Experimental study of the correlation length of critical-current fluctuations in the presence of surface disorder: Probing vortex long-range interactions

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by  J. Scola

Experimental study of the correlation length of critical-current fluctuations in the
presence of surface disorder: Probing vortex long-range interactions.
J. Scola, A. Pautrat, C. Goupil, Ch. Simon
CRISMAT, UMR 6508 du CNRS et de l’ENSI-Caen, 6 Bd Mar´echal Juin, 14050 Caen, France.
6 WereportoncriticalcurrentsandvoltagenoisemeasurementsinNiobiumstripsinthesupercon-
0 ductingstate,inthepresenceofabulkvortexlattice(B<BC2)andinthesurfacesuperconducting
0 state (Bc2 < B < BC3). For homogeneous surfaces, the correlation length of the current fluctua-
2 tions can be associated with the electromagnetic skin depth of vortex superficial instabilities. The
n modificationofthesurfacestatebymeansoflowenergyirradiationinducesastrongmodificationof
a the critical current and of the noise. The appearance of a corner frequency in the spectral domain
J can be linked with the low wave-vectors of the artificial corrugation. Since this latter occurs only
3 forB<BC2, weproposethatthelong-range interactionsallow thecorrelation length toextendup
tovalues imposed by thesurface topography.

]
n PACSnumbers: 71.27.+a,72.70.+m,72.20.My
o
c
- Noise measurements are powerful tools to go inside ysis would be notably improved if some characterization
r
p the origin of the vortex pinning, and of the dynamical of the vortex pinning is proposed beforehand.
u
interactions between the vortex lattice and the sample Inthispaper,wearethusinterestedinthemodification
s
. disorder. Thisnoise,generatedduringthe lattice flow,is ofthe flux-flow noisebyatuningoftherelevantdisorder.
t
a calledthe flux-flow noise[1]. Itisgenerallycharacterized For that, we will first discuss the nature of the pinning
m bytheshapeofitsspectraldensity,andbyitspower. As in our samples and bring some experimental arguments
- it is often proposed in noise analysis, it is convenient to on the way that the critical current can be substantially
d
define acorrelationlength,withinwhichthe fluctuations modified by a surface treatment. In a second approach,
n
are correlated. This defines the fluctuator ofthe system. the noise mechanism proposed in previous papers [4, 5],
o
c To the extent that the fluctuators are independent and will be discussed and specified by some recent results
[ that the system is large enough, the correlation length concerning the physical origin of the fluctuator. In the

