Effects of Lattice and Molecular Phonons on Photoinduced Neutral-to-Ionic Transition Dynamics in Tetrathiafulvalene- p -Chloranil
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Effects of Lattice and Molecular Phonons on Photoinduced Neutral-to-IonicTransition Dynamics in Tetrathiafulvalene- p -Chloranil Kenji
Yonemitsu , , ∗ Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan Department of Functional Molecular Science, Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan JST, CREST, Tokyo 102-0075, Japan
For electronic states and photoinduced charge dynamics near the neutral-ionic transition inthe mixed-stack charge-transfer complex tetrathiafulvalene- p -chloranil (TTF-CA), we reviewthe effects of Peierls coupling to lattice phonons modulating transfer integrals and Holsteincouplings to molecular vibrations modulating site energies. The former stabilizes the ionic phaseand reduces discontinuities in the phase transition, while the latter stabilizes the neutral phaseand enhances the discontinuities. To reproduce the experimentally observed ionicity, opticalconductivity and photoinduced charge dynamics, both couplings are quantitatively important.In particular, strong Holstein couplings to form the highly-stabilized neutral phase are necessaryfor the ionic phase to be a Mott insulator with large ionicity. A comparison with the observedphotoinduced charge dynamics indicates the presence of strings of lattice dimerization in theneutral phase above the transition temperature. KEYWORDS: photoinduced phase transition, neutral-ionic transition, electron-lattice interaction, electron-molecular-vibration coupling
1. Introduction
Nonequilibrium electronic states have drawn attentionas a field where novel electronic functions and propertiesare being searched for. Correlated electron and electron-phonon systems with rich electronic phase diagrams arepromising because synergy can be exploited, which is in-herent to respective orders at low temperatures. Amongnonequilibrium phenomena, photoinduced phase transi-tions occur synergistically since a low density of photonsrelative to the density of molecules or atoms can alterthe electronic phase realized in such a system. A varietyof photoinduced phase transitions are known to proceedvery rapidly.
1, 2)
From the viewpoint of controlling functions in nonequi-librium states, it is important to learn a means by whicha photoinduced phase transition proceeds. The most fun-damental information is on relevant interactions that sta-bilize the ground state. It is generally true that, even ifa few interaction parameters are sufficient to describeequilibrium properties, they are still insufficient for de-scribing nonequilibrium dynamics. Additional interac-tions can be crucial in determining whether and how thephase transition is photoinduced. Among organic mate-rials that have been regarded as strongly correlated elec-tron systems, some have been realized to have substan-tial electron-molecular-vibration (EMV) couplings thatcontribute to the stabilization of the ground state andphotoinduced dynamics.For instance, the charge order in the quasi-two-dimensional organic salt α -(BEDT-TTF) I [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] is basicallydriven by a long-range Coulomb interaction.
3, 4)
Rela-tively weak Peierls couplings to lattice phonons or molec-ular rotations are important for understanding the inter- ∗ E-mail: [email protected] relation between the altered charge distribution and thestructural deformation
5, 6) as well as the long-time behav-ior of photoinduced dynamics.
7, 8)
From the early-stagedynamics after photoexcitation, however, substantiallystrong Holstein couplings to molecular vibrations are ev-ident in the Fano destructive interference between vi-brations containing C=C stretching and correlated elec-trons’ motion. These molecular vibrations stabilize thecharge order to a substantial extent.Most organic compounds that show electronic phasetransitions have C=C bonds in their constituentmolecules. Their vibration frequencies are well known todepend on the charged state of the molecule. It is there-fore expected that EMV couplings are generally strongeven though the electronic state has strong electron cor-relations in terms of intermolecular spin and charge cor-relation functions. In this study, we focus on the mixed-stack charge-transfer complex TTF-CA, whose thermaland photoinduced neutral-ionic transitions have inten-sively been studied both experimentally and theo-retically.
