PHYSICAL REVIEW B 75, 115120 共2007兲

Selective optical probing of the charge-density-wave phases in NbSe3
K. Shimatake,1,2 Y. Toda,1,2 and S. Tanda1
1Department of Applied Physics, Hokkaido University, Kita 13 Nishi 8 Kita-ku, Sapporo 060-8628, Japan
2Division of Innovative Research CRIS, Hokkaido University, Kita 21 Nishi 10 Kita-ku, Sapporo 001-0021, Japan

共Received 27 October 2006; published 21 March 2007兲
We report a study of the ultrafast single particle dynamics in quasi-one-dimensional NbSe3 whisker crystals
using a two-color pump-probe measurement. A selective enhancement of the relaxation dynamics connectedwith one of the two charge-density-wave 共CDW兲 phases was realized by tuning the probe energy to around
1.5 eV, in which the temperature dependence across the corresponding phase transition shows a pronounced
anomaly. A similar selective excitation was possible in the coherent CDW oscillation.
DOI: 10.1103/PhysRevB.75.115120

PACS number共s兲: 71.45.Lr, 78.47.⫹p

I. INTRODUCTION

a two-color pump and probe setup with an objective lens, inwhich the coaxial configuration between the pump and probe
beams increases the spatial resolution up to the diffraction
limit, and allows reflectivity changes with a high signal tonoise ratio even in the thin whisker samples.
Time-resolved data for the photoinduced dynamics of
CDWs serve as snapshots of reflectivity changes 共⌬R兲. For
the excitation source, we used an optical parametric oscillator 共OPO兲 pumped by a mode-locked Ti: sapphire laser
共76 MHz repetition rate兲. The time resolution was estimatedto be around 200 fs from cross correlation measurements.
The probe energy can be set from 1.39 to 1.77 eV by using afundamental pulse and from 1.00 to 1.16 eV by using the
OPO. Note that these excitation energies are far greater thanthe CDW gaps 关typically around several tens of meV 共Refs. 8
and 9兲兴. Depending on the experimental configuration, thepump and probe beams can be generated by either the
Ti: sapphire laser or the OPO. The pump and probe pulse
polarizations were parallel to the conducting axis because⌬R is dominant in this direction, and the pulses were focusedthrough an objective lens onto a single-crystal region. The
pump and probe fluences were ⬃40 and ⬃10 ␮J / cm2, respectively. The pulse overlap with a diameter of 10 ␮m on
the sample surface was monitored using a charge coupleddevice camera, and was kept at a fixed position during themeasurements. The steady state heating caused by the laser
was accounted for by measuring the excitation power dependence. The sample was mounted on a helium-flow cryostat.

Photoinduced absorption and/or reflection spectroscopyusing ultrafast laser pulses has become a powerful tool forstudying the excitation dynamics of phase transitionmaterials.1–5 Here, the time-resolved data allows us to follow
the nonequilibrium single-particle 共SP兲 and collective electron dynamics that are inaccessible with other conventional
techniques. Recently, this optical technique was applied tomaterials characterized by the coexistence of multiple
phases,1–3 which involves interesting phenomena such as
high-TC superconductivity and quantum fluctuation effects.
However, in this case, the transient signal becomes complicated by a superposition of relaxation components derived
from the individual phases. Therefore, the selective probingof individual phases is essential if we are to obtain precise
measurements.
In this paper, we demonstrate that the phase-selective
measurement of NbSe3 crystals is possible by using a twocolor optical pump-probe measurement, which allows us toevaluate the photoexcited SP dynamics precisely even in coincidence with different phases. The temperature dependenceof the transient data shows a dramatic change in its amplitude and decay time across TC. The magnitude of thesechanges strongly depends on the probing energy, which allows the selective enhancement of the signal of the corresponding charge-density-wave 共CDW兲 phase.
II. EXPERIMENTThe samples studied in the present work are NbSe3
whisker-shaped single crystals with lengths of a few mmalong the conducting axis and widths of ⬃50 ␮m. They weresynthesized by the chemical vapor transport method. NbSe3
is the most extensively studied quasi-one-dimensional 共1D兲
CDW compound.6,7 This compound undergoes two independent Peierls transitions to CDW phases at TC1 = 145 K and
TC2 = 59 K. These two CDWs occur on two of three types ofchains with different nesting conditions in k space. The otherchains remain metallic down to the lowest temperatures.
Therefore NbSe3 is regarded as a multiple phase system.
Previous pump-probe measurements were performed witha conventional lens, and by restricting the CDW compounds
to those with a large single-domain size. Here, we employed1098-0121/2007/75共11兲/115120共5兲

