Advances in the criteria for dividing thin superconducting films into narrow and wide films

0.09 MB·English

by  V. M. Dmitriev

Advances inthe criteria fordividing thinsuperconducting filmsinto narrow andwide films
V. M. Dmitriev,1,2 I. V. Zolochevskii,1,∗ and E. V. Bezuglyi1
1B.VerkinInstituteforLow Temperature Physics and Engineering, Kharkov 61103, Ukraine
2International LaboratoryofHighMagneticFieldsandLowTemperatures, Wroclaw53-421, Poland
Theresultsofexperimentalinvestigationsofthecriticalcurrentsandcertainnonequilibriumphenomenain
thinSnfilmsofdifferentwidthwareanalyzed.Usually,thinsuperconductingfilmsaredividedintotwogroups:
narrowchannelsw<l ⊥andwidefilmsw>l ⊥.Awidetransitionalregionwheretheconditionw>l ⊥holds
1 withalargemarginandatthesametimecannotbeexplainedfromthestandpointofthetheoryoftheappearance
1 ofavortexstatehasbeenfound.Thisshowsthatthegenerallyacceptedcriterionw∼l ⊥fordividingfilmsinto
0 wideandnarrowdoesnotwork. Thetransitionintoawide-filmregime,describedbytheexistingtheoryofthe
2 vortexstate,isfullycompletedonlyforw/l ⊥(T)>10−20.

n
a PACSnumbers:74.40+k
J

0
Itisnowgenerallyacceptedthatthinsuperconductingfilms 1.0
] 1 cwaindthbewdainvdidtehdickinnteossndararroewsmaanldlerwtihdaenfithlmeps.eneFtrilamtiosnwdheopsthe GLI/Icc0.8
n l ⊥(T) of a magnetic field and the coherence length x (T), 0.6
o
which ensures a uniform distribution of the current over the
c 1 2
0.4
- film width and absence of vortex resistivity, are said to be
r
narrowchannels. Phase-slipcenters(PSCs) appearwhenthe
p 0.2
u current, exceeding the critical current IGL(T) for Ginzburg- 0 10 20 30 40 50 60 70
c
s Landau (GL) depairing, flows in a narrow channel. These w/l
t. centersconsistofthe coresof size ∼x (T) and the diffusion ^
ma tailsonbothsidesofthecore,havingthelengthofthepene- sFaImGp.l1e:sRSendWuc5ed(Nc)r,itSicnaWlc6u(r•re)n,tSdneWnsi8ty(HIc)/,IScGnLWv9er(s(cid:7)us),wS/nlW⊥1f0or((cid:4)th)e;
trationdepthofalongitudinalelectricfieldintothesupercon- curve2–ALtheoreticalcurve. Theparametersofthefilmscanbe
-
d ductor. The order parameterD and the superconductingcur- foundinRef.4.
n rentI inthecoreofaPSCoscillate,andatcertainmoments
s
o D and Is vanish and the phase changes abruptly by 2p . The AL. Itturnedout[4] thatthe vortexresistivity arises only in
c
[ frequencyof the oscillations is determinedby the Josephson afilmofsufficientwidth,w>4l ⊥,whileforI>Im thefilm
ratio fJ =2eV/h. passesnotintoanormalstatebutrathertoavortex-freestate
1
v Films whose width w>l ⊥(T),x (T) are said to be wide withphase-sliplines(PSLs)–thetwo-dimensionalanalogues
4 [1]. In such films, due to the Meissner screeningof the cur- of PSCs. Even more unexpected, and prompting us to raise
1 rent-inducedmagnetic field, the currentdistribution overthe thequestionofthetruecriterionfora“widefilm”,wasthebe-
9 width is nonuniform and exhibits sharp peaks at the edges. havior of the temperaturedependenceof the critical current,
1 AccordingtotheAslamazov-Lempitskiy(AL)theory[2],the shown in Fig. 1 for several samples as a dependence of the
.
