arXiv:1002.4767v1 [cond-mat.mes-hall] 25 Feb 2010
Surface Charge Density Wave Transition in NbSe3
Christophe Brun1,∗, Zhao-Zhong Wang1, Pierre Monceau2, and Serguei Brazovskii3
1Laboratoire de Photonique et de Nanostructures,
CNRS, route de Nozay, 91460 Marcoussis, France
2Institut N´ eel, CNRS and University Joseph Fourier,
25 Avenue des Martyrs, B.P. 166,
38042 Grenoble cedex 9, France
3Laboratoire de Physique Th´ eorique et Mod` eles Statistiques,
CNRS and University Paris-Sud,
bat.100, 91405 Orsay, France
The two charge-density wave (CDW) transitions in NbSe3were investigated by scanning tunneling
microscopy (STM) on in situ cleaved (b,c) plane. The temperature dependence of first-order CDW
satellite spots, obtained from the Fourier transform of the STM images, was measured between
5-140 K to extract the surface critical temperatures (Ts). The low T CDW transition occurs at
T2s=70-75 K, more than 15 K above the bulk T2b = 59K while at exactly the same wave number.
Plausible mechanism for such an unusually high surface enhancement is a softening of transverse
phonon modes involved in the CDW formation.The regime of 2D fluctuations is analyzed according
to a Berezinskii-Kosterlitz-Thouless type of surface transition, expected for this incommensurate 2D
CDW, by extracting the temperature dependence of the order parameter correlation functions.
Powerful techniques have been recently developed,
such as grazing incidence inelastic x-ray scattering, an-
gle resolved photoemission, or scanning tunneling mi-
croscopy (STM), to probe the surface layer(s) of corre-
lated electron systems. An important question is cur-
rently raised regarding the surface electronic states of
these systems: are they identical to the bulk ones? This
question becomes even more crucial when the material
undergoes a phase transition to a broken symmetry state,
for instance a charge-density wave (CDW) transition; the
free surface must reflect this broken symmetry. The ”ex-
traordinary transition” corresponds to the very interest-
ing case where the surface orders at higher temperature
than the bulk . It opens the opportunity to study a
truly two-dimensional (2D) system which is more perfect
than usual ones prepared on a substrate.
Up to now experimental systems known to reveal such
surface transitions are extremely scarce . The anti-
ferromagnetic system NiO(100) is one of these . Re-
cently, at the surface of the quasi-2D compound NbSe2,
the CDW was shown to order at about 1.5 K above the
bulk transition temperature . This was subsequently
corroborated by emphasizing a modified behavior of the
surface phonon modes . On the other hand ”the com-
mensurate checkerboard order” discovered by STM in the
cuprate system Ca2−xNaxCuO2Cl2 (NaCCOC) , fur-
nishes a example of charge ordering stabilized at the sur-
face whereas the bulk doesn’t show such counterpart at
lower temperature. Hereafter, we report high-resolution
in situ STM measurements on the quasi-one dimensional
(1D) compound NbSe3which undergoes in the bulk two
independent CDW transitions at T1b = 144 K and at
T2b= 59 K, involving two CDW vectors, q1= 0.24 b∗for
the high-temperature (HT) CDW and q2= 0.5 a∗+0.26
b∗+0.5 c∗for the low-temperature (LT) CDW. By mea-
suring the temperature dependence of the amplitude of
the q1and q2first-order satellites we found that at the
(b,c) surface of NbSe3, the q2transition occurs at 15 K
higher than in the bulk, demonstrating the huge effect
of the surface on the LT CDW phase transition. Owing
to the phase degeneracy of this incommensurate CDW
and to the anisotropic electronic properties of NbSe3,
the Berezinskii-Kosterlitz-Thouless (BKT) transition is
investigated for the first time in real space.
