In the format provided by the authors and unedited. DOI: 1.138/NMAT4967 Mott transition by an impulsive dielectric breakdown H. Yamakawa, 1 T. Miyamoto, 1 T. Morimoto, 1 T. Terashige, 1 H. Yada, 1 N. Kida, 1 M. Suda, 2 H. M. Yamamoto, 2,3 R. Kato, 3 K. Miyagawa, 4 K. Kanoda, 4 and H. Okamoto 1,* 1 Department of Advanced Materials Science, University of Tokyo, Chiba 277-8561, Japan 2 Division of Functional Molecular Systems, Research Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, Okazaki 444-8585, Japan. 3 RIKEN, Wako 351-198, Japan 4 Department of Applied Physics, University of Tokyo, Bunkyo-ku 113-8656, Japan *Corresponding author. E-mail: okamotoh@k.u-tokyo.ac.jp Content S1. Evaluations of optical density spectra S2. Temperature dependence of lattice constants in diamond and κ-(et)2cu[n(cn)2]br S3. Evaluation of AC Stark shift S4. Characteristic time for the Mott transition by a terahertz pulse S5. Densities of carriers generated by a terahertz pulse and a near infrared pulse S6. Analyses of oscillatory components in time evolutions of optical density changes NATURE MATERIALS www.nature.com/naturematerials 1
S1. Evaluations of optical density spectra The polarised optical density (OD) spectrum of a κ-(et) 2Cu[N(CN) 2]Br thin crystal on a diamond substrate was calculated from the polarised reflectivity (RR) and transmission (TT) spectra using the relation OD = log ( TT sub,sam TT sub 1 RR sub 1 RR sub,sam ). Here, RR sub (calculated from the refractive index of diamond 1 ) and RR sub,sam are the reflectivities of the diamond substrate and the crystal sample on the substrate, respectively, and TT sub and TT sub,sam are the corresponding transmission values. Figures S1a and S1b show the RR = RR sub,sam and TT = TT sub,sam TT sub spectra, respectively, for EE//cc at 1 K (blue solid lines) and 293 K (black solid lines). The oscillations in the lower energy region originate from interference within the diamond substrate. At ~.4 ev, it is difficult to measure precisely the TT spectrum because the OD exceeds 3, and the transmitted light is very weak. In this region, we used OD values of the absorption coefficient spectrum obtained from the Kramers Kronig transformation of the polarised RR spectrum. The OD spectra thus obtained are shown in Fig. 1d (1 K) and in Fig. S1c (293 K). OD is finite at the lower energy bound of the measured range (.1 ev) at 293 K reflecting a high conductivity, but a clear Mott gap Mott ~3 mev is open at 1 K. To investigate whether infrared-active modes exist below.1 ev or not, we measured the transmission spectrum below.11 ev at 293 K using the terahertz time domain spectroscopy. The details of the experimental setup has been previously reported 2. In this measurement, we could not evaluate precisely the phase shift of the terahertz wave transmitted through the sample, since it was very small. Therefore, we calculated the OD spectrum only from the transmission (T) spectrum using the relation OD T = log(tt). In the inset of Fig. S1c, we show the OD T spectrum from 2 mev to 2 mev at 293 K by NATURE MATERIALS www.nature.com/naturematerials 2
the black line, together with the Fourier power spectrum of the terahertz pulse (the red line). A monotonic interference pattern is observed, indicating that no infrared-active modes exist in this region. S2. Temperature dependence of lattice constants in diamond and κ- (ET)2Cu[N(CN)2]Br In this study, a thin crystal of κ-(et) 2Cu[N(CN)2]Br was placed on a diamond substrate, with the ac plane onto the surface of the substrate. As shown in Fig. S2, the shrinkage ratio ll/ll of the lattice constant ll in diamond is much smaller than those derived along the a and c axes in κ-(et) 2Cu[N(CN) 2]Br 3,4, and as a result, the substrate exerts a negative pressure on the molecular crystal, driving the transition of the crystal to the Mott insulator phase at 1 K. S3. Evaluation of AC Stark shift In this section, we evaluate a possible spectral change originating from the AC Stark shift EE s. First, we consider a two level system consisting of a ground state with the energy equal to zero and an excited state 1 with the energy of ωω 1. Here, we assume that is the even-parity state and 1 is the optically-allowed odd-parity state and that the frequency of the terahertz electric field, ωω THz, is much smaller than ωω 1. The response to the terahertz electric field can be expressed by the second-order perturbation theory as follows 5. EE s = ee2 2 EE THz xx 1 2 ħ ωω 1 + ωω THz ( (ωω 1 + ωω THz ) 2 2 + γγ + 1 ωω 1 ωω THz (ωω 1 ωω THz ) 2 + γγ 1 2 ) (S1) NATURE MATERIALS www.nature.com/naturematerials 3