1 resistive transition of a wide film is due to the instability of reducedcurrentI/IcGL on theparameterw/l ⊥, whichis pro-
0 thecurrentstatewhentheedgecurrentdensityreachesavalue portionalto1−T/Tc.AccordingtotheALtheory,forw>l ⊥
1 closetothecriticalcurrentdensity jGLintheGLtheory.This this dependenceshould be described by a universalfunction
1 c
: instability results in the creation of vortices, whose motion ofw/l ⊥,IcAL/IcGL=1.5(pl ⊥/w)1/2 (curve2). Intheexperi-
v generatesvoltageatthe endsof thefilm. Thecorresponding ment,asseenfromFig.1, thisuniversalitydoesindeedexist
Xi criticalcurrentIcALissmallcomparedtoIcGL,sincethecurrent butonlyforverylargevaluesofw/l ⊥∼10−20,whichthere-
densityinthebulkofthefilmisfarfromthecriticalvalue.On foreshouldserveastherealcriterionforatransitionintothe
r
a accountofthemotionandannihilationofthevortices,asec- wide-filmregime.
ond sharp peak in the current density forms at the center of For smaller values of w/l ⊥, the behavior of the critical
thefilm. ForcertainvalueIm ofthecurrent,themagnitudeof current is very peculiar. According to Ref. 4, samples with
this peak reachesa criticalvalue jcGL, whichresults in insta- w/l ⊥ <4 are narrow channels (in Fig. 1 the region to the
bilityofthestationaryflowofthevortices. IntheALtheory, left of the vertical straight line 1). In the interval between
itwassupposedthatforI >Im a film exhibitstransitioninto the vertical straight line 1 and the curve 2, there is a tran-
thenormalstate. sitional region where the film is “quasi-wide” (a vortex sec-
The experimental investigations of resistive transitions in tionis presentinthe current-voltagecharacteristic(IVC) but
wide films, although qualitatively confirmingthe above-des- the AL theory “does not work” yet). For the SnW10 film
cribed picture of a nonuniform distribution of the current in (w=7m m)theexperimentalcurrentIc forw/l ⊥<4equals
subcriticalandvortexstates [3, 4], haveatthe sametime re- the computed value of IGL. As temperature decreases, i.e.
c
sultedinconsiderablerefinementofthemainassumptionsof w/l ⊥ increases, vortexresistivity arisesandIc dropsrapidly
2
than the Josephson frequency, also point to the inapplicabil-
ity of the widely accepted criterion w≈l ⊥(T) for a “wide
film”. This phenomenon, called non-Josephson generation
[5, 6], arises when a certain current density j is reached,
g
andthisgenerationcurrentdensityfornarrowtin films(w≈
x ≈ 1 m m) is 2.7 times higher than for wide samples with
w>20m matthesamereducedtemperatureT/T =0.99[6].
c
Thus,forfilmwidthintherange1−20m m,asmoothtransi-
tioncanoccurfromhightolowgenerationcurrentdensities.
FIG.2: GenerationcurrentdensityversusSnfilmwidthatT/Tc= To check this assumption, a film obtained in one deposition
0.99. operation was used to prepare a series of samples with dif-
ferentwidth. The results of measurementsof the generation
toasmallervalue,whichnonethelessrevealsthetemperature currentdensity jg versusthewidthwoftinfilmsattempera-
dependenceclosetoIc(T)thatcontinuesrightuptoatransi- tureT =0.99Tc [6]arepresentedinFig. 2. Itisevidentthat
tionintoregimedescribedbytheALtheory.Thisdecreaseof the center of the transition from a narrow to a wide channel
I isevenmorerapidfortheSnW6film(w=17m m),asare- correspondstow≈12m m.Thus,fromthestandpointofnon-
c
sultofwhichtheregionofthetransitionaltemperaturedepen- Josephson generation, tin films with width up to w≈5 m m
dence I (cid:181) (1−T/T)3/2 expands considerably. Finally, for canbetreatedasnarrowchannels,whiletheybecome“wide”
c c
thewidestfilmsSnW8(w=25m m)andSnW5(w=42m m), onlyforw>20m m.