NbSe3, one of the most widely studied CDW system,
was the first inorganic low-dimensional conductor to ex-
hibit a sliding CDW state when an electric field above
a threshold value is applied [7–9]. It has a linear struc-
ture consisting of three pairs of metallic chains per unit
cell running along the b axis, which are denoted as type
I, II and III according to the strength of the chalcogen-
chalcogen bond in the triangular basis of the chain. By
STM we could unambiguously identify for the first time
the three types of chains lying in the (b,c) surface plane
in the temperature range 5-140 K . The surface CDW
wave-vectors are q1= 0.24 b∗and q2p= 0.26 b∗+ 0.5
c∗, in excellent agreement with the bulk reported values
[11–13] projected on the (b,c) plane. A detailed analysis
of the spatial distribution of the q1and q2CDWs on the
various types of chain was performed and compared to
bulk x-ray diffraction results . A long range new mod-
ulation defined by the wave-vector u ≃ 2 × (0.26− 0.24)
b∗was observed, resulting from the interaction of both
CDWs being present on chains III .
The present work was performed with an Omicron LT
ultrahigh vacuum (UHV) STM system equipped with two
UHV separated chambers. Well characterized NbSe3sin-
gle crystals with typical dimensions of 0.01 × 10 × 0.05
FIG. 1: (Color online) STM images of the in situ cleaved (b,c) surface of NbSe3 measured at T =78, 63, and 5 K (Vbias= −300
mV, I = 100 pA). Scanned areas: 60×60 to 80×80 nm2. Insets: smaller portion of the image at larger scale. Below each image,
its 2D Fourier transform shows the lattice Bragg spots (indicated by c∗normal to the chains) and the q1 and q2 superlattice
spots. At 78 K the q1 CDW superlattice is clearly seen whereas the q2 superlattice spots are diffuse. At 63 K, i.e. 4 K above
the bulk transition temperature, the q2p CDW superlattice spots are already well defined, their amplitude being larger than
the one of q1 spots. At 5 K the ratio of the q2p to q1 amplitude is slightly larger than that at 63 K.
mm3were selected, cleaved in situ at room temperature
along the (b,c) planes and cooled down to 5, 63 or 78 K.
Samples were further thermalized at temperatures be-
tween 5 and 140 K. Our thermometer is a silicon diode
in good thermal contact with the sample. Intermediate
temperatures were stabilized by a feedback system con-
trolling a heater element while the STM head is continu-
ously cooled by the cryostat through copper braids. Ex-
periments were conducted when the thermal drift became
acceptable. Both mechanically sharpened Pt/Ir and elec-
trochemically etched W tips were used leading to similar
results. All the STM images shown in the following are
measured with constant current.
Fig. 1 shows three STM images measured at 78, 63
and 5 K, on large atomically flat terraces, with their 2D
Fourier transform (2D FT). Strikingly at 78 K, almost 20
K above T2b, one can easily detect the presence of diffuse
q2p superlattice spots, having a much lower amplitude
than the q1ones. At 63 K, i.e. 4 K above T2b, the q2p
superlattice is well developed leading to sharp spots in
the FT of the STM image, their amplitude being larger
than the one of the q1 satellites. This indicates that
the q2 CDW ordering occurs at higher temperature at
the surface than in the bulk. It contrasts with the con-
ventional behavior of the q1CDW  for which we do
not find a noticeable increment of the surface transition
temperature over the bulk one.
The q2 CDW surface transition temperature surface
(T2s) was determined by analyzing the temperature de-
pendence of the amplitude of the first-order q2psatellites,
extracted from 2D FT of STM images (areas: 20×20 to
40×40 nm2) . A selection of the measured STM im-
ages is presented in Fig. 2a for 5 < T < 78 K. As we have
shown in , only chains I and III are clearly visible in
these tunneling conditions, while the location of chains
II is shown for clarity, at 5 and 78 K. The corrugation
of the q2pCDW is about 15 pm at 5 K on chains I, has
very weak variations up to 62 K, and decreases strongly
between 62 K and 78 K. This is accompanied by a simul-
taneous diminution of the beating effect between q1and
q2p on chains III (see ). At 78 K, the q2p modula-
tion nearly vanishes and the q1wavefronts on chains III
becomes quasi-parallel and regular.