can be calculated from the noise power via an usual sta- lastpartofthe paper,the effect ofsurfaceirradiationon
1
v tistical averaging (the central limit theorem) [2]. Re- thenoisepowerandthenoisespectrumwillbeshownand
1 cently, it was shown that no difference can be observed discussed. Forsakeofgenerality,thesemeasurementsare
4 betweenthe flux-flow noiseinthemixedstateandinthe made in Niobium, a well documented and conventional
0
surface superconducting state of a Niobium slab [3]. In type II superconductor.
1
otherwords,the same fluctuatoris presentwithorwith-
0
6 out a bulk vortex lattice, showing clearly its superficial
0 origin. The coupling to the bulk was shown to be due EXPERIMENTAL
/ to the conservation of the total current. This confirms
t
a previous auto and cross correlation experiments of both All measured samples are parts of the same piece of
m
flux and voltage noises [4], and explains the insensivity bulk Nb (initially 2 mm thick and 12 mm long). The
d- of the low frequency noise to bulk perturbations [5], in thicknesstwasfirstroughlyreducedto0.23mm,andthe
n Pb-In alloys. In these experiments, two parameters, the surfaces were progressively polished with 27 µm, 15 µm
o normalizedspectrumofthefluctuatoranditscorrelation then7µmroughpapers. Then,threesamplesofdifferent
c length,areexperimentallyjustifiedbutarenotexplained widthsW werecutbyawire. However,theroughnessob-
:
v [3, 4]. If the fluctuator is of superficial origin, it should tained after the finest mechanical polishing was still too
Xi be possible to induce notable changes in the noise char- largetoreducesufficientlythecriticalcurrent. Inorderto
acteristics after some surface treatments. A following reduceefficientlythissurfaceroughness,andtoeliminate
r
a change in the noise spectral density, the noise power, or the Nb O oxidesheath whichnaturally develops onthe
2 5
eventually in the underlying statistics, would give some niobium surface, a buffer chemical polishing (BCP) was
clues to understand the spectrum andthe fluctuator ori- performed. Eachsamplewasplungedintoanequivolume
gins. Wherever it takes place, it has been made clear for solutionofH PO (85%),HF(40%),HNO (69%)during
3 4 3
years that the existence of flux-flow noise is intimately eight minutes. Previous reports of the rms roughness af-
linked to the nature of the relevant disorder, i.e. to the tersuchaBCPgivevaluescloseto1nmintheµmscale
vortex pinning. In the conclusion of his review article, [6], in agreement with our AFM measurements. From
Clem states that such a flux-flow noise theory “ should the analysis of the AFM pictures (see fig. 2), we find
be intimately related to an appropriatetheory of critical 0.7 nm rms. This value is the mean values of 10 differ-
current density ” [1]. This implies that any noise anal- ent line scans takenin an area of 10 10µm2. After this
×
2
step,allsampleshavesimilarsurfacestateandtheirbulk Livingstonbarriers)[8]. Inordertoquantifythiseffectin
properties are unchanged. In the following, the samples oursamples,wehavemeasuredthecriticalcurrentofthe
(1) and (2) will correspond to the samples with respec- samples(1)and(2),whichhaveaverycontrastedwidth.
tively W=0.25 mm and W= 1.24 mm (t= 0.22 mm for If the critical current I is principally concentrated near
c
each). Thesample(3)willrefertotheirradiatedsample. the sample edges, its value should not significantly de-
Eachlargefaceofthissamplewasirradiatedbyanargon pendonthesamplewidth. Incontrast,sincewemeasure
beam for 30 minutes (acceleration voltage = 600 V, and a simple linear relation between I and W (fig. 1), I
c c
argon pressure 2.10−4 mbar). The sample holder was can be considered as macroscopically homogeneous all
≈
inclined at 45 degrees and continuously rotated in order overthewidthofthesurface. Notethat,a priori,itdoes
to make the etching very uniform in a 10 mm 10 mm notexcludesmallinhomogeneitiesandlocalI variations
c
×
area. Such low energy irradiation causes only superficial near the lateral edges, but those effects turn out to be
damages(about10nmofdepth),whichwillbediscussed on averagenegligible in our samples. We will show here-
in the text. after that the noise measurements will be a more precise
The superconductingparametersofeachsampleswere probe. Finally, macroscopic homogeneity of the critical
measuredbyDC transport,magnetization(SQUID) and currentmeansthatacriticalcurrentper unit ofwidth i
c
specific heat measurements. The following parameters (A/m)=I /(2W)isarelevantdescriptionofthe critical
c
were measured: T = 9.2 0.1 K, B (4.2K) = 2900 properties.
c c2
±
50 G and ρ (10K) 0.5 µΩ.cm. Comparing with For conventional soft type II superconductor, except
n
± ≈
the data of the ref. [7], a Ginzburg-Landau parameter theirreversibleedgeseffects,thevortexpinninghasbeen
κ=0.84canbeinferred. Thecriticalcurrentshavebeen showntoarisefrompinning ofthe tips ofthe vorticeson
measured by voltage-currentcharacteristics. the top and bottom surfaces. This is quantified by the