III. RESULTS AND DISCUSSIONS

Figures 1共a兲 and 1共b兲 show two typical examples of transient ⌬R obtained at probe energies of 1.56 and 1.07 eV,
respectively. Both sets of data are strongly temperature dependent, and are qualitatively consistent with previous measurements for similar quasi-1D compounds,10 in which thetransient ⌬R observed at temperatures well below TC consists of two components: one is exponential decay, which
predominantly reflects the photoexcited SP dynamics, andthe other is coherent collective oscillations. We focus first on
the former component.
Since the pump pulse at near-infrared energy can excite
the SPs into higher-energy states far above the CDW gap, aquick relaxation to states near the band edge results in an

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SHIMATAKE, TODA, AND TANDA

FIG. 1. 共Color online兲 The time-resolved reflectivity change ⌬R
at various temperatures observed in the two-color pump-probe measurement. The pump and probe energies are, respectively, 1.07 eV
and 1.56 eV in 共a兲 and the reverse in 共b兲.

abrupt change of ⌬R. The subsequent exponential decay reflects the transient density change of the SPs accumulated in
the vicinity of the gap. When approaching TC’s from below,
this component shows an extended decay time with a lower
amplitude. This is known as precursor behavior related togap closing, which occurs due to the efficient reabsorption of
nonequilibrium phonons across the gap.11 Above TC1, i.e.,
above the temperature at which all chains are metallic, ⌬R
becomes very small, thus suggesting that the metallic chain
contributions are negligible. When we consider the SP relaxation process in each CDW phase separately, the transient⌬R in NbSe3 is described by⌬R共t,T, ␻ pr兲 ⬀冦

S1共T, ␻ pr兲e−t/␶1共T兲 + S2共T, ␻ pr兲e−t/␶2共T兲
共T ⱕ TC2兲,S1共T, ␻ pr兲e−t/␶1共T兲
共TC2 ⬍ T ⱕ TC1兲,
共1兲

where Sn and ␶n are the amplitudes and the relaxation timesof the SP component, respectively, for each CDW phase 共n= 1 for TC1 and n = 2 for TC2兲. Note that the Sn is mainly
determined by the optical transition probabilities at the probe
energy 共␻ pr兲. On the other hand, the pump-induced SPs forabove-gap excitation average their distribution over the neargap states during the instantaneous relaxation, resulting in aminor contribution to Sn. In addition, we mainly focus on thefraction of magnitude Sn / Sm 共n ⫽ m兲. In this case, the effectof the number of SPs, which is slightly changed in accordance with the pump energy, is cancelled out. Indeed, we
found that the outline of the transient ⌬R of the
1.07/ 1.56 eV 共pump-probe兲 excitation was almost identicalto the results for 1.56/ 1.56 eV 共not shown兲. Therefore we
define the characteristic amplitude as a function of ␻ pr.
The two data sets in Fig. 1 show qualitatively the same
temperature dependence but differ quantitatively. In particular, in the temperature range just below TC2 where the TC1
and TC2 phases coexist, ⌬R in 共a兲 has a much longer decay
time and a larger amplitude reduction than ⌬R in 共b兲. Theseobservations indicate that we can selectively probe the pho-