Quantitatively, the extracted q2pFourier amplitude as
a function of temperature is shown in Fig. 2b, with x-ray
diffraction results  and CDW-CDW tunneling data
. A sharp transition is observed by STM in the range
70-75 K, much above T2b= 59 K . From the results
of  the T2sof an unfree surface can be extrapolated
to ≈ 60 K. Hence there is evidence for an ”extraordinary
transition” occurring at the (b,c) surface of NbSe3 for
the q2CDW, leading to CDW ordering at a temperature
exceeding the bulk one by about 15-20%. The tempera-
ture dependence is more abrupt in the vicinity of T2sat
the surface than in the bulk. The dispersion of the exper-
imental data reflects that at different positions along the
FIG. 2: (Color online) a) STM images (10 × 10 nm2) of the in situ cleaved (b,c) surface of NbSe3 measured between 5 K and
140 K, showing the temperature evolution of the q2p CDW (Vbias= −300 mV, I = 100 pA). Insets: 2D Fourier transform (FT)
of the corresponding 20 × 20 to 40 × 40 nm2image. b) squares: normalized amplitude of the q2p CDW satellites measured
by STM as a function of temperature (vertical bars: dispersion of the measurements); dots: x-ray diffraction results on bulk
crystals ; triangles: double q2 energy gap probed by CDW-CDW tunneling . c) Profiles across the q2p peak along the
chain direction (b∗) at different T - FT of the pair correlation function of the CDW amplitude over the STM image. d) Full
widths at half-maximum (FWHM) along (b∗) and perpendicular to the chains (c∗) as function of T, extracted from FT of
30 × 30 nm2images - inverse correlation lengths. The dashed and dotted lines correspond to the smallest measurable FWHM
along b∗and c∗.
surface the measured CDW corrugation is not identical,
particularly in the vicinity of the transition around 70 K.
To explain the increase of T2b at the surface plane,
it is appealing to consider the differences existing be-
tween phonons propagating at the surface and in the
bulk. At a crystal surface, atom displacements normal
to the surface are larger than those encountered in the
bulk . Energies of the transverse phonon modes prop-
agating in the surface plane are then smaller than those
of the bulk phonons. The charge ordering occurring at
the surface of NaCCOC has been recently explained in
this way . Also the inelastic x-ray diffraction mea-
surements on NbSe2have shown that the Kohn anomaly
at 2kFis more pronounced at the surface and occurs at a
lower energy than in the bulk underlying the changes in
the phonon spectrum to explain the increase of Tcat the
surface . We believe that a similar situation is likely to
happen in NbSe3. Above T2b, when the q2CDW fluctu-
ations become 2D, these were shown to be transverse in
the (a,b) plane and not in the (b,c) plane . This is
consistent with x-ray refinements of the q2superlattice
modulation at 4 K, showing that larger lattice displace-
ments occur along a than along c . Thus, the phonon
modes involved in the q2distortion possess a transverse
component at the surface, supporting the idea of softer
transverse phonon modes for the top NbSe3layer, which
would lead to a CDW ordering at a higher critical tem-
perature through an increased electron-phonon coupling.
We get a deeper insight on the surface transition nature
by measuring the in-plane correlation functions and ex-
tracting the inverse correlation lengths (see Figs. 2c and
d). We observe a continuous evolution with T showing
that the system is in a 2D critical regime between 88 and
62 K. At 88 K, the correlations lengths ξb(along b) and
ξc(along c) are equal to 25b and 3c respectively and in-
crease to 70b and 10c at T≈62K.Below 62 K both correla-
tion lengths saturate, whereas the q2pFourier amplitude
is stabilized according to Fig. 2b. Here, the 2D regime
connects with the bulk pre-transitional region T2b= 59
K< T < 63 K of 3D ordering  - which will lead to a
growing interaction with the bulk.