In addition, we have measured the voltage noise in- following expression ([9] and references herein):
duced during the vortex lattice motion. Voltage signals
wererecordedwiththefourprobesmethod,amplifiedby
ultra low noise preamplifier (SA 400F, 0.7 nv/√Hz). Ic/2W =ic(A/m)=ε.sin(θc) (1)
−
This signalsourceis then pluggedinto the analoginputs
of a dynamic signal analyzer (PCI 4551), converted where ε stands for the overall equilibrium magnetiza-
−
into digital signals and mathematically processed. All tion,andθc isthe characteristicsurfaceroughnessangle.
theexperimentalset-upwaselectromagneticallyshielded The topography of the surfaces was analyzed using
to avoid much of the external disruption. Such noise atomic force microscopy (AFM) in the tapping mode.
measurements are extremely sensitive to the tempera- The roughness of the virgin surfaces exhibits a random
ture stability: a special care has been taken to avoid disorder, with no characteristic scale. The fig.2 is a 3D
any excess of heating responsible of low frequency noise representationof the surface roughness. In terms of vor-
(contactnoiseorflickernoiseduetotheHeliumboiling). tex surface pinning potential, the relevant parameter is
Since Niobium is a very good conductor (R. 10 µΩ for equivalent to a contact angle θ. In order to calculate it,
oursamples), the contacts resistancesare the majorlim- wefirsttakeastatisticalrepresentativecrosssectionh(x)
iting problem. Making good electrical contacts on the (the average of several cross sections), then calculate its
bulk Niobium samples is difficult. The best solution was derivative dh/dx = tan (θ). The spectral density is then
′
to mechanically strip the end of the slabs of its oxide Sθθ =FFT( θ(x)θ(x+x) ). The main roughness angle
h i
sheath, to deposit a thin metallic layer and to press be- accessible for the vortices is given by [9]:
tweensmallcopperpieces. Finally,thiswasgoodenough
toapplyI .8Awithnospuriousnoise. Butinpractice,
Kmax 2π/ξ
inourmacroscopicsamples,thisrestrictstheexperimen-
θ2 = S dK S dK (2)
tal region relatively close to B . Z θθ ≈Z θθ
c2 Kmin 0
where ξ = φ /2πB 33 nm is the coherence
0 c2
≈
RESULTS AND DISCUSSION length. p
Inordertocalculatethecriticalcurrentwiththeequa-
Critical currents and vortex pinning: width and tion(1),the overallequilibriummagnetizationshouldbe
surface roughness effects known. Close to B , µ ε = B−Bc2 in the Abrikosov
c2 0 β(2κ2−1)
limit, with β = 1.16 for the hexagonal symmetry of the
Infig.1areshownthe criticalcurrentsversusthemag- vortex lattice. Using B = 0.29 T and κ = 0.84 in the
c2
netic field close to B for the Niobium samples. Recent equation (1), one finds, at B = 0.25 T, θ =arcsin(i /ε)
c2 c c
workshaveattributedmuchoftheirreversibleproperties = 2.1 0.1 deg. The surface topography analysis of the
±
oftypeIIsuperconductors,includingthevortexnoise,to samples (1) leads to θ = 2.3 0.2 deg (equation (2)),
±
the edges of the samples (geometrical barriers or Bean- in a close agreement. The equation (1) appears thus to
3
describe the critical current data, with θ θ as a rea- where S is the sample surface between the voltage pads,
c
≈
sonableaverageparameterdescribingthesurfacepinning and C the fluctuations correlation length. In the case
potential. We note that the same analysis was success- of stationary fluctuations, δV and thus C have a well
fully appliedinNiobiumfilms[9]. Thisconfirmsthepre- defined magnitude. In ref [4] and [5], C . 1µm was
viousassumption[9]thatthedifferenceofJ (A/m2)=2 found in Pb-In alloys.
c
ic/tbetweenbulkandthinfilmsNb(withdifferentthick- Themetallicandflux-flowresistivitiesofpureNiobium
ness t) does not mean a stronger pinning in films. This are quite low. As a consequence of the equation (3) and
simplyprovesthatJc isnotthegoodparameter,butthat for identical geometrical parameters, the flux flow noise
ic is. δV shouldbelargelyreducedcomparedtothePb-Incase
We now focus on the consequence of the surface ir- (or to any case of a relatively high resistance sample).
radiation on the vortex pinning. The measured critical This is consistent with our measurements. In addition,
currenthasbeenincreasedbyafactor 2.9inthesample using the equation (3) for Pb-In or Nb, very similar C
×
(3) (fig.1). As evidenced in the fig.2, the irradiation re- values are extracted. This means that the same noise
sultsinastrongdegradationofthesurface,withbothan mechanism controls the fluctuator size. A strong confir-
increase of the overall roughness and the appearance of mationthatC isarelevantparametercanbemadewhen
largecraters. Usingthesurfaceanalysisandtheequation comparingtwosampleswithcontrastedwidthsW >W
2 1
(2), θ = 4 0.2 deg is deduced (fig.3). The roughness C (respectively samples (2) and (1). For the same
± ≫
angle has thus been increased by a factor 1.7 by the surface state and the same (B,T) conditions, we have al-
×
irradiation. Note that the important parameter is not ready verified that i is constant (no edges effects). If
c
directly the roughness but the roughness angle which is C is constant too, the number of fluctuators should vary
