Abstract
Dynamical localization, that is, reduction of the intersite electronic transfer integral t by an alternating electric field, E(ω), is a promising strategy for controlling strongly correlated systems with a competing energy balance between t and the Coulomb repulsion energy. Here we describe a charge localization induced by the 9.3 MV cm^{−1} instantaneous electric field of a 1.5 cycle (7 fs) infrared pulse in an organic conductor α(bis[ethylenedithio]tetrathiafulvalene)_{2}I_{3}. A large reflectivity change of >25% and a coherent charge oscillation along the time axis reflect the opening of the charge ordering gap in the metallic phase. This optical freezing of charges, which is the reverse of the photoinduced melting of electronic orders, is attributed to the ~10% reduction of t driven by the strong, highfrequency (ω≧t/ħ) electric field.
Introduction
Ultrafast control of conduction and magnetic properties in strongly correlated systems^{1,2,3} has been extensively studied from the perspective of photoinduced insulatortometal transitions, or, equivalently, the ‘melting’ of electronic orders (red arrow in Fig. 1a) in Mott insulators^{4,5,6,7,8,9,10}, chargeordered (CO) systems^{11,12,13,14} and charge/spin density wave materials^{6,15,16,17,18,19,20}. Recently, the excitation of coherent phonons has been established as a leading strategy for the melting/constructing of electronic orders^{8,9,15,16,17,18,19,20}. On the other hand, the development of strong electric fields (>MV cm^{−1}) of fewcycle optical pulses and recent theoretical studies using dynamical meanfield theory suggest that extreme nonequilibrium electronic states, such as Floquet states, negative temperatures and superconducting states^{21,22}, can be achieved.
In highly nonequilibrium phenomena, reducing the intersite transfer integral t by modulating the site energy under strong continuouswave (CW)^{21,23,24,25,26} and pulsed^{22,26} alternating current (AC) fields E(ω), shown in Fig. 1b, plays an important role. Such an intense modulation of the electronic structure driven by a strong electric field, referred to as ‘dynamical localization’, provides a new strategy for controlling charge motion in strongly correlated materials, which have a competing energy balance between the onsite or intersite Coulomb repulsion and t (ref. 27).
Our target material is a layered organic conductor, α(ET)_{2}I_{3} (ET: bis[ethylenedithio]tetrathiafulvalene), which exhibits a thermal (equilibrium) metaltoCO insulator transition at T_{CO}=135 K (refs 28, 29, 30, 31, 32) and a photoinduced (nonequilibrium) transition^{14} as illustrated in Fig. 1a. Efficient photoinduced insulatortometal transitions of >200 ET molecules/photon have previously been demonstrated^{14}. However, the optical response of the metallic phase at T>T_{CO} remains unclear.
In this study, we perform pumpprobe transient reflectivity measurements for the metallic phase of α(ET)_{2}I_{3} using 7 fs 1.5 cycle infrared pulses. Our results demonstrate the optical freezing of charges or, equivalently, photoinduced charge localization in the metallic phase (blue arrow in Fig. 1a). We discuss the mechanism on the basis of theories that have been proposed for nonequilibrium states generated by highfrequency CW and pulsed AC fields.
Results
Thermal metaltoCO insulator transitions
The optical conductivity in the mid and nearinfrared region in Fig. 2a has a clear opening of the CO gap at ~0.1–0.2 eV and a spectral weight transfer to a higher energy at the thermal metaltoinsulator transition^{29,30}. Figure 2b shows the steadystate reflectivity (R) at 140 K (metal: solid red curve) and 40 K (CO: dashed blue curve). As shown in Fig. 2d, at T_{CO}, R abruptly decreases for 0.09 eV (open circles) and increases for 0.64 eV (closed circles) as the temperature decreases. Such a large change (80% at 0.64 eV, 60% at 0.09 eV) in R at the metaltoinsulator transition directly corresponds to the opening of the CO gap and the transfer of the spectral weight to a higher energy of the optical conductivity^{29,30}, as shown in Fig. 2a. Figure 2c shows the spectral differences at different temperatures. The solid curve shows [R(40 K)−R(140 K)]/R(140 K), reflecting the metaltoinsulator change across T_{CO}. The dashed and dashed–dotted curves show [R(190 K)−R(140 K)]/R(140 K) and [R(170 K)−R(140 K)]/R(140 K), exhibiting increases in the electronlattice temperature up to 190 and 170 K, respectively. Thus, the marked increase of R at >0.55 eV (blue shading) clearly characterizes the metaltoinsulator change across T_{CO}, whereas the rise of the electronlattice temperature is detected as a reflectivity decrease below 0.65 eV.
