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Submitted on 1 Jan 1978
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NONLINEAR ACOUSTIC PROPERTIES OF
CONDUCTION ELECTRONS
V. Fil, A. Gaiduk, V. Denisenko
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supp/Pment au no 8, Tome 39, aolit 1978, page
C6-543
N O N L I N E A ~ ACOUSTIC P R O P E R T I E S OF CONDUCTION ELECTRONS
V.D. Fil, A.L. Gaiduk and V.1. Denisenko
Physico-TechnicaZ I n s t i t u t e o f Low Temperatures, UkrSSR
Academy o f Sciences, 47, Lenin Prospect, Kharkov, 310164, USSR.
Rdsum6.- On a Btudid expdrimentalement diffdrents types de non-lindaritgs se prdsentant dans les Gtats normal et supraconducteur d'un mdtal sous l'effet du pompage ul tra-sonore.
Abstract.- Various types of nonlinearities appearing in the normal and supercon- ducting states of the metal due to ultrasonic pumping are studied experimentally.
In a pure metal the electron subsystem potential gradient linearly dependent on the fun- state changes essentially under intensive sound damental signal amplitude.
pumping. In the normal state these changes invol- ve a narrow strip of the effective zone of inte- raction (EZI) of electrons having the wave vector
-f +
K perpendicular to the sound wave vector q. In this case the "effective" electrons are trapped by the potential field of the sound wave and, thus they are withdrawn from the energy exchange pro- cesses. As a result, the sound absorption coeffi- cient reduces significantly / 1 , 2 / and harmonics are generated intensively. The peculiar feature of the discussed "impulse nonlinearity" (IN) is its strong dependence on weak magnetic fields, which permits its distinguishing grom the other types of nonlinearities. The magnetic field effect con- sists in withdrawing electrons from potential wells, created by a wave due to the Lorenz force.
In this work the efficiency of the 2-5 harmonic creation by the fundamental signal ampli- tude and magnetic field H was studied. Maximum amplitudes of Unw harmonics are at the level of several per cent of the fundamental signal Uw and depend nonlinearly on the corresponding power of .:U In particular, U3w % U; is for small Uu and Ujw % Uw for great ones.
Harmonic amplitudes nonmonotonically de- pend on the magnetic field and at n 2 3 have the shape of oscillating curves (Figure I); at H=O a maximum is observed for odd harmonics and a mini- mum.for even ones. The distance in H to the cor- responding extremum is linear to the fundamental signal amplitude. This is readily understandable since the only scale in this case is the rela- tionship between the Lorenz force and deformation
Fig. 1 : Dependence Ugw (H).
Simultaneously with the harmonic amplitude its phase (but not the velocity!) changes to the scale of %X. The position of the harmonic ampli- tude extrema is periodical to H1'2(Figure 2).
The reason seems to consist in that the in- tensive sound wave creates a sharply inhomogeneous distribution of electron density in space, which leads, in turn, to an appropriate distortion of the lattice deformation. Distinct oscillation de- pendence~ U (H) may result from additional quan-
nu
tization of the electron motion in a weak magnetic field.
In the course of the superconducting tran- sition a new type of nonlinearity is observed, which consists in a considerable decrease of the sound absorption coefficient due to sufficiently intensive sound pumping (Figure 3). It is found experimentally that this nonlinearity is not con-
nected with the above IN at least because it occurs in not very pure metals where IN is suppressed. A weak measuring signal probing of the space occu- pied by an intensive sound beam in different dire- tions, showed that the changes observed in the electron state refers only to EZI.
I 1
possible to find the energy gap value ant its dependence on the pumping amplitude. Near Tc this dependence appeared to be linear and at higher
intensities the gap increase reaches 100 % (Figure 4). Since the gap change is due to the EZI elec- trons, then the gap increase is unlikely, which was proved experimentally.
Fip. 2 : Dependence of extremum number U (H) on Numbers at the straight lines deno?: corres-
ponding harmonics. Fig. 4 : Change in energy gap as a function of
pumping amplitude.
Reference
/ l / Galperin, Yu.M;, Kozub, V.I., Fiz. Tverd. Tela 17 . . ( 1 9 7 5 ) 2 2 2 2 .
-
121 Fil, V.D., Denisenko, V.I., Bezuglyi, P.A., Fiz. Nizk. Temp.
-
1 ( 1 9 7 5 ) 1 2 1 8 .131 Bardeen, J . , Cooper, L., Schrieffer, Phys.Rev. 108 ( 1 9 5 7 ) 4 7 5 .
Fig. 3 : Measuring sound absorption near T :
o