We review the origin of the discontinuitiesin ionicity and optical conductivity during the neutral-ionic transition. Their quantitative understanding willbecome important for controlling photoinduced phasetransition dynamics.
2. Discontinuities during Neutral-Ionic Transi-tion
The importance of the intersite Coulomb repulsion V for discontinuities during the neutral-ionic transition hasbeen pointed out in ref. 25. Without coupling to latticephonons, i.e., without dimerization, the spin gap at thephase boundary is zero on the ionic (i.e., regular-Mott-insulator) side and V on the neutral (i.e., band-insulator)side in the limit of vanishing transfer integrals. Here,the creation of a neutral-ionic domain wall requires V / Full Paper
Author Name of energy, which allows for the phase separation of neu-tral and ionic domains at the boundary. The transferintegral t introduces quantum fluctuations. As long as2 t is smaller than V , however, the creation energy re-mains finite. The discontinuous neutral-ionic transition isdemonstrated by quantum Monte Carlo simulations. The ionic phase is known to have dimerization. Thestrongest candidate for its mechanism is due to the spin-Peierls instability.
A regular ionic phase is a one-dimensional half-filled paramagnetic Mott insulator, sothat it can be described by a spin-1/2 antiferromag-netic Heisenberg chain. If the superexchange interactionis modulated by lattice phonons, the system is stabi-lized by dimerization that produces a finite spin gap. Thedimerization in the ionic phase is demonstrated by quan-tum Monte Carlo simulations.
As lattice phonons arestrongly dimerized, i.e., as the electron-lattice coupling isstrengthened, the phase boundary is shifted because onlythe ionic phase is stabilized, which decreases the ionicityon the ionic side of the phase boundary. The discontinu-ity in ionicity is strongly reduced by the electron-latticecoupling. As a consequence, the character of the ionicphase as a Mott insulator is weakened, and the transi-tion becomes close to a continuous Peierls transition.For the discontinuous ionicity change, Painelli andGirlando have pointed out that both EMV couplings andintersite Coulomb repulsion V are important and thatthey collaborate. For finite systems, they perform ex-act diagonalization in the limit of a large on-site repulsion U and the second-order perturbation theory with respectto the electron-lattice (i.e., Peierls) and EMV (i.e., Hol-stein) couplings. The electron number configuration isroughly described as 2020 in the neutral phase and as1111 in the ionic phase, so that the Holstein couplingsstabilize the neutral phase, which are in contrast to thePeierls coupling that stabilizes the ionic phase throughdimerization.As noted above, both of the Peierls and Holstein cou-plings are suggested to be necessary for the reproductionof ionicity and optical conductivity near the neutral-ionicphase boundary. In spite of this, the Holstein couplingshave often been ignored for the following reason. Withoutthe Peierls coupling, the bond-charge densities cannotbe dimerized, and the ionic phase cannot have the fer-roelectric order. In contrast, the Holstein couplings onlyenlarge the site energy difference between the neighbor-ing orbitals in the neutral phase, so that they can beabsorbed into the renormalized site energy difference inthe adiabatic limit. The situation is quite similar to aphase transition described within the mean field theoryin the sense that the Holstein couplings stabilize the neu-tral phase in a synergistic manner and enhance the dis-continuity during the transition. Namely, the degrees ofrenormalization are different between the two phases.In this paper, we include both couplings in the model.The charge dynamics after photoexcitation of the neutralphase shows a large contribution from molecular vibra-tions. This is consistent with the ultrafast charge andmolecular-vibration dynamics recently observed by thetransient reflectivity measurements. Numerical calcu-lations show that the initial neutral state must be ac- companied with a small dimerization to reproduce theexperimentally observed, coherently oscillating dimeriza-tion immediately after photoexcitation. The presence ofstrings of lattice dimerization in the neutral phase hasindeed been observed by the latest X-ray diffuse scatter-ing.
