On dissipation and noise in weak superfluidity : the example of YBaCuO

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On dissipation and noise in weak superfluidity : the example of YBaCuO

M. Papoular

To cite this version:

M. Papoular. On dissipation and noise in weak superfluidity : the example of YBaCuO. Journal de

Physique, 1989, 50 (10), pp.1141-1144. �10.1051/jphys:0198900500100114100�. �jpa-00210983�

1141

LE JOURNAL DE PHYSIQUE

Short Communication

On dissipation and noise in weak superfluidity : ^the example ^of

YBaCuO

M. Papoular

Centre de Recherche ^sur les Très ^Basses Températures, ^{25 avenue des} Martyrs, 166X, ^{Centre de} Tri,

38042 Grenoble Cedex, ^France

(Reçu ^le 10 février ^1989, accepté ^{le 28}

1989)

Résumé. 2014 Dans les supraconducteurs à ^haut Tc, I’activation thermique ^{du mouvement de vortex}

ou

du glissement ^de phase ^{réduit le courant} critique ^Jc pratiquement à ^{zéro entre Tc et un} point

d"’irréversibilité" Tirr (~ Tc). ^Celui-ci joue le rôle d’un point ^{de stabilité} marginale induisant, ^de façon intrinsèque,

bruit en 1/f intense. Cette caractéristique semble conforme à des résultats expé-

rimentaux récents.

Abstract.

In the high-Tc superconductors, thermal activation of vortex motion or phase slippage

reduces the critical current Jc ^to practically ^{zero between Tc and a} nearby "irreversibility" point Tirr.

The latter behaves

marginal-stability point and intrinsic intense 1/f ^{noise is expected there,}

sistently ^{with recent} experimental findings.

J. Phys. ^{France 50} (1989) ^{1141-1144 15 MAI 1989,}

Classification

Physics ^Abstracts

74.60G - 74.60J - 74.70V

1. The long-standing search for high superconducting ^critical currents - at its climax, currently,

in the "new" superconductors - ^{has its exact} equivalent in the difficult progression, in, the early 70’s, ^toward Landau’s ideal critical velocity ⁱⁿ liquid 4He. ^Until extra-ordinary precautions ^were

taken in container design [1], ^ccrit remained about two orders of magnitude below the ideal 60 mls.

The reason of course was that vortices, ^{and vortex} motion, ^were easily ^{nucleated at} imperfections

-

thereby destroying pure superflow. ^{That is} just ^{what we mean} by "weak" superfluidity : ^{the order} parameter ^is fragile enough - ^{as in a} Josephson junction ^or weak link - that a significant phase gradient, ^{and the} accompanying persistent ^current vs - V p ^cannot be stabilized : the phase, instead, slips, ^{at the} expense ^of normal-fluid production ^{and flow.}

Recently, Yeshurun and Malozemoff [2] and Tinkham [3], concentrating ^on single-crystal physics, have shown that high-Tc superconductors ^{tend to} display intrinsically ^weak superfluidity

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500100114100

1142

somewhere below Te ^Vortex creep ^is already "giant" [2] ^{at low} temperatures ^{and the resistive tran-}

sition [3] may span ^ten degrees ^{K at} magnetic fields of about 5 T (B ^// c-axis). ^{These two} regimes :

creep ^{and flow are} separated by ^an "irreversibility temperature" ^{Tirr Tc,} which decreases with

increasing ^fields. Using ^standard type ^{II -} superconducting concepts (see e.g. ^Ref. [4]), ^{in the}

clean limit they ^were interested in, these authors have isolated an activation energy ^{for vortex mo-} tion : Uo, proportional ^{to the intrinsic} Ginzburg-Landau depairing ^{critical current Je} (and, ^{in the} regime they considered, inversely proportional ^{to the} magnetic ^field B). ^{Both Uo and Jeo are modest}

in thenewsuperconductors (Jco ’" 107 A/cm2) ,bothgodownasHc!ÀL ’" ^{(Te - T)3/2 where}

AL is the London penetration ^{length. Thus, thermal} activation T/Uo ^is very easy, expecially ^near Te (- ¹⁰⁰ K) . ^Jco provides ^an upper bound, ^{at low} T, ^{to the} actually measured critical current Je But, ^{closer to} Te, Je ^{will be} necessarily smaller than Je ^{even at zero field -} precisely ^{because of}

thermal activation - and will practically ^vanish [3] ^{between Tirr and Te} (Le. in the "flow" regime)

as ilustrated schematically ⁱⁿ figure ^{1. This} physics ^is conveniently expressed by ^the following (low T) ^formula [2] :

where C - 30 and the negative, activation term extrapolates ^to 1 somewhere around 7c ^{in the}

superconducting copper oxides - whereas it would remain smaller than a few percent ^{in conven-}

tional type ^II superconductors.