a derivative. As a consequence, the increase of this lat- as W and δV W−1/2. This can be observed from the
∝
ter is notas strongasa visualimpressioncouldgive (see variation of the number of fluctuators as a function of
fig. 2). Finally, the increase of the critical current is W in the fig.4. This confirms that the noise arises from
qualitatively explained, but some difference appears in the statistical averaging of small and independent noisy
the comparison of the critical angles. In fact, ε in the domains. Consistently, we do not observe any cut-off in
equation(1)standsstrictlyforthesurfacevalue,whereas the spectral shape meaning that no size effect is intro-
we use the only known bulk parameters for the calcula- duced. In addition, the spectrum is very similar to the
tion of the Abrikosov expression. If this approximation one observed in Pb-In alloys (fig.5).
seems well justified in the case of homogeneous samples, Since the number of fluctuators is found to be propor-
it becomes questionable when the surfaces have been ir- tionaltothe surfaceofthesamples,oncanalsoconclude
radiated, because the concentration of impurities near thatthe (low frequencybroadband)noise doesnotarise
the surfaces should locally modify the thermodynamic from instabilities close to the edges of the sample. This
parameters. In general, the most important change is in contrasts to the conclusion of the ref. [11], where the
thecoherencelengthwhichhastobereplacedby√ξℓ<ξ voltage noise was attributed to the dynamical anneal-
in the dirty limit, with ℓ the mean free path (see for ex- ing of a disordered vortex phase nucleated close to the
ample [10]). This leads to a local increase of Bc2, here edges. We stress that this latter interpretation was pro-
restricted close to the surfaces. We will show below that posed for the peculiar case of the peak effect in NbSe ,
2
the noise measurementsconfirmthis slightincrease,pro- where two macroscopic critical current states coexist in
viding an attractive explanation of the underestimation the sample ([12, 13] and references herein), and where
of the critical current after the irradiation in the mixed the large noise values are coming from the kinetic be-
state. tweenthesetwostates. Thiswasshowntocorrespondto
non-Gaussian noise by a second spectrum analysis [14].
No such peculiar features are observed in our samples
On the noise for the smooth surfaces where the noise is observedto be Gaussianandhas been
verified stationary using the same high order statistics
When the applied current is over-critical, the voltage method. Note that the fact that we observe stationary
inthemixedstateisgivenbyV =R (I I ),withR and Gaussian noise reinforces the modeling of the noise
ff c ff
−
the flux-flow resistance. In the surface superconducting byindependentfluctuators,andhence,isconsistentwith
state, the same expression applies with R instead of the fig.4.
n
R . It has been shownthat, inthe case ofPb-Inalloys, We define a fluctuator by its correlation length C.
ff
most of the voltage noise originates from current fluctu- Up to now, C has been taken as an adjustable parame-
ations [4, 5]. Following here the same arguments, one ter, whose relevance has been experimentally controlled
can write δV R δI , and with the assumption of N (fig.4), but whose physical basis have not been clarified.
ff c
≈
independent fluctuators under stationary conditions: Thus,it is necessaryto gofurther inside the fluctuations
mechanism. Placais et al [4] proposed that the instabil-
δV =R I /√N =R I C2/S, (3) ities in the vortex lattice flow originate from the hang-
ff c ff c
p
4
ing and releaseof the vorticesonthe surface defects, the the power of the process. This should occur only if the
hangingconditionbeingthelocalboundaryconditionfor same critical current (critical angle) was reproduced at
a vortex line. Since the same boundary condition is the each instability. In reality, the disorder effect causes the
basis of a surface critical state [15], large fluctuations of distribution of critical currents at the sample scale and
magnitude I are expected. The more a vortex is bent, necessary induces an irreproducibility of the elementary
c
the morenondissipativecurrentcanflow. Locally,when instabilitiesmagnitude. Thiscreatesfluctuationsaround
a vortex leaves its hanging condition, I decreases very i and a broadening of the central peak (the low fre-
c c
h i
fastandatthe sametime, the amountofnormalcurrent quency broad band noise). We will see that changing
∗
I localized near the surface should increase due to the the disorder,i.e. the surface roughness,by the reinforce-
c
conservation of the total current. Thus, an electric field ment of the low wave-vectors, results in a change of the
∗ ∗
E =ρ J ρ J ρ 2i /λ is generated, λ being associated low frequency spectral shape.
ff ff c ff c v v
≈ ≈
the characteristic length scale associated to the decay of
surface currents (λ ξ/√2 close to B [15]). This is
v c2
≈
