Physica B 165&166 (1990) 1459-1460North-Holland

AC-TO-DC RECTIFICATION AND MACROSCOPIC QUANTUM INTERFERENCEIN PERCOLATING SUPERCONDUCTING FILMS

A. GERBER* AND G. DEUTSCHER

School of Physics and Astronomy Raymond and Beverley Saclder Faculty of Exact Sciences,Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

Low frequency ac currents have been observed to induce a dc voltage Vdc across macroscopic percolatingfilms of lead and aluminium in the vicinity of their superconducting transition. This conversion is observeddown to a frequency of 10 Hz, which rules out an inverse Josephson effect interpretation. Vdc showssharp oscillations as a function of a magnetic field. This pattern dependence on the angle between thesample and the applied field identifies these oscillations as an Aharonov - Bohm effect

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Fig. I. The marked peaks were arbitrarily determined as themost pronounced characteristic features of the pattern,having their "twins" in the reversed field. The patternoccurs only when the applied field has a component normalto the film. Its field scale is inversely proportional to thecosine of the angle e between the applied field and thenormal to the film.

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Fig. I. Typical voltage pattern as a function of an externaldc magnetic field measured in a Pb sample close to thepercolation threshold. Magnetic field is applied at an angleof 60° from the normal to the sample's surface in Fig.laand at 75° in Fig. Ib. The pattern width is inverselyproportional to the cosinus of the angle between the appliedfield and the normal to the sample's surface. T = 4.2 K.AC current frequency is 100 kHz, amplitude - 5 mAo

An anomalous response of granularsuperconducting films to rf radiation was reported for thefirst time by Saxena, Crow and Strongin (1]. A similareffect was observed by Sadate-Akhavi et al [2] using an rfcurrent directly. In both cases a dc voltage was measuredacross the sample. Recently, rf-to-dc conversion wasobserved [3] in ceramic high Tc superconductors. Thiseffect is qualitatively similar to the appearence of a dcvoltage in Josephson junctions under the application ofmicrowave radiation at about I GHz, and was interpretedas a possible inverse Josephson effect.

We want to report here the observation of a dc voltageVdc across macroscopic superconducting percolating filmsin the vicinity of their superconducting transition, underapplied alternative currents at frequencies as low as 10 Hz,ruling out an inverse Josephson effect interpretation. Vdcshows sharp oscillations as a function of a magnetic field,the pattern dependence on the angle between the sample andthe applied field identifies these oscillations as an Aharonov- Bohm effect.

The effect was observed in all the studied macroscopicstrips of Pb and AI, 12 mm long and 4 mm wide, withtypical average thicknesses of 160 A and 30 A for Pb andAl respectively. Lead samples were prepared byevaporation on pre-evaporated germanium films 400 Athick and aluminium ones by direct evaporation onto theglass substrate. Examination of the samples in atransmission electron microscope shows a percolativeStructure with typical small loop sizes of a few thousandangstroms in Pb and about a thousand in AI. Themeasurements were carried out using a four terminaltechnique with an ac function generator connected to thecurrent leads and a dc voltmeter connected to the voltageleads, the sample being mounted in a cryostat placed in thefield of an orientable magnet. One of the current leads wasgrounded. The samples were either directly immersed inliquid He or kept in an exchange gas chamber.

Vdc was observed in the vicinity of the superconductingtransition both at zero and under applied magnetic field. Ingeneral Vdc (H) shows a peak for H of the order of theupper critical fields Be2. and an oscillating pattern at smallfields. Typical voltage pattern as a function of an externaldc magnetic field, measured in lead film, is shown in

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1460 A. Gerber, G. Deutscher

References

Fig.2. Vdc(H) measured in a Pb sample (Rlsq=960hm/sq).Voltage was measured between leads 2 and 3. Solid curvecorresponds to the arrangement, where lead 1 wasgrounded and ac current modulation was applied at lead 4.Dotted curve - lead 4 was grounded and ac currentmodulation was applied at lead I.

percolation threshold; dotted line demonstrates themeasurement under reversed sample's direction. One cansee that the value and the polarity of the observed signaldepends both on the sample's direction and on magneticfield. However, for any sample and any angle between thefield and the sample's surface, Vdc was found to be exactlyanti symmetric under simultaneous reversal of magneticfield orientation and sample's direction.

