HALF-HARMONIC OSCI LLATIONS AT rf INDUCED STEPS IN SUPERCONDUCTING MICROBRIDGES AND TUNNEL JUNCTIONS

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HALF-HARMONIC OSCI LLATIONS AT rf INDUCED

STEPS IN SUPERCONDUCTING MICROBRIDGES

AND TUNNEL JUNCTIONS

J. Mygind, N. Pedersen, O. Soerense, B. Dueholm

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, s u p p l h e n t au no 8, Tome 39, aolit 1978, page ~ 6 - 5 9 7

HALF-HARMONIC OSCILLATIONS AT

rf

INDUCED STEPS IN SUPERCONDUCTING MICROBRIDGES AND

*

TUNNEL JUNCTIONS

J. Mygind, N.F. Eedersen, O.H. Soerensen and B. Dueholm.

Physics Laboratory I , The technical University o f Dewnark, DK-2800 Lyngby, Denmark.

R6sumd.- Rgcemment une oscillation 5 la frgquence moiti6 du fondamental a 6t6 pr6dite c o m e compo- sante de la tension du palier n = 1 d'un micropont. Pour aucun des microponts examin6s, nos exp6- riences n'ont Bt6 capables de confirmer cette prgdiction. Toutefois nous avons observ6 de grands signaux 3 la frgquence moiti6 du fondamental dans le cas de jonctions "tunnel" essayges dans des conditions analogues.

Abstract.- A half-harmonic oscillation at the fundamental rf induced step was recently predicted for a microbridge. Our experiments could not confirm this in any of the microbridges tested. However, large half-harmonic signals were observed in tunnel junctions biased at the fundamental rf induced step.

In a recent communication /I/ Fjordb6ge and Lindelof discussed subharmonic generation in a Da- yem bridge. From analog computations they conclu- ded that the ac Josephson voltage at the n = 1 mi-

crowave induced step may contain a half-harmonic voltage component. The effect was found for a range of bias currents approximately in the center of the step provided the applied rf power exceeded a threshold level. This phenomenon is of much current in- terest in connection with work on microwave parame-

tric amplifiers. In a tunnel junction, for example the subharmonic generation at the n = 0 step /2/ (the supercurrent) has led to an X-band singly de- generate parametric reflection amplifier 131.

Indium microbridges /4/ of dimensions approximately 0.5 x 0.5 um2 were studied. The microbrid- ge was mounted at the low impedance end of an X- band binomial transformer connected to an X-band receiver. An 8

-

18 GHz signal could be coupled to the junction via a coaxial semirigid waveguide and a loop / 3 / .

Figure la shows a typical half-harmonic spectrum for a microbridge. The receiver frequency,

c is 8.6 GHz and the applied frequency, fa, is 17.2 GHz. The spectrum is dominated by the two large peaks seen at dc voltages corresponding to the n =

1/2 and n = 3i2 rf induced substeps ; these signals

bias at 8.9 pv where the second harmonic of the Josephson oscillation is within the receiver band- width. We note, however, that a half-harmonic voltage is not observed at bias currents corresponding to the n = 1 rf induced step. This was confirmed in all our microbridges in the temperature range from

TC down to temperatures where hysteresis due to selfheating sets in, and for a range or power levels from zero to full suppression of the supercurrent.

are due to mixing between the Josephson oscillation

Fig. 1 Typical power spectra at

ha

= 8.6 GHz with at n

.

fa and the applied signal at fa. The smaller applied microwaves at fa = 17.2 GHz. (a) An indium peak below the n =

5

structure corresponds to a dc microbridge.: (b) A Sn

-

0

-

Sn tunnel junction.

*

_{This work was supported in part by "Statens}

Using a tunnel junction (Sn-0-Sn, 0.1 x 0.2 Naturvidenskabelige ~orskningsrgd", grant No.

5 1 1-8048. m 2 , maximum supercurrent density 20A/cm2) in the

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in the same experimental set up, we obtained spectra as that shown in figure lb. Here the narrow peak corresponds to mixing at the n = 312 step. The wide peak shows half-harmonic generation at the n =

I rf induced step.

The subharmonic generation depends qualitative- ly on the applied power level, Prf, in the follo-

wing way : For small Prf no subharmonics are observed. Asathreshold level, Prf = Po, is exceeded subharmonic generation at the n = 0 step occurs as ear- lier reported 121. The explanation is a parametric exitation of the plasma resonance. Following a fur- ther increase of Prf a second threshold level, Prf

= PI, is seen as shown in figure Ib.

Two explanation for the n = 1 subharmonic oscillation seems possible (1) it is related to the phenomenon discussed by Fjordb$ge and Lindelof /1 / for a microbridge, or (2) it is a parametric plasma re-

sonance excitation taking place at finite voltage steps, even though the plasma resonance is normally associated with a zero voltage bias. To support the notion of a plasma resonance at a microwave induced step we may attempt a generalisation of the method

used for the zero voltage case. The plasma frequency

/

is given by f = 1 / 2 n q where C is the capaci- PO

tance and LJ is the "Josephson inductance", I/LJ =

2eI <cosc$>h: Assuming a junction voltage of the form V = V + Vlcos(2a fa

.

t) where Vo = nhfa/2e

0

on the n'th step we obtain for the time average of cos4 : <cos$> = Jn(a)cos@n withcl = 2eVl/hfa and where $n varies -a/2<$ <a12 along the step. Hence,

n

the plasma frequency on the n'th step becomes f = (2eIcJn (a)cosa/fic)~ 1211, n = 0,1,2

Pn

Generalizing f r o m the n = 0 case which is well un- derstood it seems a reasonable assumption that when the condition f =

$

fa is satisfied a parametric

Pn

plasma resonance excitation may occur also on the finite voltage steps. This interpretation is supported by results obtained just prior to the submission of this manuscript. It turned out that in a tunnel junction subharmonic oscillations occur on ref. induced steps with order numbers at least up to n =

7 with increasing threshold levels.

Our results may be summarized as follows. It was not possible to detect a half-harmonic genera-

tion on the n = 1 rf induced step in a Dayem bridge as predicted in / I / . However, when the same experi- ment was done on Josephson tunnel junctions the n

= 1 half-harmonic generation was observed with all

the characteristic features predicted in / I / . Alternatively, the explanation may be based on parametric excitation of the plasma resonance at a finite voltage. We cannot say at present which of the two suggested explanations are more likely to hold.

References

/ I / Fjordb$ge, B. and Lindelof, P.E., J. Low. Phys. 31 (1978) 83

-

/2/ Mygind, J., Pedersen, N.F., and Soerensen, O.H., Appl. Phys. Lett.

2

(1976) 317

/ 3 / Mygind, J., Pedersen, N.F. and Soerensen, O.H., Appl. Phys. Lett.

32

(1978) 70