Fig. ^{1.- Schematic} representation of critical current Je, intrinsic critical current Jco, ^{and order} parameter,

as a function of temperature. Je is essentially ^zero in the flow region 11rr ^{T Te.}

Attention should be paid ^{to the} "vortex - melt" phase ^which, in YBaCuO, ^{occurs a few} degrees

below Te [5], ^{and is} probably ^{connected to the} quasi two-dimensional nature of these systems. ^As this phase ^shows up ^{even in} comparatively ^{low fields, we} might still have up ^{and down} vortices with

zero overall flux - as in the Kosterlitz - Thouless problem. ^{It is not clear at the moment whether}

or not this vortex - melting plays ^a major role in the vanishing ^of Je ^for 11rr ^T Te

2. The specific point ^{we want to make here,} is that this same thermally ^activated "fragilization"

of the superfluid ^order parameter will result in another kind of dissipation - namely ^intrinsic,

intense 1/ f ^{noise around Tirr.} In the irreversible region ^{below Tirr, the noise is not} significant ^since

the phase of the order parameter creeps slowly. ^Above Tirr, ^the rapid flow of the phase ^is practically structureless, resulting ⁱⁿ ordinary Nyquist ^noise. Thus, Tirr ^{behaves in some sort as a} marginal - stability point. ^{This concept} has been discussed by Langer ^{in the context of} pattern ^selection [6].

Near such a point, microscopic fluctuations are considerably, ^and nonlinearly, amplified, ^{and may}

induce random macroscopic defects in the main pattern. ^The equivalent ^{of these} defects hère

will be a structured noise, comparable ^{in nature to the low- f,} intermittent noise associated, ^for

example, ^{with the sliding of} charge-density ^waves [7].

Avoiding ^the complex [3, 4] details of collective vortex motion, ^our reasoning goes ^as follows.

The elementary movable unit in the problem is the celebrated flux bundle [4], ^the radius of which

we take to be AL. ^After Tinkham, ^and others, ^we regard ^{a local} region ^{where bundles slide} past

one another, ^{as a} phase-slip ^center [8] : the motion of vortex tubes is mimicked by ^the periodic vanishing, ^{at the} Josephson frequency

of the local order parameter, and attendant 27r-phase slippage. ^Po = 2 is the flux quantum

and V the local voltage increment, schematically represented ⁱⁿ figure 2, after reference [8]. ^The

threshold current I, ^{is an} equivalent ^{for our} activation energy Uo, ^{and the current shift} AI = )

represents (at ^constant voltage V) ^{an extra} dissipation - vIe

^an elementary condensation energy ^{is lost} hysteretically every period ^2-xlw [8].

Fig. ^2- Characteristic current-voltage ^{curve for a} Josephson ^{weak link} (after ^Ref. [8]). R is the normal resistance of the link.

However, ^{in as much as we are now} considering fluctuations (rather ^{than mean} values such as, for example, ^the apparent resistance in the resistive transition region), ^{we must go one} step

farther. We assume that each flux bundle is characterized by ^{a whole} spectrum S(i) ^{of activable}

currents i

I - le, ^{and that this} spectrum ^{has the} property ^of self-similarity. ^{This means that}

within a broad enough range ^of i’S, ^the spectral density S(ï) (in amp-1 ^of "modes" i depends only ^{on i itself :} S(1) - ^{i-l. This} assumption ^{of course leads} directly ^to 1/ f ^noise. Translating to frequencies : S (w) dw S(1)di, and making use ofw - ^{V _} (I - lc)a = ^{i a with} a = ) (Fig. 2), gives ^S (w) ^{w- 1 . Th} get the order of magnitude of the numerical coefficient,

we use our previous ^{remark on marginal} stability : the noise will be concentrated around Tirr ^and

it is therefore natural to assume : S (w) - 1 ¥fI (see ^{Fig. 1). So we write :}

where Je (0) ^{is the low-T critical current} and the normalized slope 1 a:,¡ 1 j ^{leaves a trivial nu-}

merical coefficient which couldn’t significantly differ from unity.