FIG. 2. 共Color online兲 Temperature dependence of ␶eff 共upper兲
and Seff 共lower兲 obtained at probe energies of 共a兲 1.56 eV and 共b兲
1.07 eV. The solid line in ␶eff shows a theoretical fit to the data, andthe lines in Seff is a guide for the eye. The inset represents the
expanded view of ␶eff around TC1.

toexcited SP dynamics in the TC2 phase as described in detailbelow.
In Fig. 2, we plot the effective decay time 共␶eff兲 and theamplitude 共Seff兲 at probe energies of 共a兲 1.56 eV and 共b兲
1.07 eV, in which we have fitted the exponential function to
the data without distinguishing the components given in Eq.
共1兲. In the TC2 to TC1 temperature range, where Seff and ␶eff
are actually identical to S1 and ␶1, respectively, the results
show similar temperature dependences for 共a兲 and 共b兲 关compare the inset of 共a兲 with 共b兲兴. As the temperature approaches
TC1 from below, S1共T兲 decreases suddenly and ␶1共T兲 increases divergently, suggesting a reduction in the gap energyof the TC1 phase. In contrast, below TC2, there is a significant
difference between 共a兲 and 共b兲. Seff in 共a兲 shows a great reduction at TC2 and its magnitude is 5 times greater than thatat TC1, while the magnitudes of TC1 and TC2 in 共b兲 are almost
identical. Correspondingly, one can see that ␶eff in 共a兲 diverges up to almost 10 ps around TC2 while ␶eff in 共b兲 reaches
only 1 ps. These results clearly indicate that S2  S1 isachieved in 共a兲 while S2 ⬇ S1 in 共b兲. Therefore ⌬R共t兲 isapproximately described by S2共T兲e−t/␶2共T兲 at ␻ pr = 1.56 eV.
Note that at ␻ pr = 1.07 eV, where ⌬R共t兲 ⬀ S1共T兲e−t/␶1共T兲
+ S2共T兲e−t/␶2共T兲, the divergence of ␶eff can be assumed to be
due to the relatively large S1共T兲 contribution around TC2. Inother words, the strong divergence of ␶eff observed at ␻ pr
= 1.56 eV reflects ␶2共T兲 more precisely. Also note that thedegree of divergence ␶1共T ⬇ TC1兲 is much smaller than that of
␶2共T ⬇ TC2兲, which will be discussed later.
To clarify the energy dependence of the selectivity on the
SP dynamics in the TC2 phase, Fig. 3共a兲 shows a series oftransient ⌬R obtained at a temperature just below TC2, where␶2 exhibits an extended decay. Because we used an OPO as
the incident light source, the pump energy is also changed bytuning the probe energy, which may modify the number ofphotoexcited SPs. To compensate for this effect, we compare␶eff rather than Seff in Fig. 3共b兲. This figure indicates that thelonger ␶eff becomes, the more Seff includes the contributionof the TC2 phase. The spectrum shows a slowly varying distribution, suggesting the energy dependent enhancement of
the contribution of the TC2 phase. The maximum value of ␶eff
is located at ␻ pr = 1.56 eV. Thus we conclude that selective

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FIG. 3. 共Color online兲 共a兲 The transient ⌬R at various probe
energies measured at 58 K. The fundamental and OPO excitation
limits are between 1.16 and 1.39 eV. The dotted line shows thelongest fast decay component observed at a probe energy of
1.56 eV. 共b兲 Semilogarithmic plots of ␶eff as a function of probe
energy. The solid line is a guide for the eye.