the elementary instability. On the noise for the rough surfaces
Its duration can be estimated as follows. Using the
Josephson relation, the line velocity reached by one vor- We have shown that the substantial rise of the criti-
∗ ∗
texendingduringtheinstabilityisgivenbyVL ∼=E /B. cal current in the mixed state can be mainly ascribed to
To the extent that one instability occurs per vortex pe- the increase of the surface roughness. For the samples
riod(individual process),the associateddiffusion time is with the homogeneoussurface states, the noise regime is
∗
τ =a0 /VL =a0Bλv /ρff2ic. Onetheotherhand,itis similar above and below Bc2, with comparable values of
known from classical electromagnetism that, for a given C. For B & B , the noise magnitude of the sample (3)
c2
time duration, the diffusion is restricted in a skin depth (rough surfaces) is enhanced in the same proportion as
δ =(ρffτ / µ0π)1/2. This leads to for the critical current, meaning that the same C value
is found again. For B . B , a noise rise of two orders
c2
of magnitude more than I is observed. It is clear that
δ (a Bλ /µ π2i )1/2 (4) c
0 v 0 c
≈ no fundamental change in the pinning mechanism has
For typical values (B = 0.27T, a 0.08µm, , ρ been introduced by the irradiation, since this latter was
0 ff
≈ ≈
ρ B/B 0.3µΩ.cm, i 700 A/m, λ 23nm), accounted for by the increase of the surface roughness.
n c2 c v
≈ ≈ ≈
τ . 0.07 ns. One can note that these instabilities Inaddition,specific heatmeasurementsconfirmthatthe
are extremely short compared to the flux-flow period bulk second critical field B remains unchanged. Any
c2
T = a /V a Bt/ρ 2i 1 µs. The skin depth cal- modifications of ρ were observedneither. As expected
0 0 L 0 ff c ff
≈ ≈
culated from (4) is δ 0.3 µm, a value very close to the by the very low kinetic energy of the ions, the surface
≈
correlationlengthC. Thecomparisonbetweentheequa- irradiationhas noinfluence onthe bulk propertiesofthe
tion (4) and the experimental data for the Nb (1) and sample. Anextranoiseregimeduetoastrongincreaseof
(2) is shown in the fig. 6 for B <B . The agreement is the bulk defects concentration is thus very unlikely. An
c2
satisfactory. For B > B , in the surface superconduct- increase of the correlation length C of the surface cur-
c2
ing state, the equation (4) is not very accurate because rents fluctuations, resulting in less statistical averaging,
λ has not been estimated in this case. Nevertheless, it is a more consistent track. All samples being identical,
v
appears clearly from the experimental data that there is apart from their surface state, this increase has to be
no change of regime. This can be explained by the fact linked to the introduction of the artificialsuperficial dis-
that in Niobium, λ ξ, which is the order of magni- order. In addition to the enlargement of the coherent
v
≈
tude of the surface sheath [16]. It can be noted that in domain, a striking change can be observed in the spec-
the equation (4), the important parameter which deter- tralshape. The usually smoothdecayofthe noisepower
mines the range of the fluctuations is not the flux-flow with the frequency is here replaced by a strong decrease
resistivity but the surface critical current i . Nb and at high frequencies (S f−4.4) and a nearly white
c vv
∝
Pb-In have very different resistivity but similar i val- noise below a kink at a frequency f (fig. 7). f corre-
c c c
ues (i (T =4.2 K, B/B = 0.9) 700 A/m for Nb and sponds to a characteristic time τ = 1/f , above which
c c2 c c
≈
300 A/m for Pb-In). This explains why Nb and Pb-In correlationvanishes. f turnsouttohaveatoosmallvor-
c
samples exhibit also similar C values. texvelocitydependencetobeobviouslyconnectedwitha
One concludes that C can be described as the skin time of flight or a transit time. Anyway, the appearance
length of very fast instabilities close to the surface. We of a large C and of f are simultaneous. Since the char-
c
stress that this mechanism determines the noise power acteristic length r V /f is very far away from W or
c L c
≈
via the size of a coherent domain, but it is clear that, a , but always found to be of the order of magnitude of
0
ideally, such a stick-slip like process generates only a C, this suggests that τ is associatedto the collective re-
c
highfrequencypeakatf =T−1 (andtheassociatedhar- arrangement of the surface currents within the coherent
0
monics), and a sharp peak centered at f = 0 containing domain [17].
5
Some large scale defects can be easily evidenced on regime of the mixed state and the surface superconduct-
the degraded surface (fig.2). To be more precise, we ing state. It appears that the critical current is quan-
haveplottedtheroughnessspectrumS (K)inthefig.8, titatively controlled by the surface roughness, and as a
θθ
where the increase of spectral weight due to the irradi- consequencecanbemodifiedbycontrolledlowenergyir-
ation is clearly shown. The lowest wave-vectors are the radiation. Themechanismofvoltagenoisewhichreflects
most affected. They correspond to the large bumps of the underlying surface current fluctuations is not modi-