In a device with cross-sectional area A, ^{we have on} the order of A/,B 2 L random-walking ^bun-

dles. On the other hand, only a ^small, geometry-dependent, ^fraction

^{1 of the} random local

2x-phase steps ^will trigger ^an actual flux variation Ao (measured ⁱⁿ quanta ^of Po) : ^{the flux tubes}

are simply displaced - except ^near the borders of the sample, ^and except for closed loops acting

as local, microscopic squids. Summing up, ^we expect ^{a flux noise of the form}

1144

3. Crude as it is, this result seems to be consistent with a recent experiment performed by ^Clarke

and his group [9]. They measured the fluctuating screening of the flux through ^a (conventional) SQUID, ^{due to a} nearby ^small sample ^of ’YBa2 CU307- y. Their main findings ^{were :} (i) ^intense

low- f f ^{noise arising from} local fluctuations and sharply peaking (for crystallographically ^oriented samples) ^{at 85 K;} (ii) ^{at a} given frequency, ^the peak heigth itself did not depend ^much upon sample quality ; (iii) ^{on the} higher - ^T side, ^{the noise} intensity ^falls very steeply ^{and the} spectrum ^flattens

to white noise on the lower-frequency ^side.

One might regard point (ü) ^{as an} intrinsic-mechanism signature, ^and point (iii) ^as reflecting

loss of correlation at longer ^{times as one enters the T} > Tirr flow regime.

In the best sample, ^{at 1 Hz,} the f ^{noise at 77} Kwas still three orders of magnitude larger ^than

in a typical conventional SQUID ^{at 4} K. We suggest ^{that this} important result is understandable via the scaling ^factor ( j ) ^{1 ojl-} in the above formula for So (w) . Again, Tc as Uo ^{is thirthy or}

fifty ^times larger in YBaCuO. And the steepness ^{of Je} (T) ^at Ti (Fig. 1) ^is certainly considerably larger. (In ^a material of poorer quality, ^{Tirr smears out} (and Je decreases) ^{and the} residual noise away ^{from the} peak ^is larger).

It would be interesting ^to explore ^{the noise} magnetic-field dependence. Aside from shifting Tirr downwards, the main effect of B could be to reduce 1 V# I and ^{therefore Sep itself.}

We may conclude - after others (see e.g. ^Ref. [3]) - ^that superfluidity ^{in the} high - ^{Te su-} perconductors ^becomes intrinsically, ^and conspicuously, fragile ^{at T} Te. ^This places ^{a severe,} built-in, obstacle, ^at liquid nitrogen temperatures, ^{on both} "technological routes" : electronics and

SQUIDS, ^{as well as} high-magnetic field coils and current transport

References

[1] ^{HULIN J.P, LAROCHE C., LIBCHABER} A. and PERRIN B., Phys. ^{Rev. A 5} (1972) ^1830.

[2] ^YESHURUN Y. and MALOZEMOFF A.P, ^{P.R.L. 60} (1988) ^2202.

[3] ^{TINKHAM M., P.R.L. 61} (1988) ^1658.

[4] ^{ANDERSON RW and KIM Y.B., Rev. Mod.} Phys. ³⁶ (1964) ^39.

[5] ^{GAMMEL PL.,} SCHNEEMEYER L.F, ^WASZCZAK J.V and BISHOP D.J., ^{P.R.L. 61} (1988) ^1666.

[6] ^{LANGER J.S., Rev. Mod. Phys. 52 (1980) 1 ; P.R.L. 44 (1980) 1023.}

[7] ^{COLLAUDIN B., PAPOULAR} M. and WANG Z., ^J. Phys. ^{France 47} (1986) ^1463.

[8] RIEGER T.J., SCALAPINO D.J. and MERCEREAU J.E., Phys. ^{Rev. B 6} (1972) ^1734.

[9] ^{FERRARI M.J., JOHNSON M., WELLSTOOD EC., CLARKE J., ROSENTHAL PA., HAMMOND R.H.}

and BEASLEY M.R., AppL Phys. ^{Lett. 53} (1988) ^695.