted by i. The first term represents the instantaneous response proportional to the THz electric field E_THz(t) and the second term is a convolution of E_THz(t) and n damped oscillators. By assuming three damped oscillators (n = 3), the experimental results are well-reproduced as shown by the blue lines in figures 18(e) and (f). Each oscillatory component is shown in the lower parts of those figures. The frequencies ω_i of three oscillators are evaluated to be 12, 35, 43 cm⁻¹ for E_THz//a and 11, 32, 40 cm⁻¹ for E_THz//b. The errors in ω_i are very small (≤1%), while finite discrepancies between the experimental and calculated time evolutions of ΔR(t)/R exist. For those discrepancies, we suppose two reasons. First, a simple exponential decay might not be sufficient to reproduce the results. The decay of the oscillation would be caused by complicated processes including both the decay of amplitude itself and the disturbance of oscillation phase, so that a single exponential decay model might be too simple to reproduce the results. Second, besides the three oscillations included in the analyses, other weak oscillation modes might be generated. In this case, their oscillatory signals are superimposed on the reflectivity changes, which might cause the discrepancy.

In the polarized absorption spectra in the range 15–75 cm⁻¹, the corresponding peaks of ∼35 and ∼40 cm⁻¹ are observed, indicating that these oscillations are infrared-active molecular oscillations [36, 97]. Below 15 cm⁻¹, no absorption spectra are reported. The observed oscillations are considered to be caused by the initial CTs induced by the THz electric field, or directly driven by the THz electric field. The amplitudes of oscillatory components were as large as that of instantaneous response to the THz electric field. This suggests that in α-(ET)₂I₃, the electron-lattice interaction was significant and the CO phase was stabilised by the molecular displacements as well as by the repulsive intermolecular Coulomb interactions. In figure 19(b), the candidates of molecular displacements responsible for the oscillations observed in the time evolutions of ΔR(t)/R are indicated by green and orange arrows. Note that such large oscillations were not observed in the SHG probe measurements. This demonstrates that the ferroelectric polarization originates from the intermolecular CTs and the modulation of the polarization by the THz electric field were purely electronic in nature. Further, the molecular displacements and their oscillations driven by the THz electric field did not play dominant roles in polarization formation and modulation but dominated only the stabilisation of the CO and its modulation triggered by the THz-electric-field-induced CTs.

The studied material for the electric-field-induced Mott insulator to metal transition is κ-(ET)₂Cu[N(CN)₂]Br. Hereafter, this compound is abbreviated as κ-Br. This compound is located on the metal phase near the Mott insulator−metal boundary. It shows a metallic behaviour below 60 K and exhibits superconductivity below 10 K as shown by the blue line in figure 25(c) [134]. To prepare a Mott insulator near the Mott insulator−metal boundary, a thin single crystal of κ-Br is placed on the diamond substrate shown in the inset of figure 26(a). An electronic phase in κ-(ET)₂X can be controlled by the strain from the substrate, as was reported first by H M Yamamoto, M Suda and their collaborators [137–139]. When the temperature is decreased, the crystal experiences the negative pressure from the diamond substrate, since the expansion coefficient of κ-Br is much larger than that of diamond [140, 141]. As a result, κ-Br on the diamond substrate becomes a Mott insulator at low temperatures as shown by the red broken line, although the bulk crystal becomes metallic (figure 25(c)) [137, 138].

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The quantitative evaluation of the Mott gap is possible by the measurements of absorption (optical density: OD) spectrum. Figure 26(a) shows the OD spectra along the c-axis in the κ-Br single crystal on the diamond substrate at 10 K and 293 K, which was obtained using a Fourier transform IR spectrometer. The thickness of the crystal is 0.6 μm. The oscillations on the low-energy region below 0.15 eV are due to the interference of light in the diamond substrate. At 293 K, the OD value is finite at the lower energy bound of the measured range (0.01 eV) reflecting a high conductivity. In contrast, at 10 K, the OD value is equal to zero below 30 meV. This demonstrates that a clear Mott gap Δ_Mott ∼ 30 meV is open at 10 K.

To measure the OD spectrum below 10 meV, the THz time-domain spectroscopy was performed. The details of the experimental setup was reported elsewhere [142]. In this measurement, the phase shift of the THz wave transmitted through the sample was difficult to be determined, since it was very small. Therefore, the OD spectrum was calculated only from the transmission (T) spectrum using the relation OD_T = −log(T). The OD_T value does not include the reflection loss, so that it is slightly larger than the OD value. In figure 26(b), the OD_T spectrum from 20 meV to 2 meV at 293 K is shown by the black line. A monotonic interference pattern is observed, indicating that no absorptions exist in this region. These results demonstrate that in the thin crystal of κ-Br on the diamond substrate at 10 K is a Mott insulator with a Mott gap of 30 meV, below which it does not show any electronic or phonon absorption.