Here, γγ 1 is the damping constant of the excited state and xx 1 is the dipole moment between the ground state and the excited state. Using this formula, OD can be calculated. Here, we assume that the energy of the lowest excited state, ωω 1, is equal to the peak energy or equivalently the gravity of the Mott-gap transition. In dimer Mott insulators of several ET compounds, a broad peak or a shoulder structure of the interdimer transition, that is, the Mott-gap transition is observed in the mid-ir region in common 6. As seen in Fig. 2a, a broad shoulder structure is located at around.3 ev at 1 K in the ET compound on the diamond substrate studied here. The higher energy peak at around.45 ev is attributed to the intradimer transition. By assuming two Lorentz oscillators, the absorption spectrum in Fig. 2a at 1 K is almost reproduced as shown in Fig. S3a. The evaluated peak energy of the Mott-gap transition, ωω 1, is.28 ev. The other parameters are evaluated to be γγ 1 =.38 ev and xx 1 = 1.14 A. Using those parameter values, ωω THz =.7 THz, the maximum terahertz electric field EE THz = 18 kv/cm, and eq. (S1), we obtain the AC Stark shift EE s =.34 mev, which shows a blue shift of the lowest transition. We also calculated the corresponding change ( OD) of the OD spectrum and showed it by the blue solid line in Fig. S3b and its inset. The blue shift of the transition cannot explain the absorption change ( OD) spectrum experimentally obtained (yellow circles in Fig. 2b and Fig. S3b). In addition, the maximum of OD thus evaluated, Ca..3, is by more than one order smaller than the maximum of the experimental OD signals, Ca..12. These results indicate that the observed absorption change cannot be explained by the AC Stark effect in the two level system. NATURE MATERIALS www.nature.com/naturematerials 4
If we assume the optically-forbidden second-lowest excited state with even parity exists above the optically-allowed lowest excited state with odd parity, another kind of AC Stark shift might appear, as previously reported 7,8. In this case, the lowest excited state, that is, the Mott-gap transition band with the peak energy of.28 ev would show the red shift, although its magnitude cannot be estimated due to the lack of the information about the second-lowest even-parity state. Since the experimental OD signals monotonically increase with decrease of energy (Fig. 2b), it is obvious that the OD spectrum cannot be reproduced by a simple red shift. In addition, the signal due to the AC Stark effect appears only under the presence of the electric field and no signals should be observed after the electric field disappears. However, the experimental OD signals exist in the picosecond time domain under no electric fields. These results demonstrate again that the AC Stark shift is not an origin of the observed OD signals. The reason why the signal due to the AC Stark shift was not observed, is probably because it is small as compared to the signal originating from the quantum tunneling processes. S4. Characteristic time for the Mott transition by terahertz pulse As shown in Fig. 3b, the EE THz () dependence of OD THz (tt =.7 ps) does not adhere to the formula of tunnelling probability (the green broken line) in the low electricfield region; this lies in contrast with the initial OD THz (tt = ps). For EE THz () < 7 kv/cm, OD THz (tt =.7 ps) is much larger than OD THz (tt = ps). The substantial increase of OD THz from tt = ps to.7 ps is attributable to an electronic state change from a Mott insulator with doublon holon pairs (the middle panel in Fig. 3c) to a metal (the right panel in Fig. 3c), i.e., a Mott transition driven by doublon holon-pair NATURE MATERIALS www.nature.com/naturematerials 5