3. Model with Lattice and Molecular Phonons
We use the one-dimensional half-filled extended ionicHubbard-Peierls-Holstein model H = − X jσ [ t − α ( u j +1 − u j )]( c † jσ c j +1 σ + c † j +1 σ c jσ )+ ∆2 X jσ ( − j c † jσ c jσ − X mjσ β ( m ) j v ( m ) j c † jσ c jσ + U X j n j ↑ n j ↓ + V X j n j n j +1 + X j (cid:20) K α u j +1 − u j ) + 2 K α ω α ˙ u j (cid:21) + X mj " K ( m ) βj v ( m )2 j + K ( m ) βj ω ( m )2 βj ˙ v ( m )2 j , (1)where c † jσ creates an electron with spin σ at site j , n jσ = c † jσ c jσ , and n j = P σ n jσ . The parameter t denotesthe transfer integral on a regular lattice (i.e., withoutlattice distortion), ∆ the site energy difference betweenneighboring orbitals when molecular distortions are ab-sent, U the on-site repulsion strength, and V the nearest-neighbor repulsion strength. The lattice displacement u j at site j modulates the transfer integral between the( j − j th orbitals and that between the j th and( j + 1)th orbitals with the coefficient ∓ α . The displace-ment v ( m ) j in the m th mode on the j th molecule modu-lates the site energy with the coefficient β ( m ) j . The quan-tities ˙ u j and ˙ v ( m ) j are the time derivatives of u j and v ( m ) j ,respectively. The parameters K α and K ( m ) βj are their elas-tic coefficients, and ω α and ω ( m ) βj are their bare phononenergies, respectively.For these model parameters, we take eV as the unitof energy and use t =0.17, U =1.5, and V =0.6; wevary ∆ around the phase boundary depending on thePeierls and Holstein coupling strengths. We define thestrengths of these couplings as λ α ≡ α /K α and λ βj ≡ P m β ( m )2 j /K ( m ) βj . As long as the displacementsare treated classically, the ground state is given by theirstatic configuration, and the ground state is determinednot by the distribution of β ( m )2 j /K ( m ) βj , but by their sum, λ βj . The displacements are scaled using α = β ( m ) j =1,so that we have λ α = 1 /K α and λ βj = P m /K ( m ) βj . Forsimplicity, we set λ β i − = λ β i = λ β .As for phonons, we take one mode for the donormolecule and two modes for the acceptor molecule inaddition to the lattice phonon mode, and use param-eters that approximately reproduce the experimentallyobserved phonon energies: ω α =0.013 (this energy is soft- . Phys. Soc. Jpn. Full Paper
Author Name 3 ened to be about 0.0066 when strongly coupled to elec-trons), ω (1) β i ≡ ω β A1 =0.040, ω (1) β i − ≡ ω β D =0.055, and ω (2) β i ≡ ω β A2 =0.12. Donor and acceptor molecules arespecified by odd and even j ’s, respectively. For simplic-ity, we set K (1) β i = K (2) β i because the conclusion does notdepend on the detailed distribution of EMV-couplingstrengths. The displacements v A1 , v D , and v A2 corre-spond to CA’s a g ν (320 cm − ), TTF’s a g ν (438 cm − ),and CA’s a g ν (957 cm − ) modes, respectively, in ref. 24,whereas we ignore TTF’s a g ν (740 cm − ) mode becauseits coupling to electrons is very weak.Photoexcitation is introduced through the Peierlsphase c † iσ c jσ → e ( ie/ ~ c )( j − i ) A ( t ) c † iσ c jσ . (2)The time-dependent vector potential A ( t ) for a pulse ofan oscillating electric field is given by A ( t ) = Fω pmp cos( ω pmp t ) 1 √ πT pmp exp (cid:18) − t T (cid:19) , (3)where ω pmp is the excitation energy, T pmp is the pulsewidth, and F is the electric field amplitude.The time-dependent Schr¨odinger equation for the ex-act many-electron wave function on the chain of N =12sites with periodic boundary condition is numericallysolved by expanding the exponential evolution operatorwith a time slice dt =0.02 eV − to the 15th order andby checking the conservation of the norm. The initialstate is set in the electronic ground state. The classi-cal equations for the lattice and molecular displacementsare solved by the leapfrog method, where the forces arederived from the Hellmann-Feynman theorem:4 K α ω α d u j d t = K α ( u j +1 − u j + u j − )+ α X σ h c † jσ c j +1 σ + H . c . − c † j − σ c jσ − H . c . i , (4) K ( m ) βj ω ( m )2 βj d v ( m ) j d t = − K ( m ) βj v ( m ) j + β ( m ) j X σ h c † jσ c jσ i . (5)Unless otherwise stated, the initial displacements areat the minimum adiabatic potential for the electronicground state, so that the initial velocities are zero.