Now, we can proceed to the discussion about the results of THz-pulse-pump optical-absorption-probe spectroscopy on the thin crystal of κ-Br on a diamond substrate, which are summarised in figure 27. The inset of figure 27(b) shows the schematic view of the measurement. The electric-field waveform of a THz pump pulse used in the measurement is displayed in the inset of figure 27(c). The maximum electric-field amplitude, E_THz(0), is 180 kV cm⁻¹. The Fourier power spectrum of the THz pulse is shown by the red lines in figures 26(a) and (b). The comparison of this THz-pulse spectrum with the absorption spectrum of the sample demonstrates that the sample is completely transparent to the THz pulse. Thus, this sample is an appropriate choice to investigate the electric-field-induced carrier generations via the quantum tunnelling mechanism.

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Before the detailed discussions of the results, we refer to the spectral change between the metal phase and the Mott insulator phase at 10 K. Figure 27(a) shows the optical density spectra of a bulk κ-Br crystal in the metal phase (OD_M) and of the thin κ-Br crystal on the diamond substrate in the Mott-insulator phase (OD_I) at 10 K. The two spectra are different in the wide energy region from 0.9 eV down to 0.1 eV. The green line in figure 27(b) shows the differential OD spectrum, ΔOD(=OD_M − OD_I), which corresponds to the absorption change expected when a Mott insulator to metal transition occurs at 10 K. With decrease of the photon energy, ΔOD increases monotonically, which is the signature of the metallic state.

In the lower part of figure 27(c), we show the time evolutions of the absorption change ΔOD_THz at 0.124 eV for various maximum electric fields of THz pulses, which can be a measure of the metallisation. The absorption change ΔOD_THz is rapidly increased at t_d = 0 ps in all the electric fields in common. These initial rises in the signals seem to follow the square of the THz electric field shown by the red line in the upper part in figure 27(c). Subsequently, the ΔOD_THz signals show the fast decay up to ∼5 ps and the slower decay up to ∼100 ps. Moreover, oscillatory components are observed, which are ascribed to coherent molecular oscillations [143, 144].

To obtain information about the electronic-state changes, similar measurements were performed at various probe photon energies, and the spectrum of ΔOD_THz signals was obtained. The red circles in figure 27(b) show the probe-photon-energy dependence of the ΔOD_THz signals at t_d = 0.7 ps, at which the ΔOD_THz signals reach their maxima. This ΔOD_THz spectrum shows the decrease of the original absorption peak around 0.4 eV. Below 0.3 eV, the absorption increases monotonically as the photon energy decreases. This change of ΔOD_THz is quite similar to the differential absorption spectrum between the metal phase and the Mott insulator phase ΔOD, shown by the green line. Such a spectral change of ΔOD_THz clearly demonstrates that a Mott insulator to metal transition is induced by a THz electric field.

The absorption change ΔOD_THz is comparable to ΔOD_MI × 0.11 (ΔOD_MI = OD_M − OD_I). This indicates that the carrier number generated by the THz electric-field pulse is 11% of the carrier number in the metallic phase of a bulk crystal. In a bulk crystal, the effective carrier number was estimated to be 0.5 per dimer from the analyses of the steady-state optical conductivity spectrum [145, 146]. Hence, in the metallic phase induced by the THz pulse with E_THz(0) = 180 kV cm⁻¹, the carrier number is estimated to be 0.055 per dimer.

Here, we discuss the mechanism of carrier generation and metallisation by a THz electric-field pulse in κ-Br crystal on diamond substrate. A possible mechanism to be considered is the impact ionisation process observed in semiconductors [17–22]. We can exclude this possibility, since the κ-Br crystal has a clear Mott gap of 30 meV at 10 K and no carriers are originally introduced, as seen in figures 26(a) and (b). If some vibrational or lattice modes are directly excited by the THz pump pulse, the Coulomb repulsive energy U_d on each dimer is modified [147], which might give rise to the metallisation. This possibility can also be excluded, since no infrared-active modes exist below 2.5 THz (figure 26(b)).