whereanarrow-channelregimeisnotobservedbecauseofthe A similar conclusion concerningthe inapplicability of the
extremeproximityofthecorrespondingtemperatureregionto widelyacceptedcriterionw≈l ⊥(T)[1]fordeterminingthe
Tc,thedependenciesofIc/IcGLonw/l ⊥arecompletelyidenti- boundarybetween narrowand wide films can also be drawn
cal,andthewidthofthetransitionalregionreachessaturation. on the basis of an analysis of changes in the dependence of
It should be noted that the observed wide transitional re- thecriticalcurrentIconthepowerPofanexternalmicrowave
gion, where the conditionw>l ⊥ holdswith a large margin field for films with differentwidth [7]. Figure 3a shows the
andatthesametimethedependenceIc(T)isidenticaltothe functionIc(P)inrelativeunitsfortinfilmsofdifferentwidth
behaviorofIGL(T), cannotbeexplainedfromthestandpoint underidenticalexperimentalconditions. Thedescendingsec-
c
of the AL theoryof the mechanismof the appearanceof the tions of the curves Ic(P)/Ic(0) in Fig. 3a can be fit by the
vortexstate. Acharacteristicfeatureofthisregionisa sharp functionIc(cid:181) (1−P/Pc)a .ForthesampleSnW10(w=7m m),
transitionofIc(cid:181) (1−T/Tc)3/2toIcAL(T)(cid:181) 1−T/Tc.Ournu- whichatT/Tc=0.99isanarrowchannel[4],thedependence
merical solution of the London integral equation [2] for the Ic(P)/Ic(0)isconvexand,correspondingly,a =0.53<1.For
currentdistributionoverthefilmwidthforarbitraryvaluesof thesampleSnW6(w=17m m)thisdependencebecomescon-
w/l ⊥ also shows the absence of a wide transitional region caveanda =1.4islargerthan1,whilefortheobviouslywide
betweenIGL(T)andIAL(T)providedthecriticalcurrentden- filmSnW5(w=42m m)a =2.9. Thedependenceoftheex-
c c
sity jGL is reachedat the edge of the film at the pointof the ponent of the fitting functions of the critical current versus
c
transition. This could signify that the condition for the ap- thesample width, presentedinFig. 3b, showsthatthevalue
pearance of vortices for w/l ⊥ < 10−20 weakens because a =1canbeexpectedforafilmofwidthw≈12m m,andthe
of the existence of a competing mechanism for the penetra- descendingsectionofthefunctionIc(P)isa straightline. In
tion of vortices into the film when the edge current density otherwords, as the film width increases, the sign of the cur-
reachessomevalue j (T)smallerthan jGL(T). Toexplainthe vatureofthedescendingsectionsofthecurveschanges,anda
c c
observedconstancyofthe valueof Ic/IGL in the transitional filmwithw≈12m misaboundarybetweenquasi-narrowand
c
region,it mustbe assumedthatas thetemperaturedecreases quasi-widesamples,asinthecasedisplayedinFig. 2.