4. Ground-State Properties
Figures 1 and 2 show the ionicity ρ ≡ /N ) N X j =1 ( − j h n j i (6)as a function of the site energy difference ∆ near thephase boundary with different combinations of λ α and λ β . In the vicinity of the phase boundary, one phase isstable and the other is metastable. By comparing theirenergies, only the ionicity in the stable phase is plot-ted. It is clearly shown that, as λ β increases, the neu-tral phase is stabilized, the discontinuity in ionicity isenlarged, the ionicity in the neutral phase on the large-∆ side of the phase boundary becomes smaller, and the ρ ∆ λ α = . (a) λ β = . β = . β = . β = . ρ ∆ λ α = . (b) λ β = . β = . β = . β = . Fig. 1. Ionicity ρ as a function of site energy difference ∆ for (a)weak Peierls coupling λ α =0.05, and (b) strong Peierls coupling λ α =0.167 with different strengths of λ β . ionicity in the ionic phase on the small-∆ side becomeslarger (Fig. 1). As a consequence, in order for the ionicphase to be a typical Mott insulator, i.e., in order forthe ionic phase to have nearly one electron per site, λ β should be so large that the neutral phase is sufficientlystabilized. In particular, when λ α is large, λ β needs tobe large [Fig. 1(b)]. Otherwise, the ionicity is too smalleven in the ionic phase.Figure 2 has essentially the same information as Fig. 1.It is evident that, as λ α increases, the ionic phase is sta-bilized, and the discontinuity at the transition is sup-pressed. When λ β is large, the phase boundary does notshift monotonically as a function of λ α [Fig. 2(b) and λ β =0.33 (not shown)]. This is caused by the competi-tion between the bond charge P σ h c † jσ c j +1 σ + c † j +1 σ c jσ i localized by λ α and the site charge P σ h c † jσ c jσ i localizedby λ β . The coupling λ α stabilizes only the ionic phase,while λ β stabilizes both phases (i.e., the neutral phasestrongly and the ionic phase weakly). When λ α is smalland the dimerization is weak (i.e., when lattice phononsonly slightly lower the energy of the ionic phase), the in-creasing λ α gains energy by localizing the bond charge,but it loses more energy by delocalizing the site charge.As a consequence, for large λ β , the intermediate λ α sta-bilizes the neutral phase more strongly than the ionicphase. This counterintuitive result cannot be obtainedusing the second-order perturbation theory. Neverthe-less, the shift of the phase boundary is small in this case.Experimentally, it is known that the thermal transi-tion from the neutral to ionic phases is accompanied bya large ionicity jump from 0.3 to 0.7.
This indicates alarge λ β . Of course, a finite λ α is certain to induce dimer- J. Phys. Soc. Jpn.