generation. Using EE THz () > 7 kv/cm, the OD THz (tt = ps) and OD THz (tt =.7 ps) values were found not to differ substantially, as the IR responses of a Mott insulator containing a large number of doublon holon pairs are similar to those of the metallic phase to which the insulator finally transitions. Thus, it is expected that the characteristic time of the Mott transition could be evaluated by comparing the initial dynamics of OD THz in the low- and high-electric-field cases. The open circles in Figs. S4a and b show the evolution of OD THz over time for both the high-electric-field (EE THz () = 17 kv/cm) and the low-electric-field cases (EE THz () = 45 kv/cm), respectively. In Fig. S4b, we present OD THz for EE THz () = 17 kv/cm (broken orange line) for comparison. The red lines show the time profiles for EE THz (tt ) exp ( ππ EE th EE THz (tt ) ), indicating the carrier generation probability, for which the vertical scale is arbitrary. The initial rise of OD THz in Fig. S4a (EE THz () = 17 kv/cm) tracks with the waveform of EE THz (tt ) exp ( ππ EE th EE THz (tt ) ), and no delay was observed. In contrast, the initial rise of low-electric-field OD THz in Fig. S4b (EE THz () = 45 kv/cm) was delayed in comparison to that in Fig. S4a, and a subsequent nonlinear increase of the signal was observed. To evaluate the rise time of OD THz for EE THz () = 45 kv/cm, we performed a fitting analysis using the following formula. OD THz tt EE th EE THz (tt ) exp ( ππ EE THz (tt ) ) {[1 exp ( tt tt tt tt )] exp ( )} ddtt (S1) ττ 1 ττ 2 The parameters ττ 1 and ττ 2 are the rise time and the decay time of the signal, respectively. The initial response of OD THz for EE THz () = 45 kv/cm can be well reproduced NATURE MATERIALS www.nature.com/naturematerials 6
using values of ττ 1 =.13 ps and ττ 2 = 2.4 ps, as shown by the blue line in Fig. S4b. As mentioned in the main text, the effective on-site Coulomb repulsion UU d on each dimer is equal to 2t, where t is the intra-dimer transfer energy. Therefore, UU d might be changed by molecular displacements modifying t. However, a period of a phonon mode associated with molecular displacements is in the order of 1 ps, which is much longer than the observed rise time ττ 1 =.13 ps of the signals. Thus, we cannot relate ττ 1 to the carrier generations due to the suppression of UU d, which originates from molecular displacements. It is reasonable to compare ττ 1 =.13 ps with the inter-dimer transfer energies, which are expected to dominate in an insulator-to-metal transition. Two types of interdimer wavefunction overlap are known for κ-(et) 2Cu[N(CN) 2]Br, for which the corresponding transfer energies are 78 mev and 33 mev 6, and their time scales are.5 ps and.12 ps, respectively. It is noted that the latter time scale is nearly the same as ττ 1,.13 ps. From these results, we can infer that the collapse of the Mott gap takes.1 ps after doublon holon pair generation by a terahertz electric-field pulse, and that this characteristic time is dominated by the inter-dimer transfer energy. S5. Densities of carriers generated by a terahertz pulse and a near-infrared pulse From the analysis of the optical conductivity spectra measured in a bulk single crystal, the effective carrier number per dimer was evaluated to be.5 at 4 K 9,1. The difference in the optical density ΔODM-I at.124 ev between the metal phase (a bulk single crystal) and the Mott-insulator phase (a thin single crystal on a diamond substrate) was 1.4, which is attributed to carriers (.5 per dimer) in the metal phase. A terahertz pulse with electric field strength of 18 kv/cm induced a change in the optical density to OD THz = NATURE MATERIALS www.nature.com/naturematerials 7