thequantity jc(T)increasesmorerapidlythan jcGL(T),andis In summary, the result of the investigationsof the critical
proportionalto(1−T/Tc)2. Atthepointwheretheybecome currentsanddifferentnonequilibriumphenomenainthinfilms
equal,atransitionoccursintotheALregime,whichexplains ofdifferentwidthmakeitpossibletoconcludethatthewidely
thesharpnessofthecrossovertothelineartemperaturedepen- acceptedcriterionw∼l ⊥fordividingfilmsintowideandnar-
denceofIAL(T)seeninFig.1.Inprinciple,suchamechanism rowdoesnotwork. Thetransitionintothewide-filmregime,
c
can be associated with edge microdefects, which have virtu- describedbytheexistingtheoryofthevortexstate, fullyoc-
allynoeffectontheGLdepairingcurrentinthenarrow-film curs only for w/l ⊥ >10−20. It can be supposed that the
regime,buttheyareasourceofvorticesinawidefilm.Atthe simplecriterionw>l ⊥ doesnotworkinpracticebecauseof
same time the excellent quantitative agreement between the the structural particularities of a Pearl vortex in a thin film,
critical currents Ic(T), Im(T) and the predictions of the AL which is not a truly localized formation [8]: in contrast to
theoryfor large valuesof w/l ⊥ casts doubton this supposi- an Abrikosov vortex in a bulk superconductor, its fields de-
tion. creasewithincreasingdistancenotexponentiallybutratherin
Other nonequilibrium phenomena, for example, the gen- a power-lawfashion. Specifically, Kogan[9] hasshown that
eration of electromagnetic oscillations with frequencylower the magnetic flux trapped by a single vortex in a thin film,
3
even at a distance 24l ⊥ from the vortex core, is 90% of the
(a) fluxquantum.Theratiobetweenthefilmwidthandthepene-
1.5 3
0) trationdepthofanelectricfield,whichforw/l ⊥∼10isclose
I(c to1,canalsoplayacertainrole.The“anomalous”vortexstate
/
) (transitionalregion)whichwediscoveredandwhicharisesin
P
I(c the interval 4<w/l ⊥ <10−20 for the computed value of
1.0 theedgecurrentdensity(cid:181) (1−T/T)2muchsmallerthanthe
c
2 depairing current density jGL(T) draws attention also. The
c
mechanismofthepenetrationofvorticesintoafilmforsuch
small edge currentsand the reason why it vanishesfor large
0.5 valuesofw/l ⊥arenotdescribedbyexistingtheoriesandhave
noexplanationatthepresenttime.
1
0.0
0.0 0.5 1.0 ∗ Electronicaddress:[email protected]
P /P [1] I.M.Dmitrenko, Fiz.Nizk.Temp.22, 849(1996)[LowTemp.
c Phys.22,845(1996)].
3
[2] L.G.AslamazovandS.V.Lempitskiˇi,Zh.Eksp.Teor.Fiz.84,
2216(1983)[Sov.Phys.JETP57,1291(1983)].
[3] A. G. Sivakov, A. P. Zhuravel, O. G. Turutanov, and I. M.
Dmitrenko,Czech.J.Phys.46,877(1996).
(b) [4] V.M.DmitrievandI.V.Zolochevskii,Supercond.Sci.Technol.
19,342(2006).
[5] G.E.Churilov,V.M.Dmitriev,andA.P.Beskorsyˇi,PismaZh.
2
Eksp.Teor.Fiz.10,231(1969).
[6] G. E. Churidov, V. N. Svetlov, and V. M. Dmitriev, Fiz. Nizk.
Temp.12,425(1986)[Sov.J.LowTemp.Phys.12,242(1986)].
a [7] V. M. Dmitriev, I. V. Zolochevskiˇi, T. V. Salenkova, and E. V.
Khristenko,Fiz.Nizk.Temp.31,1258(2005)[LowTemp.Phys.
31,957(2005)].
[8] J.Pearl,Appl.Phys.Lett.5,65(1964).
1
[9] V.G.Kogan,Phys.Rev.B49,15874(1994)
0
0 10 20 30 40
w, m m
FIG. 3: Relative critical current Ic(P)/Ic(0) versus the reduced•ir-
radiationpowerP/Pc fordifferenttinfilms: SnW5(N),SnW6( ),
andSnW10((cid:4))(a)andtheexponentofitsfittingfunctionversusthe
widthwofthesampleat9.2GHzatT/Tc≈0.99(b).