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Author Name ρ ∆λ β = . (a) λ α = . α = . α = . α = . ρ ∆λ β = . (b) λ α = . α = . α = . α = . Fig. 2. Ionicity ρ as a function of site energy difference ∆ for(a) weak Holstein coupling λ β =0.10, and (b) strong Holsteincoupling λ β =0.25 with different strengths of λ α . ization and the three-dimensional ferroelectric order witha broken inversion symmetry. As shown below, a large λ α is also necessary for the reproduction of the opticalconductivity alteration during the transition [Fig. 3(b)].Therefore, both λ α and λ β are large in TTF-CA.The optical conductivity σ ( ω ) in the ground state | ψ i is calculated using σ ( ω ) = − N ω Im h ψ | j ω + iǫ + E − H j | ψ i , (7)where j is the current operator j ≡ − ∂H/∂A , ǫ is a peak-broadening parameter set at 0.05, and E = h ψ | H | ψ i .Figure 3 shows σ ( ω ) in both phases close to the phaseboundary. When only λ β is large, σ ( ω ) is largely alteredduring the transition [Fig. 3(a)]. The optical gap in theneutral phase strongly stabilized by λ β is large, whilethat in the ionic phase is small in the present choice of U for TTF-CA. Experimentally, such a large alteration isnot observed at the transition. When only λ α is large, thediscontinuities in physical quantities at the transition aresuppressed: the σ ( ω ) spectra in both phases are similar[Fig. 3(c)].
5. Photoinduced Dynamics from Ground State
In the case of a large λ α and a large λ β [Fig. 3(b)], theneutral phase near the phase boundary is photoexcitedwith an energy ω pmp =0.65 just above the optical gap.The time evolution of the ionicity ρ ( t ) during and afterphotoexcitation is plotted in Fig. 4(a). For comparison,the displacement on the acceptor molecule v A1 ( t ) (witha lower ω β A ) is shown in Fig. 4(b), the displacement onthe donor molecule − v D ( t ) [( −
1) is multiplied so as tooscillate in the same phase with ρ ( t ).] in Fig. 4(c), and σ ( ω ) ωλ α = . , λ β = . (a) ∆ = . (I) ∆ = . (N) 0 0.5 1 1.5 2 2.5 0.2 0.4 0.6 0.8 1 1.2 σ ( ω ) ωλ α = . , λ β = . (b) ∆ = . (I) ∆ = . (N) 0 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 σ ( ω ) ωλ α = . , λ β = . (c) ∆ = . (I) ∆ = . (N) Fig. 3. Optical conductivity spectra in ionic (with smaller ∆) andneutral (with larger ∆) phases near the phase boundary with(a) λ α =0.05 and λ β =0.33, (b) λ α =0.167 and λ β =0.20, and (c) λ α =0.20 and λ β =0.05. the displacement on the acceptor molecule v A2 ( t ) (witha higher ω β A ) in Fig. 4(d). As ρ ( t ) increases, the electrondensity increases for the acceptor molecule and decreasesfor the donor molecule [eq. (6)], so that the displacementincreases at the acceptor molecule and decreases at thedonor molecule [eq. (5)]. Thus, the quantities shown inFigs. 4(b)-4(d) basically behave as ( −
1) times the co-sine function. The ionicity ρ ( t ) receives a positive feed-back from these molecular displacements and oscillatesin the same phase with them. This − cosine behavior isconsistent with the experimental observation, demon-strating that the neutral phase is stabilized by EMV cou-plings.To investigate quantum effects, we treated the molec-ular vibration with the highest phonon energy quantum-mechanically as in ref. 9. The difference between the waveprofile when classically treated and that when quantum-mechanically treated was small (not shown). This is incontrast to the case reported in ref. 9, where the pho-toinduced transition is from an insulator to a metal, so . Phys. Soc. Jpn. Full Paper
Author Name 5 that low-energy electronic excitations exist and interferequantum-mechanically with phonons. In such a case, thedifference is large. In the present case, where the pho-toinduced transition is from an insulator to another in-sulator, the electronic excitations maintain a gap muchlarger than the phonon energies. The wavelet analysisdoes not show a trace of quantum interference.In the present calculation, we did not adjust the dis-tribution of β ( m )2 j /K ( m ) βj so as to fit to the experimentaldata. Therefore, we can only roughly compare the ex-perimental and theoretical results for contribution ofmolecular vibrations to the photoinduced ionicity mod-ulation. They are comparable in that the oscillation am-plitude in the photoinduced ionicity change amounts toapproximately one third in the present calculation andone fifth