.114. Hence, it can be concluded that 11.% of the carrier density in the metal phase (.55 per dimer) is generated by the terahertz pulse. The near-ir (.93 ev) pulse, possessing a photon density of 3.7 1 4 photon/dimer (the fluence per unit area, 7.73 J/cm 2, was the same as for a terahertz pulse with an amplitude of 18 kv/cm), generated carriers with a density of.18, which is ~3% of.55/dimer. The carrier generation efficiency by near-ir (.93 ev) excitation was calculated to be 5 carriers/photon. S6. Analyses of oscillatory components in time evolutions of optical density changes As shown in Figs. 2d and 2e, several oscillations seem to appear in the dynamics of the optical density changes ( OD) induced by both the terahertz and near-ir pulses. To analyse these oscillations, we derived the oscillatory components OD OSC (tt) at.124 ev from the time evolutions of OD (shown in Figs. 4c and 4d) using a Fourier filter. We assumed that the time characteristics of OD OSC (tt) can be expressed by the sum of several damped oscillators; FF OSC (tt) = AA ii exp ( tt ) cos(ωω ττ ii tt + φφ ii ). ii ii (S2) Here, AA ii, ττ ii, ωω ii, and φφ ii are the amplitude, decay time, frequency, and phase of each oscillation, respectively. For OD OSC (tt) generated by the terahertz pulse, we convoluted the three oscillatory components with the probability of the carrier tunnelling process, EE THz (tt) exp ( ππ EE th EE THz (tt) ), using the following relation, OD OSC (tt) = tt EE th EE THz (tt ) exp ( ππ EE THz (tt ) ) [FF OSC (tt tt )]dddd. (S3) NATURE MATERIALS www.nature.com/naturematerials 8
Using this formula, the time evolution of OD OSC and its Fourier power spectrum were well reproduced, as shown by the red lines in Figs. 4c and 4e, respectively. The frequencies of the three oscillations were 27.8 cm 1, 36.7 cm 1, and 45.7 cm 1, and the obtained parameter values are listed in Table S1. The three oscillations are of the cosinetype; hence, they are considered to arise from the changes in the equilibrium positions of the molecules during the Mott-insulator-to-metal transition driven by the application of the terahertz pulse. In the case of near-ir optical excitation, the oscillatory structures in the time evolutions of OD at.124 ev (Fig. 2e) were found to be less prominent than those that arose on terahertz excitation (Fig. 2d). In fact, the maximum amplitude of the oscillatory component OD OSC in the former (Fig. 4d) is one quarter of that in the latter (Fig. 4c). To analyse the time characteristic of OD OSC observed in the case of near-ir optical excitation, we convoluted one oscillatory component with the Gaussian time profile exp ( tt2 δδ2) corresponding to the time resolution (δδ =.11 ps) (the blue line in Fig. 4b): OD OSC = tt exp ( tt 2 δδ 2) [FF OSC (tt tt )]dddd. (S4) Using this formula, the time evolution of OD OSC at.124 ev was well reproduced, as shown by the blue line in Fig. 4d. The frequency of the oscillator was 27.8 cm -1, and was shown to be of a damped cosine-type: the obtained parameters for this oscillation are listed in Table S1. The phase of the oscillation was 52, and so was not defined as a purely cosine-type damped oscillation: this is accounted for by recognising that the metallisation process is not instantaneous, but delayed by ~.3 ps, as discussed in the main text. Previous Raman studies suggest that the mode at 27.8 cm 1, observed in both the terahertz and near-ir-optical excitations, is an oscillation that modulates the distance NATURE MATERIALS www.nature.com/naturematerials 9
between the two molecules in each dimer 11,12. However, the other oscillations have not been assigned yet. It is reasonable to consider that they are also related to the modulations of intra-dimer or inter-dimer molecular interactions, such as transfer energies and Coulomb repulsive energies. Possible candidates are the librational and shear-type modes, in which the two molecules in each dimer slide parallel to each other. References 1. The CVD diamond booklet, available at http://www.diamondmaterials.com/en/cvd_diamond/overview.htm 2. Takeda, R., Kida, N., Sotome, M., Matsui, Y. & Okamoto, H. Circularly polarized narrowband terahertz radiation from a eulytite oxide by a pair of femtosecond laser pulses. Phys. Rev. A 89, 33832 (214) 3. Kund, M. et al. A study of the thermal expansion of isostructual organic radical cation salts κ-(et)2cu[n(cn)2]x (X=Br, Cl, I). Synth. Met. 7, 951-952 (1995). 4. Slack, G. A., Bartram, S. F. Thermal expansion of some diamondlike crystals. J. Appl. Phys. 46, 89-98 (1975). 5. Bacos, J. S. AC Stark shift and multiphoton processes in atoms. Phys. Rep. 31C, 29-235 (1977). 6. Faltermeier, D. et al. Bandwidth-controlled Mott transition in κ-(bedt- TTF)2Cu[N(CN) 2]Br xcl 1 x: optical studies of localized charge excitations. Phys. Rev. B 76, 165113 (27). 7. Nordstrom, K. B. et al. Excitonic dynamical Franz-Keldysh effect. Phys. Rev. Lett. 81, 457 (1998). NATURE MATERIALS www.nature.com/naturematerials 1