diameter d & 1µm which are also visible in the AFM fiedwhenthebulkvortexlatticechangesintothesurface
pictures (fig.2). Since they were introduced by the irra- vortices. The associated correlation length can be asso-
diation,theyofferanattractiveexplanationforthe large ciatedwiththeskinlengthofthesuperficialinstabilities.
C values. Weproposethattheydeterminethemaximum An artificial surface corrugation with large scale defects
availablecorrelationlength,withinwhichtheinstabilities causesanenlargementofthis correlationlength,onlyfor
are correlated, instead of δ in the virgin samples. This B . B . This reveals likely the long range interactions
c2
implies also that a slower diffusion of the instabilities is of the mixed state .
involved. For such a large scale mechanism to be effec- Acknowledgments: We would like to thank L. Me´chin
tive, the possibility of strong collective effects between (GREYC, Caen) for the surfaces irradiation, V. Hardy
vortex endings is necessary. Because of the magnetic (CRISMAT, Caen) for the specific heat measurements,
long-rangeinteractions,the FLL is much softer for short and BernardPlac¸ais(ENS, Paris)for fruitful discussion.
wave vectors of distortion (the elastic non-locality) [18]. Thisworkwassupportedbyla”re´gionBasse-Normandie
Evenifwedonothaveaquantitativeanalysisofthepro- ”.
cess, the followingresults arequalitatively accountedfor
by the introduction of the long-range interactions: (i) C
increases with the magnetic field close to B (fig.9), as
C2
expectedfromthesofteningofthevortexlattice,and(ii)
C returnstothevirginsamplevalueassoonasB &B . [1] J. R.Clem, Phys. Rep.75, 1 (1981).
c2
[2] M. B. Weissman, Rev.Mod. Phys. 60, 537 (1988).
Indeed,thesurfacesuperconductingstateispopulatedby
[3] J. Scola, A. Pautrat, C. Goupil, L. Me´chin, V. Hardy,
very short vortices which melt away rapidly in the bulk
and Ch. Simon Phys. Rev.B 72, 012507 (2005).
[19],sotheirresponseisexpectedtobeindividual(local).
[4] B. Pla¸cais, P. Mathieu, and Y. Simon, Phys. Rev. Lett.
Intheabsenceoflongrangeinteractioninthelattice,the 70, 1521 (1993).
instabilities process can not involve distortions at small [5] J. Scola, A. Pautrat, C. Goupil and Ch. Simon, Phys.
wave-vector,but is limited to the smallrangeroughness, Rev. B 71, 104507 (2005).
like in the virgin samples. One of the key points is that [6] S. Casalbuoni, L. von Sawilski, J. Kotzler,
cond-mat/0310565.
the large scale roughness affects the spatial extension of
[7] W. DeSorbo, Phys. Rev.135, A1190 (1965).
eachfluctuation, but not their power. The latter is fixed
[8] Y. Paltiel, E. Zeldov, Y. Myasoedov, M. L. Rappaport,
bythe criticalcurrentI thatexhibits amoremonotonic
c G. Jung, S. Bhattacharya, M. J. Higgins, Z. L. Xiao, E.
trend towards Bc2. Y. Andrei, P. L. Gammel, and D. J. Bishop, Phys. Rev.
It can be observed that C returns strictly to its “ vir- Lett. 85, 3712 (2000).
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c2
B = B , where B is the bulk v≈alue, as measured by Domenge`s, Y. Simon, C. Guilpin, and L. Me´chin Phys.
c2 c2
Rev. B 69, 224504 (2004).
specificheat. Aspreviouslynoted,thesurfaceirradiation
[10] H. Ulmaier, Irreversible properties of type II supercon-
causesaconcentrationofArionsonlyinthefirstnmun-
ductors, p 147, Edited by G. Ho¨hler, Springer-Verlag
der the surface. As a consequence, the coherence length
Berlin Heidelberg New York (1975).
is modified by mean free path effects (for example [10]) [11] Y.Paltiel, G.Jung,Y.Myasoedov,M.L.Rappaport,E.
and the surface second critical field is locally increased, Zeldov,S.Bhattacharya,andM.J.Higgins, Fluctuation
explaining why the surface properties are now slightly and Noise Lett. 2, 31 (2002).
shifted from the bulk properties. Finally, one can note [12] W. Marchevsky, M.J. Higgins and S. Bhattacharya, Na-
ture 409, 591 (2001).
that any change in the noise statistics can be observed
[13] A. Pautrat, J. Scola, Ch. Simon, P. Mathieu, A. Bruˆlet,
in any sample and in any regime. The noise is always
C. Goupil, M. J. Higgins, and S. Bhattacharya, Phys.
Gaussian and stationary, even after the surface irradia-
Rev. B 71, 064517 (2005).
tionwherethecorrelationlengthsarefoundtobenotably [14] R. D. Merithew, M. W. Rabin, M. B. Weissman, M. J.
increased. This canbe attributedto the largesize ofour Higgins, and S. Bhattacharya Phys. Rev. Lett. 77, 3197
samples which impedes any deviation from gaussianity (1996).
because of statisticalaveraging. If the size of the sample [15] P. Mathieu, B. Pla¸cais and Y. Simon, Phys. Rev. B 48,
7376 (1993).
is made small enough, a more peculiar behavior can be
[16] H. J. Fink and R. D. Kessinger, Phys. Rev. 140, A1937
expected and is observed [20].
(1965).
In conclusion,we havestudied the criticalcurrentand [17] Wehavealsoobservedsharppeakscorrespondingtof0 =
the voltage noise in Niobium slabs, in the high field VL/W in the sample (1). In contrast to fc, f0 can be
6
linked to a time of flight effect. This is an additional “