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* Present address : CNRS - Laboratoire de MagnetismeLouis Neel - 25, Avenue des Martyrs, I66X, 38042Grenoble-Cedex, France.I. A.M. Saxena, J.E. Crow, and M. Strongin, SolidState Commun., 14,799 (1974).2. H. Sadate~Akhavi, J.T. Chen, A.M. Kadin, J.E.Keem, and S.R. Ovshinsky, Solid State Commun.,50,975 (1984).3. J.T. Chen, L.E. Wenger, C.J. McEwan, and E.M.Logothetis, Phys. Rev. Lett., 58, 1972 (1987).4. A. Gerber and G. Deutscher, Jap. Joum. AppI. Phys.26, SuppI. 26-3, 1307 (1987) 5. S. Ikegawa, T. Honda,H. Ikeda, A. Maeda, H. Takagi, S. Uchida, K.Uchinokura and S. Tanaka, 1. Appl. Phys. 64 (10), 5061(1988).

We are far yet from a complete understanding of ourexperimental results. The experiments contradict the knownac-to-dc conversion mechanisms like the inverse Josephsoneffect or rectification due to high harmonics interferenceacross a non-linear resistance element [5].Theantisymmetry of the measured V(H) pattern distinguishes itfrom the usual Aharonov-Bohm effect observations. It isalso remarkable that inspite of the broad spread in the sizeof the loops, one observes a sharp pattern corresponding toloop sizes in the sub-micron range, and even sometimes apattern corresponding to a single loop size (the typicalsmallest one).

This is illustrated by the comparison between Fig.la (8 '=

60°) and Fig.lb (8 '= 75°). Field intervals between theidentified peaks 1- - 1+ ; 2- - 2+ ; ... ; 6- - 6+ measured at8 = 75° relate to those measured at 8 =60° as 1.91, 1.94,1.89, 1.93, 1.96 and 1.95 respectively.Comparing thesevalues to the ratio cos600/cos75° = 1.93, we can claim thatthe scale of the pattern is inversely proportional to thecosine of the angle between the applied field and the normalto the film : ~H DC l/cos6. In some samples only onedominant period have been observed. In this case, the fieldperiodicity is in agreement with the flux quantization in thesmallest loops of the film, ~HS =4>0, 4>0 = 2.07 x 10-7

Gausscm2 (the average dimensions of the smallest loopswere defined as the half sum of their internal and externaldiameters, being of the order of 3000 Aand 1500 A for Pband Al films respectively). The pattern is in general morecomplex and varies from sample to sample. The signaldependence on the angle between the sample and theapplied field and the main field period identifies it with anAharonov-Bohm interference effect primarily in thesmallest loops of the sample. A contribution of larger loops(up to about 10 11m diameter) can also be cleraly seen atlow fields. It appears clearly when the angle 6 between thesample and the applied field is increased. (Compare forexample intervals 1- - 1+ in Figs.la and 1b).

In two respects, our results are clearly different fromprevious works measuring V(H) at constant current inperiodic normal metal or in regular quasiperiodic andfractal superconducting networks, as well as insuperconducting networks containing different irrationalarea tiles: first, we do not observe a periodic V(H) patternwithin our resolution range (above 0,1 11V) when a dccurrent only is passed through the sample, equivalently, adc current component added to the ac current does notmodify the observed pattern; second, our Vdc(H) isantisyrrunetric.

We have studied the influence of the amplitude Jac andfrequency of the ac current on Vdc' At any giventemperature and field value, a finite Vdc appears only abovea minimum value of Jac ' This threshold value is reduced athigh temperatures (near Tc) and high fields (near Hc2),and also for samples closer to the percolation threshold Pc.For samples very close to Pc' the ac noise level of a dcvoltmeter may be sufficient to produce a finite Vdc [4]. Atlow ac current a detectable Vdc appears only close to He2.When Jac increases, one can observe Vdc at lower fields,including in zero field. The amplitude of the high field peakof Vdc as well as the average amplitude of the Aharonov­Bohm pattern increase with Jac.

Similar measurements have been performed on 400 Athick films of lead. These films are far enough from thepercolation threshold that all the voids are filled. A highfield Vdc peak was measured near the transition point,however no low field oscillating pattern was observed.

Two parameters have been found to govern the polarityof the Vdc : orientation of the magnetic field with respect tothe film's plane and the direction of the sample. We showin Fig.2 Vdc measured in a sample relatively far from the