ULTRASONIC STUDIES OF CONDUCTIVITY OF SUPERCONDUCTORS

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ULTRASONIC STUDIES OF CONDUCTIVITY OF

SUPERCONDUCTORS

V. Fil’, V. Denisenko, P. Bezuglyi

To cite this version:

JOURNAL DE PHYSIQUE

_Colloque

_{C6, supplkment au}

no

8,

Tome

39,

aozit

1978,

page

C6-679

ULTRASONIC S T U D I E S OF C O N D U C T I V I T Y OF SUPERCONDUCTORS

V.D. Fil', V.I. Denisenko and P.A. Bezuglyi

Physico-Technical I n s t i t u t e o f Low Temperature, UkrSSR, Academy o f S c i e n c e s , 47, Lenin Prospect, Kharkov, 310164, USSR

R6sud.- La mesure de la constante complexe de propagation du son transversal au voisinage de la tem- perature critique permet de determiner les parties r6elle et imaginaire de la conduction d'un su- praconducteur et leur anisotropie.

Abstract.- The measurement of the complex constant of the transverse sound propagation near Tc per- mits the real and imaginary parts of the superconductor conductivity and their anisotropy to be found.

In the course of transverse sound propagation in metals at frequencies w obeying the conditions ql>>l

,

q6<<1 ;( is the sound wave vector, 1 the mean free path, 6 the skin-depth) one of the main mechanisms of the electron-wave interaction is the electromagnetic one. This interaction contributes to the sound absorption coefficient

a

and leads

em

to renormalization of the,wave velocity S. In Kon- torovich's paper/l/ an expression was obtained for the complex constant of the transverse sound propa- gation in the metal, which shows that

aem

and the velocity variation are described by

where al+ian is the complex conductivity of the me- tal, the specifically Fermi surface weighted defor- mation potential, p the density. In the normal sta- te an % (vF

-

is the Fermi velocity)

and therefore the electron contribution to the sound velocity for q6<<1 is negligible.

The above expressions are also valid for the superconducting state, if 01 and 6 2 stand for the

corresponding superconductor parameters. It is known that the imaginary component of conductivity increases sharply below T varying near T by the linear law. As a result, the transverse sound velo- city near T also changes appreciably. A simultaneous measurements of

a

and AS/S under the superconduc-

em

ting transition permits an estimation of the com- plex superconductor conductivity als/aLN+ia2s/cr,N normalized to the real part of the normal metal conductivity through the transformation of the abo- ve expressions. As an example, figure 1 shows.data for one of the tin orientations, which were obtai- ned using to fitting parameter. The magnitude

Fig. 1 : Dependences of a 2 S / ~ l N (*) and O ~ ~ / U , ~ ( O ) on T -T.

~ ~ is seen to change linearly with temperature, ~ / a ~ ~ the line slope being in good agreement with that obtained in / 2 / for the same orientation by the me- thod of the electromagnetic sound excitation.

Figure 2 shows the AS/S(T) dependence for gallium. Unlike the tin, in which the second veloci- ty is affected, in addition to electrons, by dislo- cations, in Ga this effect is negligible and the electron contribution to the velocity can be esti- mated at lower temperatures. In the superconducting state far off T the sound velocity appears to ex- ceed its normal state value, the excess increasing with frequency. This behaviour results from the fact that in the normal state the electron contri- bution to S becomes appreciable, while in a super- conductor far off T it is negligible. The measure- ment of the velocity difference permits an estima- tion of a l N in addition to the above parameters.

Fig. 2 : Behaviour of sound velocity in gallium near T

c'

-.

Tc

T(K,J

Fig. 3 : Dependence of o2 and Aol above Tc.

References

A specific feature of all the absorption cur-

/I/ Kontorovich,V.M., Zh. Eksp. Teor. Fiz.

45

ves and the sound velocity variation for both tin (1963) 1638

and gallium is the presence of slowly varying "tail" /2/ Dobbs,E.R., Lea,M.J., Proc. LT-14 Vol. 2, 203, Helsinki, 1975

above T (which is found through extrapolating the most steep portions of the curves). Experiment rea- dily shows that the "tails" are not related to the sample imperfection, since they are well reproduci- ble on different samples and are characterized by noticeable anisotropy. The sample state in the "tail" region may be classified as superconducting since it is destroyed by the magnetic field. The restored 02S and (alS -0 ) values are exponential-

1N