noise ” mechanism with long range coherence. Since its 100
power turns out to be negligible compared to the broad sample(1) ( s = 2.3 deg)
sample(3) (s = 4 deg)
band noise, it can be ignored for the present discussion. 10-1
[18] E.H. Brandt, E. H. Brandt, Rep. Prog. Phys. 58, 1465 m
a
(1995). gr 10-2
[19] I.O.Kulik, Sov.Phys. JETP 28, 461 (1969). sto
[20] J.Scola, A.Pautrat et al, in preparation. Hi 10-3
10-4
-10 -5 0 5 10
10 10000 q (degres)
sample(3) (irradiated surfaces)
(1) /m) sample(2) (virgin)
2)/Ic 5 (Aic x 2.9 FIG . 3: Color online. histograms of the roughness angles
I(c 1000 deduced from the AFM pictures analysis. The standard-
deviations of each histogram are noted.
0
0.24 0.26 0.28 0.24 0.26 0.28
B(T) B(T)
FIG. 1: Color online. Left: variation of the ratio of thesam-
ples (1) and (2) critical currents, versus the magnetic field
(mixed state, B < Bc2 = 0.295T). The dotted line corre-
spondstotheratiooftheirwidths. Right: thesurfacecritical
current for the sample (1) and for the sample (3) (irradiated
surfaces).
250 nm
100 nm
FIG. 2: Left: AFM picture of the virgin sample (2). Right:
AFM pictureof theirradiated sample (3).
7