The THz pulse is located in the transparent region, so that metallisation is attributed to the impulsive dielectric breakdown of the Mott insulator via doublon−holon pair production [122]. The Mott gap Δ_Mott(∼30 meV) is much larger than the THz-pulse photon energy (2–7 meV). Consequently, multiphoton processes are neglected. The most plausible mechanism involves quantum tunnelling between the lower Hubbard band and the upper Hubbard band, as mentioned in sub-section 4.1 (figure 21). This phenomenon corresponds to the Zener tunnelling in band insulators [115]. In the case of Mott insulators, doublon–holon pairs can be generated via similar tunnelling processes [122], which might lead to a Mott transition.

The electric-field dependence of absorption changes at 0.124 eV and at the time origin, ΔOD_THz(0), is plotted by black circles in figure 28(a). ΔOD_THz(0) values show a clear threshold behaviour. To see the ΔOD_THz(0) data at the low-electric-field region, we also show a logarithmic plot in figure 28(b). As mentioned in the previous sub-section, in the quantum tunnelling process in Mott insulators induced by a monocyclic THz pulse, the electric-field dependence of the carrier number N can be expressed by $N\propto {E}_{{\rm{THz}}}(0)\exp \left(-\pi \tfrac{{E}_{{\rm{th}}}}{{E}_{{\rm{THz}}}(0)}\right)$ with the threshold electric field E_th. The E_THz(0) dependence of ΔOD_THz(0) given in figures 28(a) and (b) (black circles) is in agreement with this formula with E_th = 64 kV cm⁻¹ as shown by the green broken lines. The correlation length ξ, which represents the effective distance of a doublon and a holon thus generated (see figure 28(c)), is given by $\xi =\tfrac{{{\rm{\Delta }}}_{\mathrm{Mott}}}{2{E}_{\mathrm{th}}}$ [122]. Using the Mott-gap energy of Δ_Mott = 30 meV and the threshold electric field of E_th = 64 kV cm⁻¹, ξ is evaluated to be 23 Å. This value is reasonable as a spatial extension of the electron wavefunction shown schematically by the yellow shaded area in figure 28(c), since it is approximately three times as large as the inter-dimer distance (7.7 Å) along the c-axis [134].

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As seen in figure 27(c), each absorption change ΔOD_THz is the maximum at t_d = 0.7 ps, which is considered as the end point of Mott transition. ΔOD_THz values at t_d = 0.7 ps are plotted by the red circles as a function of maximum electric field in figures 28(a) and (b). The scrutiny of figure 28(b) makes us notice that the electric field dependence of ΔOD_THz at t_d = 0.7 ps deviates from the formula of $\mathrm{\Delta OD}\propto {E}_{\mathrm{THz}}\exp \left(-,\tfrac{{E}_{\mathrm{th}}}{{E}_{\mathrm{THz}}}\right).$ Such a deviation is prominent at the lower electric-field region below E_THz = 70 kV cm⁻¹. It shows that finite time is necessary for the Mott insulator to metal transition after the carrier generation at t_d = 0 ps.

To obtain more detailed information about the dynamics of the Mott insulator to metal transition, we analyse the time evolution of ΔOD_THz for the strong electric-field case with E_THz(0) = 170 kV cm⁻¹ and the weak electric-field case with E_THz(0) = 45 kV cm⁻¹, which are shown in figures 28(d) and (e) respectively. The red line shows the waveform of $| {E}_{{\rm{THz}}}(t)| \exp \left(-\pi \tfrac{{E}_{{\rm{th}}}}{| {E}_{{\rm{THz}}}(t)| }\right)$ calculated from the THz electric-field waveform. This waveform denotes the possibility that a doublon–holon pair can be generated through the quantum tunnelling process. Note that the two waveforms shown by the red lines depend nonlinearly on the magnitudes of THz electric field and therefore are different from each other. The time evolution of ΔOD_THz for E_THz(0) = 170 kV cm⁻¹ in figure 28(d) shows no delay compared to the waveform of $| {E}_{{\rm{THz}}}(t)| \exp \left(-\pi \tfrac{{E}_{{\rm{th}}}}{| {E}_{{\rm{THz}}}(t)| }\right).$ On the other hand, the initial rise of ΔOD_THz(t) for E_THz(0) = 45 kV cm⁻¹ in figure 28(e) is delayed in comparison to ΔOD_THz(t) for E_THz(0) = 170 kV cm⁻¹ in figure 28(d). The time evolution of the latter is also shown by the broken orange line in figure 28(e) for comparison. To evaluate the rise time of ΔOD_THz(t), we performed a fitting analysis using the following formula:

$$\begin{eqnarray}&&{\mathrm{\Delta OD}}_{\mathrm{THz}}(t)={\int }_{-{\rm{\infty }}}^{t}| {E}_{\mathrm{THz}}(t^{\prime} )| \exp \left(-,\pi ,\frac{{E}_{\mathrm{th}}}{| {E}_{\mathrm{THz}}(t^{\prime} )| }\right)\\ &&\,\,\times \left\{\left[1,-,\exp ,\left(-,\frac{t-t^{\prime} }{{\tau }_{1}}\right)\right],\exp ,\left(-,\frac{t-t^{\prime} }{{\tau }_{2}}\right)\right\}dt^{\prime} .\end{eqnarray} \tag{ 5 }$$

