PHYSICAL REVIEW B 70, 033106 (2004)

Anomalous coherent phonon oscillations in the commensurate phaseof the quasi-two-dimensional 1T-TaS2 compoundY. Toda,1,2 K. Tateishi,1 and S. Tanda1
1Department of Applied Physics, Hokkaido University, Kita 13 Nishi 8 Kita-ku, Sapporo 060-8628, Japan
2PRESTO Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332–0012, Japan(Received 24 March 2004; published 30 July 2004)

We have investigated the coherent dynamics of the collective motions of phonons in the commensurate
phase of quasi-two-dimensional 1T-TaS2 using femtosecond laser pulses. One of the coherent phonons increased in intensity as a function of time, this behavior being strongly correlated with the decay of chargedensity-wave oscillations as well as the slow decay component in single-particle relaxation.
DOI: 10.1103/PhysRevB.70.033106

PACS number(s): 78.47.⫹p, 63.22.⫹m, 71.45.LrCoherent phonon motion excited by ultrashort laser pulses
sometimes shows time anomalies, which are deeply connected with electronic/structural instabilities and are eventually responsible for transient phenomena in materials
systems.1–4 For example, coherent phonons in Bi under highdensity excitation show time-developed frequency changes,
which is a precursor phenomenon to photoinduced phasetransitions and laser ablation.1 Recently, coherently excitedcharge-density waves (CDW’s) in low-dimensional compounds have been realized and extensively studied from various viewpoints.5–8 Since the formation of CDW ordering isaccompanied by ionic displacements, instantaneously excitedelectrons change their equilibrium positions and result in collective motion. This occurs in the same manner as displacive
excitation of coherent phonons (DECP) as predicted in various materials.9–11 Unlike bulk materials, however, lowdimensional systems have an underlying instability that plays
an important role in generating coherent motion even in lowdensity excitations.
The material used in the present study is a layered quasitwo-dimensional (2D) compound 1T-TaS2, which was thefirst material for which CDW’s were experimentallyobserved12 and is now a typical example used for showing
coherent CDW motion in time-domain measurements.6,7 Twophase transitions, incommensurate to nearly commensurate(NC) and NC to commensurate (C), take place at 350 K and⬃200 K, respectively. Below ⬃200 K共TC-NC兲, the CDW undergoes the first lock-in transition with a periodic lattice distortion (PLD). The excitation of CDW’s has been studied
extensively by electron, x-ray, and neutron diffraction measurements. Despite its simple lattice structure, the electronic
properties, including the dynamics, are not fully understood.
Below TC-NC, where the Fermi surface (FS) nesting is important for CDW formation, the residual density of states (DOS)at the Fermi level has been observed by angle-resolved photoemission spectroscopy (ARPES).13 Such pseudogap (PG)
behavior in 2D materials is important because of the similarity with high-temperature superconducting cuprates (HTSC)
for which the evolution of a PG is characteristic of hightemperature superconductivity.
Here we report the first observation of a temporalanomaly of coherent phonon motion in the C phase
1T-TaS2. Transient pump-probe reflectivity changes show
0163-1829/2004/70(3)/033106(4)/$22.50

several phonon oscillations including an efficient CDW amplitude motion (AM) below TC-NC. In high-resolution experiments at 3.3 K, time-dependent spectra clearly indicate that
one of the Eg phonons exhibits a unique delay for its generation, which depends on the decay of the AM mode. The slow
decay component of the single-particle (SP) response, which
is attributable to the relaxation in a gap state in the C CDW,
is also identical to the decay of the AM, and therefore also
accounts for the increase of Eg. These results suggest that theobserved time anomaly is closely associated with the SP dynamics in the C-phase 1T-TaS2.
Time-domain reflectivity data for phonon motion as well
as SP relaxations are measured with a standard pump-probe
setup. For the excitation source we use a mode-locked Ti:
sapphire laser with a full-width at half maximum (FWHM)
of 130 fs centered at an energy of 1.55 eV with a repetition
rate of 76 MHz. The pump and probe pulses were orthogonally polarized and focused by an objective lens onto asingle crystallite with a domain size of ⬃100 ␮m. The spot
size of the pulses was estimated to be about 10 ␮m in diameter. To reduce heating effects in the sample, the average
power was set to 0.1 nJ/ pulse. The pump pulse was chopped
at a frequency of 2 kHz and the reflectivity change of theprobe was detected at the chopping frequency by a lock-in
amplifier.
Figure 1(a) shows the typical transient reflectivity change
measured at 3.3 K. Since the excitation photon energy of
1.55 eV can excite the carriers into continuum states far
above a CDW gap, the general trend of the data can be
attributed to a transient response of the photoexcited carriers,i.e., associated with SP transitions.5 As shown in the inset,
the time evolution of the SP shows a large abrupt change
within 1 ps and a subsequent slower decay. The signal returns almost to the initial level after 10 ps following thepump excitation. Subtracting the SP contributions, we canobtain a strong modulation signal as shown in Fig. 1(b). The
corresponding Fourier transform (FT) spectrum clearly reveals several vibrational modes [Fig. 1(c)]. The dominant
oscillation at 2.4 THz shows a good correspondence with aCDW AM mode observed in Raman data. Several transient
properties of the AM oscillation including its temperaturedependence have been reported by Demsar et al.6
Besides the AM mode, the FT spectrum also shows small
peaks with frequencies at 1.5, 2.1, and 3.2 THz. Below