20 B = 0.28 T
10
)
60
1
* 0
(
20 B = 0.27 T
N

10
0
0.0 0.5 1.0
W (m m)
FIG.4: Thenumberoffluctuators(N =S/C2),deducedfrom
the noise values, versus the samples width, for two magnetic
fields B<BC2.

100
2 10-1
m
r
o10-2
Vn
10-3
d
10-4
10 100
f (Hz)
FIG. 5: Color online. Normalized flux-flow noise spectral
densities in Pb-In (mixed state B =0.75.Bc2,I =3.06A [3]),
Nb(1)inthemixedstate(B=0.86.Bc2,I =0.8A)andinthe
surface superconducting state (B = 1.12.Bc2,I = 1A), Nb
(3) (irradiated surfaces, surface superconducting state only,
B=1.12.Bc2,I =4A) ). T = 4.2 K for all.

10 sample(1)
sample(2)
)
calculated
m
1
(mmm
m
c
0.1
0.8 1.0 1.2
B/B
c2
FIG.6: Coloronline. Thecorrelation lengthintheNbvirgin
samples (sample (1) and sample (2)) as a function of the re-
duced critical field. Also shown is the calculated skin depth
ofthesuperficialinstabilitiesusingtheequation(4)(T =4.2
K).
8

10-13
)
z sample(3) f -4.4
H (irradiated surfaces)
/
2(V 10-17 f -1.8

2
V sample(2)
dddd 10-21
10 100 1000
f (Hz)
FIG. 7: Color online. Flux-flow noise spectral density in Nb
(1) and (3) (T = 4.2 K, B = 0.27 T <Bc2). Note the huge
increaseofthenoiseandthechangeofthespectralshapeafter
thesurface irradiation.

) )
-1/2.m8.0x10-4 sample(3) A tFipM -1/2.m 10-3 1 m mmm m-1
d d
a resolution a
r r
( (

sample(1)
Sqqqqqqqq 0.0 Sqqqqqqqq10-4
0 k (m-1) 1x108 DDDD 106 k (1m0-71) 108
FIG.8: Coloronline. Left: Theroughnessanglespectralden-
sities Sθθ for thevirgin sample (1) and theirradiated sample
(3). Forthislatter,forsmallwave-vectors,astrongriseofthe
spectral density can be observed. Right: Difference between
thetwospectral densitiesin alog-log scale, so asto evidence
moreclearlythelargeincreaseofthespectralweightforscales
larger than roughly 1 µm.

100
Nb (1)
Nb (2)
rough Nb (3)
) Pb-In
m
µ 1
(

c
0.01
0.6 0.8 1.0 1.2 1.4
B/B
c2
FIG.9: Coloronline. Thecorrelationlengthasfunctionofthe
reducedmagneticfieldB/BC2(BC2isthebulkvaluededuced
fromspecificheatmeasurements,T=4.2K).Notethestrong
increase of C for B.B∗ ≈1.1Bc2 for theNb (3) (irradiated
surfaces).