in the experimental result. We have calculatedthe photoinduced dynamics for different combinations of( λ α , λ β ), (0.167, 0.2), (0.167, 0.25), (0.167, 0.33), and(0.2, 0.33), all of which roughly reproduce the disconti-nuities in ionicity and optical conductivity at the transi-tion. In these cases, the above contribution of molecularvibrations is roughly one third.However, there is a qualitative difference between theexperimentally observed and present numerical results,which originates from the fact that the initial state hereis the ground state with the regular and static latticeconfiguration. It does not contain thermal fluctuations.In the experiment, the lattice phonons are ready to bedimerized. The photoinduced ionicity dynamics has alarge contribution from their slow oscillation, which fitsto a damped oscillator. In the present case, the inversionsymmetry of the neutral phase is broken by the oscillat-ing electric field, so that lattice phonons begin to dimer-ize. However, its growth rate is quite low because it essen-tially corresponds to the spontaneous broken symmetry.The dimerization becomes significant only after t=600 inFig. 4. If the initial state contains random numbers in u j , v ( m ) j , ˙ u j , and ˙ v ( m ) j , according to the Boltzmann distribu-tion at a finite temperature of 0.01 eV, these fluctuationsaccelerate the growth of ( − j u j , but they do not oscil-late it like ( −
1) times the cosine function as experimen-tally observed. It should be noted that this calculationcannot simulate thermally induced domains larger thanthe present system.
6. Dynamics with Precursory Dimerization
In this section, we introduce in the initial state adimerization ( − j u j =0.01, which is much smaller than( − j u j =0.058 of the ground state at ∆=0.218 on theionic side of the phase boundary. After obtaining theelectronic ground state with fixed ( − j u j =0.01, we takeit as the initial state and apply to it a pulse of an oscil-lating electric field with energy ω pmp =0.65 again. Thetime evolution of the ionicity ρ ( t ) is plotted in Fig. 5(a).For comparison, the dimerization ( − j u j ( t ) is shown inFig. 5(b), and the displacement on the donor molecule − v D ( t ) in Fig. 5(c). Now, ( − j u j rapidly increases with ρ ( t ) and oscillates like ( −
1) times the cosine function.Thus, ρ ( t ) receives a positive feedback from ( − j u j froman early stage. It is also clear that the oscillations of v ( m ) j are temporally modulated by ( − j u j , as observed exper-imentally. In our calculation, the molecular vibrationsand lattice phonons are indirectly coupled through elec-trons.In this calculation, fluctuations are not introducedinto u j , v ( m ) j , ˙ u j , or ˙ v ( m ) j . This leads to the fact thatan ultrafast charge transfer between neighboring donorand acceptor molecules continues to oscillate without de-phasing. Although it appears as a very thick curve inFig. 5(a), an ultrafast and large-amplitude oscillation isapparent if magnified on the time axis. In experimentsperformed at finite temperatures, such electronic motionis rapidly dephased. Indeed, if random numbers are intro-duced according to the Boltzmann distribution at a finitetemperature of 0.01 eV in u j , v ( m ) j , ˙ u j , and ˙ v ( m ) j of theinitial state, such an ultrafast and large-amplitude oscil-lation disappears but the slow oscillations caused by u j and v ( m ) j survive. The resultant evolution of ρ ( t ) becomescloser to that observed in ref. 24. These fluctuations in-crease the ionicity on both sides of the phase boundary,which also becomes close to the experimentally observedbehavior. As a consequence of the increased ionicity, thephase boundary is shifted to a larger ∆. We show an ex-ample of transient ionicity ρ ( t ) in Fig. 6 in such a caseof dephased charge transfer in a neutral state near theshifted boundary. The ultrafast and large-amplitude os-cillation [the very thick curve in Fig. 5(a)] is indeed sup-pressed here.The above facts indicate the presence of strings of lat-tice dimerization before the photoexcitation of the neu-tral phase in the experiment performed at 90 K abovethe neutral-ionic transition temperature, i.e., 81 K. They are also consistent with the X-ray diffuse scatter-ing showing the characteristic length of 16 molecules forthermally induced ionic strings at 105 K.