Photoinduced charge localization
Figure 3a shows the transient reflectivity (ΔR/R) spectra for time delays (t_{d}) of 30 fs (closed blue circles for an excitation intensity I_{ex}=0.8 mJ cm^{−2}, open blue circles for I_{ex}=0.12 mJ cm^{−2}) and 300 fs (closed black circles for I_{ex}=0.8 mJ cm^{−2}) after excitation by a 7fs pulse covering the spectral range 0.6–0.95 eV. The spectrum shown by crosses represents ΔR/R at t_{d}=300 fs after a 100fs pulse excitation for I_{ex}=0.8 mJ cm^{−2}. A large increase of R (ΔR/R=0.28 at 0.66 eV) was observed at t_{d}=30 fs for I_{ex}=0.8 mJ cm^{−2}, as shown by the blue shading in Fig. 3a. The spectral shape of ΔR/R is analogous to that of the temperature differential spectrum [R(40 K)−R(140 K)]/R(140 K) in Fig. 2c, suggesting that a photoinduced metaltoinsulator change occurred. In contrast, as shown by the crosses, the black closed circles and the red shading, the spectral shapes and the magnitude of ΔR/R measured at t_{d}=300 fs are analogous to the differential spectrum [R(190 K)−R(140 K)]/R(140 K), reflecting an increase in the electronlattice temperatures up to 190 K. In such a time domain (300 fs), the lattice system cannot be thermalized and a quasithermalized state is formed as a result of the interaction between the charge and various shortperiod vibrational and optical phonon modes. Therefore, the lattice temperature shown in the reflectivity spectrum at t_{d}=300 fs can be defined as a local temperature consisting solely of shortperiod modes. For I_{ex}=0.12 mJ cm^{−2}, the ΔR/R spectrum shown by the open blue circles indicates that the metaltochargelocalized change does not occur under weak excitation conditions.
Chargeordering gap oscillation along the time axis
The temporal change of the ΔR/R spectrum is plotted as a twodimensional (probe energy—delay time) map in Fig. 3b. Positive and negative ΔR/R are shown by the blue and red shadings, respectively. The spectrum for t_{d}<50 fs, reflecting the transient CO state, oscillates with a period of 20 fs as indicated by the red dotted lines. Then, the spectral shape of ΔR/R markedly changes with the melting of the transient CO and the increase of electron/lattice temperatures shown as the red area in the time scale of 50–100 fs. Such spectral change occurs simultaneously as the oscillation decays. The time profile of ΔR/R sliced at 0.64 eV is shown in Fig. 4a. A positive ΔR/R (solid curve with blue shading) at I_{ex}=0.8 mJ cm^{−2} persists for t_{d}=50 fs after the excitation pulse. Then, ΔR/R becomes negative (red shading), indicating that the photoinduced CO state collapsed because of the increase of electronlattice temperature. In contrast, for I_{ex}=0.12 mJ cm^{−2}, a positive signal was not detected at 0.64 eV, as shown by the dashed–dotted curve. It is worth noting that the time profile was modulated by the oscillating component with a period of 20 fs. This oscillation, shown in Fig. 4b, can be attributed to the intermolecular charge oscillation reflecting the CO gap, because the timeresolved spectrum of the oscillating component at t_{d}=0–40 fs obtained by the wavelet (WL) analysis (blue curve, inset of Fig. 4b) corresponds to the optical conductivity spectrum near the CO gap of ~0.1 eV at 10 K (black curve in the inset).
Although the C=C vibration energy is near the CO gap^{29,30}, the vibrational contribution can be detected separately after t_{d} >50 fs, that is, the wavelet spectra at t_{d}=80–120 fs indicated by the red curve in the inset of Fig. 4b shows a dip at ~0.15 eV (which equals the vibration peak of the optical conductivity at 140 K (refs 29, 30) in the inset) reflecting the destructive interference between charge motion and vibration^{33}. Therefore, the intense 20 fs oscillation detected before the appearance of the chargevibration interference dip is attributed to the oscillation of the CO gap. Such CO gap oscillation has been detected in the precursor step to the CO melting^{33}, although the amplitude was much smaller (<1% of the ΔR/R signal) than the present case. Because of the ultrafast decay within 50 fs (corresponding to the energy scale of ħ/50 fs=0.08 eV) of the photoinduced state, we cannot verify the insulating gap below 0.1 eV. However, the gaplike spectral shape at 0.1–0.2 eV, as described above, clearly indicates that the charge motion on the corresponding energy scale is frozen as if the charge distribution on the ET molecules were analogous to that in the CO insulator. In this limited sense, the CO gap is regarded as opened.