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FIG. 2. (a) Gray-scale plots of TRFT spectra corresponding to
the data in Fig. 1(b) as a function of delay time and frequency. (b)Cross-sectional view of the TRFT amplitudes. The solid and open
circles correspond to the AM and Eg oscillations, respectively.

FIG. 1. (a) Time-resolved reflectivity change at 3.3 K. Inset: thenonoscillatory component for SP response. (b) Oscillatory component in (a), and (c) corresponding FT spectrum. (d) Expanded viewsof (b) with a different time range. Dashed line: a damped sinusoidal
fit for the AM oscillation with the frequency of 2.43 THz and thedecay of 6 ps.

TC-NC, several Raman studies have also shown a number ofphonon peaks and attributed them to folded-phonon features
expected in C-phase 2D CDW due to the formation ofPLD.14 The observed phonon frequencies and their temperature dependences also seem to be consistent with those of theRaman data while their relative intensities are quite different.
The discrepancy with the relative peak intensities of the Raman spectra is consistent with the DECP process for coherent
phonon generation.8 A feature of interest in the present study
is the intense peak at 2.1 THz. On the basis of polarized
Raman measurements, Sugai et al. attributed this peak to oneof the folded phonons with Eg symmetry.14 Thus, we tentatively attribute the oscillation with the frequency of 2.1 THz
to the Eg phonon.
To understand the time evolution of the coherent oscillations, we first tried to fit the modulation signal with a single
exponentially damped sinusoidal function, in which the parameters are optimized for the AM mode. As shown in Fig.
1(d), the fitting function reproduces the experimental dataquite well up to 10 ps. The oscillation in the initial time
domain is found to be dominated by the AM mode. In contrast, the calculated AM oscillation does not match the datain the time range beyond 10 ps, suggesting contributions
from other phonon motions.1,3
In order to clarify the time dependences of the phonons
spectra, we next employed a time-resolved FT (TRFT)
analysis, where iterative FT was carried out by dividing theoscillation data into time windows with intervals of 10 ps

and a resolution of 0.83 ps. Figure 2(a) shows a gray-scale
plot of the modulus of the TRFT as a function of delay timeand frequency. The vertical cross section of this plot corresponds to the FT spectrum in each time window. In theTRFT spectra, each phonon mode exhibits constant frequency, suggesting that laser-induced lattice heating wassmall. On the other hand, the time evolutions of amplitudesof each phonon mode are completely different from eachother. Figure 2(b) shows horizontal cross sections of the AMand Eg peaks. In contrast to the abrupt appearance of the AM
amplitude with a single exponential decay, the Eg mode does
not initially contribute to the signal. Its contribution gradually increases until 15 ps, then decreases as a slow oscillation. This difference in the evolutions suggests that these two
motions originate from different processes. Note that Demsaret al. has also observed phonon modes with nearly the same
frequency as the Eg mode.7 However, because the amplitudeof the Eg mode was so small during the observation timescale, they focused only on the AM motion in terms of transient properties of collective excitation. Indeed, the amplitude of the Eg mode in our data is also negligible under
10 ps. It is interesting to note that the Eg phonon motion
remains around 30 ps after the pump excitation, which ismuch longer than the lifetime of the AM, as shown in Fig.
1(b). The long-lived coherence of the Eg phonon suggests theexistence of homogeneously distributed PLD with longrange order.
It is surprising that there is little oscillation amplitude
corresponding to the Eg phonon motion in the initial interval
despite the relatively large oscillation in the time range
above 10 ps. However, the absence of a signal does not mean
the absence of coherent motion during that time. It is reasonable to consider that the coherent oscillation of the Eg phonon occurs during the optical excitation but cannot contribute to the reflectivity change. The observed long-lived
coherence of the Eg phonon is a proof of such instantaneousexcitation. The generation mechanism for the collective
CDW motion is known to result from the instantaneous perturbation of the charge density. On the other hand, the PLD