probing of the TC2 phase is achieved in this energy region.
Let us discuss the degree of divergence of ␶n in each
CDW phase. On the basis of the theoretical framework developed by Kabanov et al.,11 the SP dynamics reflects theBardeen-Cooper-Schrieffer 共BCS兲-type temperature dependence of the gap 关⌬g共T兲兴. In the simplest approximation, themodel yields a ␶n value that is proportional to the inverseof ⌬gn共T兲. In this case, ␶n diverges to infinity when the temperature is increased close to TCn. In a real system, ␶n issaturated by the thermal-phase fluctuations. The effectsof thermal fluctuation are marginal since here we studied the
SP relaxation on a picosecond time scale. The difference inthe maximum value of ␶n in the TC1 and TC2 phases cantherefore be explained by the difference in phase fluctuations
at TCn. In this case, the suppressed 共enhanced兲 divergenceof ␶1 共␶2兲 indicates the suppressed 共enhanced兲 phase coherence for three-dimensional 共3D兲 CDW ordering, which isconsistent with the difference in the modulation wave vectors, namely Q1 = 共0 , 0.241, 0兲 for the TC1 phase and Q2= 共0.5, 0.260, 0.5兲 for the TC2 phase. We note that the maximum of ␶1 is comparable with the results obtained for theother CDW compounds: ␶eff in 1T-TaS2 and 2H-TaSe2
reaches only 1 ps 共TC = 170 K兲 and 0.4 ps 共TC = 140 K兲, respectively, and K0.3MoO3 reaches almost 1 ps at TC = 180 K.
Therefore it is possible to consider that the divergence of ␶2
is extremely large. One possibility for such an enhancementof the maximum ␶2 is the phase locking of the coexisting
CDWs below TC2, which has been predicted for the zeromodulation wave vectors in the superposition of two
CDWs.12
Although these explanations are still speculative, we emphasize that the considerable difference in ␶n indicates astrong sensitivity to the phase transition properties and thus
provides a useful parameter for investigating the dynamics
and interactions of coexisting CDWs. In this sense, our results connect with recent reports on the sliding properties of
NbSe3 CDWs.13,14 Indeed, a motional 1D coherence accompanied by a loss of transverse correlation above TC2 and asliding induced decoupling of coexisting CDWs have been
observed, both of which are consistent with our results.

FIG. 4. 共Color online兲 共a兲 The oscillation transient signal ⌬Rafter subtraction of the decay components at various probe energies
obtained at 8.5 K. 共b兲 The FFT spectra of their signals. 共c兲 Semilogarithmic plots of the FFT amplitude of AM 共the lower peak at
1.13 THz兲 as a function of probe energy. The fundamental and OPO
excitation limits are between 1.16 and 1.39 eV.

We note a difference in the ␶eff saturation behavior was
also found in a comparison of topological NbSe3 crystals,
where the divergence of ␶2 in the ring NbSe3 is clearly suppressed even in the vicinity of TC2. In accordance with thepower-law decay of the transient ⌬R around TC2, we haveconcluded that the results can be explained in terms of thephase fluctuation enhanced by closed-loop topology.3,15,16
We now investigate the selectivity of the TC2 phase in thelowest temperature regime 共T  TC2兲. For this purpose, we
consider the coherent oscillation part of ⌬R, in which one of
the CDW oscillations 共amplitude mode, AM兲 clearly exhibitsenergy dependence. Since coherent AM oscillations are directly connected with optical transitions involving the CDW
gap states, the excitation energy dependence of the AM allows us to evaluate the corresponding CDW phase separately.
Figure 4共a兲 shows a series of such oscillating data at various probe energies after subtraction of the exponential decay.
For clarity, the corresponding fast Fourier transform 共FFT兲
spectra are shown in Fig. 4共b兲. Two characteristic peaks are
dominant in these spectra. The lower peak at 1.13 THzshows a softening behavior with increasing temperature andcompletely disappears above TC2, indicating AM associatedwith the TC2 phase. The higher peak at 1.22 THz is identified
as a coherent phonon because of its less pronounced temperature dependence.
It is important to note that at T  TCn, the SP dynamics
from each CDW phase exhibit almost the same decay time共␶1 ⬇ ␶2兲 mainly due to the completion of the CDW gap 共see
the bottom two curves in Fig. 1兲. Consequently, we cannot
distinguish the contributions of the different TCn phases inthe exponential part of ⌬R. On the other hand, the AM os-