Considering that the chargevibration interference dip appears after the photoinduced charge localization occurs, the vibrationinduced mechanism is ruled out, that is, the charge localization is driven by the electronic interaction, although vibration may play some role in stabilizing the transient CO state. Here the lifetime of the transient CO state (<50 fs) is much shorter than that of the coherent phononinduced state (~1 ps or longer), which has been reported as the melting of a Mott insulator^{8,9} or the ordering of the transient spin density wave^{19,20}. Such a short lifetime indicates that the transient CO state is not adequately stabilized by vibrational and lattice motions.
From ΔR/R=0.28 at 0.64 eV and the temperature difference [R(40 K)−R(140 K)]/R(140 K)=0.8 at the same energy, the volume fraction of the photoinduced CO state is evaluated to be ~35%. As I_{ex}=0.8 mJ cm^{−2} corresponds to ~0.0145 photons/ET molecule, the efficiency of this process is 25 ET/photon. This is much lower than that for photoinduced melting of the CO state(>200 ET/photon^{14}), demonstrating that the mechanism of the photoinduced charge localization is completely different from that of the insulatortometal transition.
Discussion
Figure 5a shows ΔR/R at 0.64 eV as a function of the instantaneous electric field for various temperatures. An increase in R (positive ΔR/R) is detectable only for I_{ex}>0.31 mJ cm^{−2} (E_{0}=5.8 MV cm^{−1}) at 138 K, whereas the negative ΔR/R for I_{ex}<0.31 mJ cm^{−2} is due to the rise in the electronlattice temperature. As shown in the inset, the efficiency of the photoinduced charge localization becomes larger near T_{CO}. We can evaluate the positive component of ΔR/R by subtracting the negative component of the time profile shown in Fig. 4a, assuming that the negative component grows exponentially along the time axis (the dashed red curve in Fig. 4a). The resultant positive component exhibits a nonlinear increase as a function of E_{0}, as shown in Fig. 5b.
In nonequilibrium states induced by a strong AC field E(ω), t is reduced for CW^{21,23,24,25} and pulsed^{22,26} light. According to the dynamical localization theory^{23,24,25,26} for a CW AC field, the effective t (= t′) can be represented as,
where t_{0} is the transfer integral for zero field. Here, Ω_{AB}≡e r_{AB}·E_{0}/ħ, where E_{0} and ω, respectively, denote the amplitude and angular frequency of the electric field of the light; E(t)=E_{0} sin(ωt); r_{AB} is the vector from the A site to its nearestneighbour B site of α(ET)_{2}I_{3}, as shown in Fig. 1a; and e is the elementary charge. Equation (1) is satisfied for CW light. In addition, on the basis of the numerical solution of the timedependent Schrödinger equation for the twosite tightbinding model and a model for a CO molecular conductor^{26}, this relation has recently been shown to be satisfied by pulsed light, with respect to the efficiency of the intersite electronic transition (that is, the energy increment due to the pulsed light). Also, in the dynamical meanfield theory calculations, the change in the electronic state into one with modified t appears within the time scale of a few optical cycles after the sudden application of a CW AC field^{21}. This fact also suggests that the dynamical localization functions transiently with the fewcycle pulse. If we use the parameter r_{AB}cosθ=5.4 angstroms (refs 34, 35); where θ represents the relative angle between r_{AB} and E, t is reduced, as it is proportional to the zeroth order Bessel function J_{0}, and becomes zero at 40 MV cm^{−1} (Ω_{AB}/ω=2.40), as shown in Fig. 5c. From Fig. 5c, we can estimate that the change in J_{0}∝t′ is approximately 10% for a typical instantaneous field of 9.3 MV cm^{−1} (I_{ex}=0.8 mJ cm^{−2}).
To demonstrate the instability of the metallic phase induced by this 10% change in t, we roughly estimated the change of T_{CO} by changing t. Figure 6a shows the temperature dependence of the hole densities (ρ_{H}) at the A and A′ molecules in Fig. 1a as a function of the normalized temperature T/T_{CO}, calculated using the Hartree–Fock approximation for an extended Hubbard model^{36}. A charge disproportionation occurs below T/T_{CO}=1, as indicated by the closed (A: charge rich) and open (A′: charge poor) circles for the original t_{0}. We also calculated the ρ_{H} versus T/T_{CO} relation with changing t, where the rectangles, upward triangles and downward triangles show the calculated values for 0.95t_{0}, 0.9t_{0} and 0.85t_{0}, respectively. Figure 6b illustrates that the change in T_{CO} (=ΔT_{CO}/T_{CO}) is proportional to the decrease in t (=−Δt /t), indicating that a 10% change in t causes a 12% change in T_{CO} from 135 to 152 K. Thus, T_{CO} increases across the measured temperature (138 K).