At 90 K,the characteristic length would be larger and already be-yond the size for which we can treat the exact many-electron wave function. Such one-dimensional precursorslocally break the inversion symmetry and make the quickgrowth and the − cosine-type oscillation of the dimeriza-tion possible. Considering the fact that the photoinducedneutral-to-ionic dynamics decays much faster than thephotoinduced ionic-to-neutral dynamics, the growthof such one-dimensional ionic domains is saturated be-fore they form a three-dimensional ionic domain that issufficiently metastable for longevity.The picture of the photoinduced neutral-to-ionic tran-sition obtained here is different from the previous one, which suggested ultrafast growth of an ionic domainwithout dimerization, based on the static and regularneutral initial state without couplings to lattice phononsor to molecular vibrations. In reality, the neutral phasein equilibrium above the phase transition temperaturecontains strings of lattice dimerization, already beforephotoexcitation. Photoexcitation rapidly grows and os-cillates the dimerization [Fig. 5(b)], which enhances thecharge transfer between neighboring molecules [Fig. 5(a)compared with Fig. 4(a)]. In other words, precursors aretransformed into ionic domains after photoexcitation.For clarity, the Fourier transform of ρ ( t ) during 50 < J. Phys. Soc. Jpn.
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Author Name t < | R e iωt ρ ( t ) dt | , is plotted inFigs. 7(a) and 7(b). The presence of a low-frequencycomponent at ω < ρ ( t ) after the pe-riod shown in Fig. 4(a). When the dimerization is in-troduced in the initial state, the dimerization oscillatesfrom the beginning [Fig. 5(a)] and contributes more tothe low-frequency component in Fig. 7(b). With the ex-ception of such a low-frequency component, Figs. 7(a)and 7(b) are quite similar. All of the molecular vibra-tions evidently contribute to ρ ( t ): a peak at ω =0.038due to v A1 ( t ) with ω β A1 =0.040, a peak at ω =0.050 dueto v D ( t ) with ω β D =0.055, and a peak at ω =0.11 due to v A2 ( t ) with ω β A2 =0.12. All of them oscillate in the samephase as that in Figs. 4(b)-4(d).
7. Conclusions
Neutral-ionic transition and photoinduced dynamicshave intensively been studied for the mixed-stack charge-transfer complex TTF-CA. The importance of the cou-pling to lattice phonons has been recognized from thedimerization and the consequent ferroelectric order inthe ionic phase. The roles of the couplings to molecu-lar vibrations have not been paid much attention to, ex-cept for a few theoretical studies.
27, 39)
They are found tobe important for the ionic phase to be a Mott insulatorwith large ionicity. The couplings to molecular vibrationsstabilize the neutral phase, making the ionicity in theionic (neutral) phase near the boundary large (small).The couplings to lattice phonons (molecular vibrations)reduce (enhance) the discontinuities in physical quanti-ties. Both couplings are necessary for the reproductionof the experimentally observed ionicity, optical conduc-tivity, and photoinduced charge dynamics.The photoinduced ionicity dynamics also shows a largecontribution from molecular vibrations. The comparisonwith the experimentally observed, photoinduced chargedynamics indicates the presence of strings of latticedimerization as local and precursory symmetry breakingin the neutral phase above the transition temperature.Only when a small but finite dimerization is introducedin the initial state can we reproduce its − cosine behaviorand its large contribution to the photoinduced ionicity. Acknowledgment
This work was supported by Grants-in-Aid for Scien-tific Research (C) (Grant Nos. 19540381 and 23540426),Scientific Research (B) (Grant No. 20340101) and Scien-tific Research (A) (Grant No. 23244062), and by “GrandChallenges in Next-Generation Integrated Nanoscience”from the Ministry of Education, Culture, Sports, Sci-ence and Technology of Japan, and the NINS programfor cross-disciplinary study (NIFS10KEIN0160).
