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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

(Dated: 13-01-2010)

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 [1]. 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 [2]. The anti-

ferromagnetic system NiO(100) is one of these [3]. 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 [4]. This was subsequently

corroborated by emphasizing a modified behavior of the

surface phonon modes [5]. On the other hand ”the com-

mensurate checkerboard order” discovered by STM in the

cuprate system Ca2−xNaxCuO2Cl2 (NaCCOC) [6], 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 [10]. 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 [13]. 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 [10].

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

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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 [10] 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) [15]. A selection of the measured STM im-

ages is presented in Fig. 2a for 5 < T < 78 K. As we have

shown in [10], 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 [10]). 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 [12] and CDW-CDW tunneling data

[14]. A sharp transition is observed by STM in the range

70-75 K, much above T2b= 59 K [12]. From the results

of [14] 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

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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 [12]; triangles: double q2 energy gap probed by CDW-CDW tunneling [14]. 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 [16]. 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 [17]. 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 [5]. 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 [18]. 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 [13]. 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

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connects with the bulk pre-transitional region T2b= 59

K< T < 63 K of 3D ordering [18] - 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 [19] promotes the regime with phase-only

fluctuations: the 1D regime coalesces directly into the

BKT state [20]. 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 [21]; 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-

A window

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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