8. Yada, H., Miyamoto, T., and Okamoto, H. Teraherz-field-diriven sub-picosecond optical switching in a one-dimensional Mott insulators enabled by large third-order optical nonlinearity. Appl. Phys. Lett. 12, 9114 (213). 9. Merino, J. et al. Quasiparticles at the verge of localization near the Mott metal-insulator transition in a two-dimensional material. Phys. Rev. Lett. 1, 8644 (28). 1. Sasaki, T. et al. Optical probe of carrier doping by X-ray irradiation in the organic dimer Mott insulator κ-(bedt-ttf)2cu[n(cn)2]cl. Phys. Rev. Lett. 11, 2643 (28). 11. Kawakami, Y. et al. Optical modulation of effective on-site Coulomb energy for the Mott transition in an organic dimer insulator. Phys. Rev. Lett. 13, 6643 (29). 12. Pedron, D. et al. Phonon dynamics and superconductivity in the organic crystal κ- (BEDT-TTF)2Cu[N(CN)2]Br. Phys. C 276, 1 (1997). NATURE MATERIALS www.nature.com/naturematerials 11
a b R T 1.8.6.4.2 1.8.6.4.2 293 K 1 K c OD 4 3 2 1 OD T 2 1.1.2 Photon Energy (ev).1.5.1.5 Photon Energy (ev) Figure S1. (a, b) Reflectivity (R) and transmission (T) spectra of κ-(et) 2Cu[N(CN)2]Br on a diamond substrate for E//c at 1 K (blue lines) and 293 K (black lines). The oscillations in the low energy region are due to the interference in the substrate. (c) The OD spectrum at 293 K. The inset shows the OD T spectrum at 293 K (the black line). The red line shows the Fourier power spectrum of the terahertz pulse. NATURE MATERIALS www.nature.com/naturematerials 12
diamond a axis 1 2-1 c axis κ-(et) 2 Cu[N(CN) 2 ]Br b axis -2 1 2 3 Temperature (K) Figure S2. Temperature dependence of relative length changes of diamond substrate and κ-(et)2cu[n(cn) 2]Br. Gray solid line shows the dependence of relative length changes ll/ll of diamond on temperature. Green, blue and red solid lines show that of κ- (ET) 2Cu[N(CN)2]Br along a, b and c axis, respectively. NATURE MATERIALS www.nature.com/naturematerials 13
a OD 4 3 2 Metal (OD M ) Insulator (OD I ) 1 K 1 b 1 2 ΔOD THz 1 5 1 2 ΔOD.2 -.2.1.2.4.8 Photon Energy (ev) (OD M OD I ).11.1.2.4 Photon Energy (ev).8 Figure S3. (a) The red and black solid line show the OD spectra of metal phase (ODM) and Mott insulator phase (ODI) at 1 K, respectively (the same as Fig. 2a). ODI spectrum is reproduced by two Lorentz functions as shown by the blue solid line. The Lorentz oscillators at.45 ev (the orange broken line) and at.28 ev (the green broken line) correspond to intradimer and interdimer transitions, respectively. (b) The yellow circles show transient absorption changes ODTHz induced by a terahertz electric field at tt =.7 ps, and the green line shows the differential absorption spectrum (ODM-OD I).11 (the same as Fig. 2b). The blue solid line shows the calculated change of the OD spectrum ( OD) when the AC stark shift in the two level system is assumed (see S3). The inset shows the magnified view of the calculated OD spectrum. NATURE MATERIALS www.nature.com/naturematerials 14
a ΔOD THz.1.5 THz pulse 17 kv/cm b ΔOD THz.2.1 THz pulse 45 kv/cm -.4 -.2.2.4.6 Delay Time (ps) Figure S4. Time characteristics of OD THz at.124 ev in κ-(et) 2Cu[N(CN) 2]Br (circles). (a) High-electric-field case of EE THz () = 17 kv/cm and (b) Low-electricfield case of EE THz () = 45 kv/cm. The blue solid line and the orange broken line in (b) are the fitting curve and OD THz for EE THz () = 17 kv/cm, respectively. The red lines are explained in the text. NATURE MATERIALS www.nature.com/naturematerials 15
ii AA ii ττ ii (ps) ωω ii (cm 1 ) φφ ii (deg.) 1.18 5.8 27.8 17 THz pulse 2.42 2. 36.7 17 3.21 6.5 45.7 2 Near-IR pulse 1.11 7. 27.8 52 Table S1. Obtained parameters for the analyses of coherent oscillations NATURE MATERIALS www.nature.com/naturematerials 16