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Author Name 7 ρ ( t ) t λ α = . , λ β = . , ∆ = . (N) ω pmp = . ,T pmp = ,F= . (a) 0 0.01 0.02 0.03 0.04 0.05 0 100 200 300 400 500 600 v A ( t ) t ω β A1 =0.040(b)-0.39-0.38-0.37-0.36-0.35-0.34-0.33-0.32-0.31 0 100 200 300 400 500 600 − v D ( t ) t ω β D =0.055(c) 0.01 0.02 0.03 0.04 0 100 200 300 400 500 600 v A ( t ) t ω β A2 =0.12(d) Fig. 4. (Color online) Transient quantities during and af-ter charge-transfer photoexcitation of neutral phase using ω pmp =0.65, T pmp =10, and F =1.4 in case of strong Holstein andPeierls couplings λ α =0.167 and λ β =0.20: (a) ionicity ρ ( t ) anddisplacements (b) v A1 ( t ) with bare energy ω β A1 =0.040 for theacceptor molecule, (c) − v D ( t ) with bare energy ω β D =0.055 forthe donor molecule, and (d) v A2 ( t ) with bare energy ω β A2 =0.12for the acceptor molecule. J. Phys. Soc. Jpn. Full Paper
Author Name -0.2 0 0.2 0.4 0.6 0.8 0 200 400 600 800 1000 ρ ( t ) t λ α = . , λ β = . , ∆ = . (N) ω pmp = . ,T pmp = ,F= . j u j ( t= −20) = . (a) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 200 400 600 800 1000 ( − ) j u j ( t ) t ω α =0.013(b)-0.38-0.36-0.34-0.32-0.3-0.28-0.26-0.24 0 200 400 600 800 1000 − v D ( t ) t ω β D =0.055(c) Fig. 5. (Color online) Transient quantities after setting initialdimerization ( − j u j ( t = −
20) = 0 .
01 and charge-transfer pho-toexcitation of neutral phase using ω pmp =0.65, T pmp =10, and F =1.4 in same case as that in Fig. 4: (a) ionicity ρ ( t ), (b) dimer-ization ( − j u j ( t ), and (c) displacement − v D ( t ) with bare en-ergy ω β D =0.055 for the donor molecule. -0.2 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 ρ ( t ) t λ α = . , λ β = . , ∆ = . (N) ω pmp = . ,T pmp = ,F= . j u j ( t= −20)〉 = . Fig. 6. Transient ionicity ρ ( t ) after setting initial dimerization( − j u j ( t = −
20) = 0 .
01, adding random numbers to phononvariables as explained in text, and charge-transfer photoexcita-tion of neutral phase using ω pmp =0.65, T pmp =10, and F =4.2 insame case as that in Fig. 4, but for ∆=0.30.. Phys. Soc. Jpn. Full Paper
Author Name 9 FT o f ρ ( t ) ωλ α = . , λ β = . , ∆ = . (N) ω ext = . ,T ext = ,E ext = . j u j ( t= −20) = . (a) 0 2000 4000 6000 8000 10000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 FT o f ρ ( t ) ωλ α = . , λ β = . , ∆ = . (N) ω ext = . ,T ext = ,E ext = . j u j ( t= −20) = . (b) Fig. 7. Fourier transform of ionicity after photoexcitation, (a)without and (b) with initial dimerization ( − j u j ( t = −
20) =0 ..