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FIG. 3. (a) TRFT amplitude changes of Eg at various temperatures. The data are shifted vertically for clarity. The ticks indicate
the estimated rise time. Inset: gray-scale plots of TRFT at 140 K.
(b) TRFT amplitude changes of AM.

is formed at the expense of elastic energy of the lattice subsystem in the C phase. Therefore, the instantaneous modulation of the electronic system also induces a displacement ofion cores of the PLD, resulting in coherent folded-phonon
motion as well as CDW AM motion.
Coherent phonons coupled with multiple electronic
ground states is a plausible cause for the observed timeanomaly. The superposition of phonon motions with slightly
different energies results in a beat oscillation in their time
evolutions. In this case, however, the superposition of phonon oscillations with a relative phase differing by ␲ isneeded to explain the absence of signal in the initial interval
just after optical excitation. To our knowledge there is no
generation mechanism that can account for such coherent
phonon motion. In the present data it is difficult to infer acomplete mechanism for the observed time anomaly of theEg phonon. However, as discussed below, the SP dynamics in
the C-phase 1T-TaS2 is intimately associated with such timedependent contributions of the phonon motion to the reflectivity changes.
In Fig. 3(a), we plot the TRFT amplitudes of the Eg mode
as a function of time at different temperatures within thetemperature range of the C phase. As observed at 3.3 K, aprofound increase is measured for all temperatures except at
140 K where the Eg mode amplitude involves a contribution
from the AM mode because these two frequencies are veryclose. A contour plot of TRFT at 140 K is shown in the inset,
showing substantially the same time evolutions as shown inFig. 2(a). Whereas the Eg shows a gradual increase at eachtemperature, its rise time shortens with increased tempera-ture. In contrast, the AM exhibits an increasingly fast decay
with increasing temperature, as shown in Fig. 3(b), whichindicates that the AM decay is strongly correlated with the Egincrease.
The inverse correlation between AM and Eg is also correlated with the decay of the slow component of the SP relaxation, as seen in the inset of Fig. 1(a). Note that the decay
time of the SP shows a gradual decrease with increasing
temperature, which is again in good correspondence with thetemperature dependence of the phonon motion. A relaxation
process was proposed to account for the SP dynamics in such
1D structures.5 The SP, excited above the band gap, canquickly relax by a number of possible scattering events, andthen reach the band edge that arises from the FS nesting.
Because the gap acts as a bottleneck for relaxation, the SP’s
around the band edge undergo a slow decay process. A similar bottleneck should be expected in the C-phase 2D CDW;
however, the situation seems to be more complicated in1T-TaS2. At 140 K, i.e., even below TC-NC, a small but finite
DOS at Fermi level has been observed by ARPES.13 In ourtime-resolved data, the initial abrupt SP relaxation may be
responsible for such a gapless feature wherein the instantaneously excited SP can relax very quickly to the groundstate.15 However, SP relaxation also involves a slow decay,
which implies that a gap still exists.16 Since our results arefrom measurements far below TC-NC, that is, deep in theC-phase CDW, strongly localized electrons can produce agap feature even in the presence of a remnant DOS. Indeed,a strong emission peak shifted well away from the Fermi
level has also been observed in ARPES at 20 K.17 The
slowly decaying SP signal thus reflects the partially existing
gap states.
On the basis of this idea, the observed correspondence
between SP and AM decay indicates that the AM motion
contributes to the reflectivity change through the electrons in
the gap state. This in turn explains the reflectivity change
after the AM decay, which is determined by the SP responsein the vicinity of the ground state. From the gradual increaseof the Eg amplitude and its inverse correlation with the AM
decay, we conclude that the Eg phonon motion cannot contribute to the signal in the presence of SP’s in the gap state,
but rather in the ground state. To date, little consideration has
been given to the coherent phonon motion from PLD. However, their time evolutions show time anomalies, suggesting
coherent phonon motions associated with different electronicstates.
In summary, we have performed time-resolved spectroscopy of coherent phonon motions in C-phase 1T-TaS2 andhave observed an anomalous behavior in their time evolution. Time-resolved FT showed that one of the coherent
phonons with Eg symmetry showed a gradual increase, incontrast to the AM motion which appeared instantaneously.
Their temperature dependences indicated that the rise time ofthe Eg mode was strongly correlated to the decay of both AM
and SP relaxation.
The authors acknowledge Dr. Oliver B. Wright for very
useful discussions.

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