For our experimental conditions (<12 MV cm^{−1}), 1/t′ (in units of 1/t_{0}) shows a nonlinear dependence on E_{0} (red curve in Fig. 5b). This nonlinear dependence of 1/t′ on E_{0} is consistent with the relation between ΔR/R and E_{0} (closed circles in Fig. 5b). Considering that R reflects the metaltoinsulator transition (Fig. 2b), it is reasonable to assume that ΔR/R is proportional to the efficiency of the transient charge localization. As such, the E_{0} dependence of ΔR/R, can be described by 1/t′.
According to recent studies on subcycle asymmetric pulses^{22}, the momentum shift of the band structure is given by the ‘dynamical phase’ φ=∫ dtE(t) (ref. 22). However, in the present case, this is estimated to be φ=1.66 × 10^{−4}[rad] at most, which is much smaller than φ=π/2[rad], and is too small to cause a detectable momentum shift. Such shift would be detected if the width of the asymmetric pulse were shorter than ~3 fs at this wavelength. Another problem lies in the mechanism driving the reduced t, which should be applicable to events before the excitation ends, that is, ~7 fs. The reason why the photoinduced CO persists for ~50 fs after the 7 fs pulse is unclear at the moment. Further experiments and theoretical considerations will be needed to clarify this issue.
In summary, this report demonstrates a large reflectivity increase (>25%) and a coherent CO gap oscillation along the time axis indicating the opening of a CO gap by the 9.3 MV cm^{−1} electric field of a 1.5 cycle, 7 fs nearinfrared pulse in an organic conductor α(ET)_{2}I_{3}. The plausible mechanism for such a dramatic change in the electronic state is the reduction of t (~10%) driven by this strong highfrequency field.
Methods
Sample preparation
Single crystals of α(ET)_{2}I_{3} (2 × 1 × 0.1 mm) were prepared using a method described in a previous study^{28}.
7fs Infrared pulse generation
A broadband infrared spectrum for the 7fs pulse covering 1.2–2.3 μm, shown by the orange curve in Fig. 2a, was obtained by focusing a carrierenvelope phase stabilized idler pulse (1.7 μm) from an optical parametric amplifier (Quantronix HETOPAS pumped by SpectraPhysics SpitfireAce) onto a hollow fibre set within a Krfilled chamber (Femtolasers). Pulse compression was performed using both active mirror (OKO Technologies, 19ch linear MMDM) and chirped mirror (Femtolasers, SigmaKoki) techniques. The pulse width derived from the autocorrelation of the generated second harmonic was 7 fs, which corresponds to 1.5 optical cycles. The instantaneous electric field on the sample surface (excitation diameter 200 μm) for a typical excitation intensity can be evaluated as , where I_{peak}=1.14 × 10^{11} W cm^{−2} represents the peak power for an excitation intensity I_{ex} of 0.8 mJ cm^{−2}.
Transient reflectivity measurements
We performed transient reflectivity experiments using both 7 and 100 fs pulses. The excitation photon energies for 7 and 100 fs pulses were 0.6–0.95 eV (7 fs) and 0.89 eV (100 fs), respectively. In the transient reflectivity measurement using a 7fs pulse, the probe pulse reflected from the sample was detected by InGaAs detector (NewFocus model 2034) after passing through a spectrometer (Bunkoukeiki, M10). The pumpon and pumpoff were alternately switched by the feedbackcontrolled optical chopper (New Focus, Model 3501), synchronized with the laser driver. Each probe shot was sampled using boxcar integrators (Stanford Research, SR250). After normalization by a reference pulse, the observed intensity of respective shots was recorded in the PC.
Additional information
How to cite this article: Ishikawa, T. et al. Optical freezing of charge motion in an organic conductor. Nat. Commun. 5:5528 doi: 10.1038/ncomms6528 (2014).
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Acknowledgements
We are grateful to T. Oka (University of Tokyo) and Y. Kayanuma (Tokyo Institute of Technology) for their insightful discussions. This work was supported by GrantinAid for Scientific Research (A) No. 23244062.
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T.I. and Y.K. developed the 7fs light source and carried out the transient reflectivity measurements using them. Y.S., Y.N. and H.I. performed the 100fs transient reflectivity experiments. T.I., Y.S. and Y.N. analysed the data. K. Yamamoto, K. Yakushi, H.K. and T.S. performed the synthesis and the characterization of the single crystal. S. Ishihara, Y.T. and K. Yonemitsu made theoretical considerations and calculations. S.Iwai devised the experiments. T.I. and S. Iwai and K. Yonemitsu wrote the paper after discussing with all the coauthors.
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Ishikawa, T., Sagae, Y., Naitoh, Y. et al. Optical freezing of charge motion in an organic conductor. Nat Commun 5, 5528 (2014). https://doi.org/10.1038/ncomms6528
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