To analyze the experimental results further we should
take into account some limitations regarding the length
scale, a finite window in the STM experiment, as well
as regarding the time scale, which is not instantaneous
like e.g.in X-ray diffraction experiment.
of size L × L with L = 30 nm, comprises 85 lattice
units - 20 CDW periods - along b and 20 lattice units
- 10 CDW periods - along c. We see from Fig. 2d that
L = 30 nm determines the smallest measurable FWHM
which are reached at ≈ 62 K. A useful scale to com-
pare with is the expected correlation length at T = 70
K due to the thermal fluctuations of an isolated chain,
ξT = ¯ hvF/(πkBT) ≈ 10˚ A≈ 3b, with vF = 3 · 107cm/sec.
This value is an order of magnitude smaller than the ob-
served one, supporting the presence of the observed 2D
regime. We infer from this analysis of the correlation
lengths that at 62 K appears a ghost transition because
of i) the finite size of the observation window, ii) the be-
ginning of 3D correlations in the bulk which suppresses
the surface 2D fluctuations.
The BKT transition refers to 2D systems like the He4,
a superconductor or an incommensurate CDW, described
by a complex order parameter. The BKT scheme con-
tains two features; i) below TBKT the order parameter
correlation falls off as a power law ∼ r−2η; ii) approaching
TBKT the correlation length grows very fast, the nature
of the transition being the confinement of vortex/anti-
vortex pairs which may become unbound at T > TBKT.
In principle this description applies to the regime where
the instantaneous local order parameter amplitude At,1D
(unlike the coherent component A2D≪ At,1Dmeasured
by the 2D FT) is already fixed, i.e. at low T starting from
a close vicinity of a mean-field (MF) transition at TMF,
which usually limits the observations. This region may
be extended to higher T in anisotropic systems like the
CDWs, where the planes consist of chains. The 1D-2D-
3D hierarchy  promotes the regime with phase-only
fluctuations: the 1D regime coalesces directly into the
BKT state . In our case this facilitates the observa-
tion of the wide 2D fluctuating regime.
The lack of true long range order in space is ultimately
related to its lack also in time. In the 1D regime, i.e. for
T > TBKT (above ≈ 90 K), the estimated fluctuation
time scale is orders of magnitude smaller than the typ-
ical STM acquisition time of 1 sec per line ; hence
the temporal fluctuations wash out the CDW from ob-
servations. For T < TBKT, the tremendous slowing down
of the fluctuations allows for the order observation (the
local order time decay law ∼ t−ηis characterized by
the very small η ≤ 1/8). This discussion leads us to a
usually overlooked fundamental distinction between the
slow STM measurement and the instantaneous one by X-
rays. Grazing incidence x-ray diffraction would be suit-
able tools to compare with our conclusions by tracking
the q2transition at the surface and in the bulk. Finally
we mention that some of our scans allow to visualize di-
rectly the vortices (dislocations in the CDW language)
and their pairs (phase solitons) which strengthens the
advocated BKT scenario.
In conclusion, high-resolution STM images of NbSe3
show that the q2 CDW, unlike the q1 one, undergoes
a sharp ”extraordinary” transition at the surface. Our
analysis of the correlation lengths shows at ≈ 88 K a
transition from the 1D regime to the 2D BKT state. This
seems to be the first real space observation of the BKT
regime. Below ≈ 63 K, 2D correlations are stabilized by
the critical increase of 3D correlations in the bulk. When
probing the fluctuations of the local CDW order by STM,
our analysis emphasizes that the time decay of the local
order dominates over the space one. This conclusion may
have impact on other STM studies in strongly fluctuating
systems like stripes in doped oxides.
The high-quality NbSe3 samples were synthesized by
H. Berger and F. L´ evy.We thank J.-C. Girard, E.
Machado and E. Canadell for many helpful discussions
and C. David for technical assistance. This work was
partly supported by the ANR grant BLAN07-03-192276.
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