The parameters of τ₁ and τ₂ show the rise time and the decay time of carriers responsible for the absorption change ΔOD_THz(t), respectively. The initial response of ΔOD_THz for E_THz(0) = 45 kV cm⁻¹ can be reproduced as shown by the blue line in figure 28(e) with a rise time τ₁ of 0.13 ps and decay time τ₂ of 2.4 ps. On the other hand, in the time evolution of ΔOD_THz(t) for E_THz(0) = 170 kV cm⁻¹, the delay of the initial response is not observed. In fact, ΔOD_THz(t) can be reproduced well by equation (5) with the rise time τ₁ = 0 ps.

The results of these analyses can be explained in the following way. When the electric field strength is low, the number of carriers generated via the quantum tunnelling processes at t_d ∼ 0 ps are relatively small, and thus the Mott gap does not collapse as shown in the middle part of figure 28(c). Subsequently, the Mott transition occurs in the period up to t_d = 0.7 ps with nonlinear increases in carrier population, as indicated by the arrow in figure 28(b). The rise time of the absorption change ΔOD_THz(t) for the weak electric field E_THz(0) = 45 kV cm⁻¹, 0.13 ps, is considered to be a characteristic time for the collapse of the Mott gap. It is natural to compare this characteristic time (0.13 ps) to the inter-dimer transfer energies. In κ-Br, two kinds of inter-dimer molecular overlaps with the transfer energy of 78 meV and 33 meV, the characteristic time of which is 0.05 ps and 0.12 ps, respectively [148, 149]. The latter time 0.12 ps almost accords with τ₁ = 0.13 ps, suggesting that the time scale of Mott transition would be determined by the smaller inter-dimer transfer energy.

After the electric-field-induced Mott insulator to metal transition occurred, an oscillatory structure was observed on the time evolution of absorption changes ΔOD_THz(t) (see the lower part of figure 27(c)). We briefly discuss the origin of this oscillation. Detailed analyses of the oscillatory component revealed that it consisted of three oscillation modes with the frequencies of 28 cm⁻¹, 37 cm⁻¹, and 46 cm⁻¹. We consider that these oscillation modes were related to the dimer structure characteristic of κ-type ET compounds and the corresponding molecular displacements stabilised the original Mott insulator state [143, 144]. When two molecules in a dimer neared each other, the intra-dimer transfer energy t_dimer increased. This led to an increase of the effective Coulomb repulsive energy U_d on each dimer, since U_d is equal to 2t_dimer [132, 133]. The enhancement of U_d made the Mott insulator state stable. When the electric-field-induced Mott insulator to metal transition occurred, these molecular displacements were released, giving rise to the coherent oscillations. Thus, the observation of the coherent oscillations suggests that the effect of the electron−lattice interaction cannot be neglected in κ-type ET compounds. As discussed here, a response to a strong THz electric field sometimes includes information about an important interaction hidden in the material.

Finally, we will compare the electric-field-induced Mott insulator to metal transition with a photoinduced transition. In the same thin single crystal of κ-Br on the diamond substrate, a photoinduced Mott insulator to metal transition was investigated using the near-IR pump pulse with the temporal width of 100 fs and the photon energy of 0.93 eV. After such a photoexcitation, the monotonic increase of the absorption change with decrease of photon energy similar to the ΔOD_THz signals (red circles in figure 27(b)) was observed (not shown). When the excitation fluence I_ex of the near-IR pump pulse was set to be the same as the THz electric-field pulse with E_THz(0) = 180 kV cm⁻¹, that is, I_ex = 7.7 μJ cm⁻², the number of carriers generated was found to be 0.018 per dimer. In other words, the carrier generation efficiency (0.055 per dimer) due to the THz pulse excitation is about three times as large as that due to the near-IR pulse excitation. This evaluation demonstrates that the THz-electric-field-induced carrier generation is fairly effective. In the case of the near-IR excitation, the pump photon energy (0.93 eV) is much larger than the Mott gap (30 meV), so that the initial photoexcited states have large excess energies, which will be transferred to phonons rather than used to excite other carriers. This is the reason why the carrier generation efficiency of the THz pulse excitation is higher than that of the near-IR pulse excitation.