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SHIMATAKE, TODA, AND TANDA

cillation shows a significant energy dependence as shown in
Fig. 4共b兲. Therefore we consider the AM oscillation amplitude to be an alternative parameter with which to evaluate
the contribution of the TC2 phase at T  TC2.
Figure 4共c兲 shows plots of the FFT amplitude of AM as afunction of probe energy. In this case, the more intense the
AM is, the more the signal includes the contribution of theTC2 phase. As seen in Fig. 4共b兲, the spectrum exhibits a distribution, where AM becomes dominant by tuning the probe
energy to the lower limit of the laser, suggesting an energy
dependent contribution of the TC2 phase.
We now discuss the mechanism by which the selective
excitation for one of two CDW phases was achieved in thetransient reflectivity measurements. Previous optical experiments on the NbSe3 whisker have shown that there are several small but distinct resonances originating from interband
transitions above the plasma edge.17–20 Theoretically, theband electronic structure based on tight-binding calculations
also predicts the number of higher excited states with flat
dispersions parallel to the CDW band where we can expect alarge transition probability for the resonant opticalexcitation.21,22 As mentioned by Demsar et al.,1 the probe
signal for above-gap excitation reflects the interband transitions from the band edge to an appropriate higher excited
band. Therefore, the excitation energy dependence in ourpresent results suggests a transition to the excited state witha large transition probability that increases the contributionof the corresponding CDW phase in the signal 关see Fig.
5共a兲兴.
We comment on the difference between the resonance energies in the two experiments at different temperatures. Although the exact spectrum peak is obscured by the laser limit
in Fig. 4共b兲, the energy corresponding to the efficient CDW
oscillation shifts toward a lower energy than the SP decay
spectrum 关Fig. 3共b兲兴. This shift can be explained by the transition schemes summarized in Figs. 5共a兲 and 5共b兲. The SP
decay was evaluated just below TC2, at which we observed
the opening of 2⌬g2. On the other hand, we obtained the
CDW oscillation at the lowest temperature where the complete gap exists. When we consider the transition from the
CDW band edge as the dominant process for the probe signal, the resonance energy should be shifted by the amount of
gap energy. 2⌬g2 is approximately 65– 100 meV,3,8,9 whichis consistent with the difference in the resonance. Note thatthe probe signal also reflects the upper edge of the occupied
electron band. Figure 4共c兲 also shows a small peak around1.56 eV, which may account for this resonance condition.

FIG. 5. Schematic diagram of the resonant probe transitions
measured in the vicinity of TC2 共a兲 and well below TC2 共b兲. For
simplicity, only the transitions from occupied states 共E0 and E1兲 toan unoccupied state 共E2兲 are shown. These two transitions are overlapped in 共a兲.
IV. SUMMARY

In summary, we have performed energy-selective pumpprobe reflectivity measurements on whisker NbSe3 with amicron size spatial resolution. The SP dynamics clearlyshows two anomalies in the temperature dependence, whichreflects the CDW phase transitions. The magnitudes of theanomalies in the SP decay constant and the SP excitation
amplitude are changed by changing the excitation energies,
indicating selective probing of the CDW phases. We havealso demonstrated that the AM oscillation can be employed
as another selective probe at the lowest temperature. The
results allow us to identify the transient signals in each CDW
phase and to clarify the differences in the phase transition
properties. In addition, the temperature dependence of selectivity could help to verify the selective excitation mechanism
in terms of the optical transitions connected with the CDW
gap states. These selective excitation experiments have great
potential as regards undertaking precision measurements ofnonequilibrium dynamics characterized by the coexistence ofmultiple phases.

ACKNOWLEDGMENTS

The authors sincerely thank P. Monceau, M. Oda, R.
Morita, and K. Inagaki for fruitful discussions. This work
was partially supported by a Grant-in-Aid for the 21st Century COE program “Topological Science and Technology.”

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