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Observation of integer and fractional giant Shapiro steps in arrays of SNS Josephson junctions
Physica B 165&166 (1990) 1571-1572 North-Holland
OBSERVATION OF INTEGER AND FRACTIONAL GIANT SHAPIRO STEPS IN ARRAYS OF SNS JOSEPHSON JUNCTIONS H. C. LEE, D. B. MAST, R. S. NEWROCK, L. BORTNER, K. BROWN, and F. P. ESPOSITO Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA' D. C. HARRIS and J. C. GARLAND Department of Physics, Ohio State University, Columbus, OH 43210, USA" We observe giant Shapiro steps in the I-V curves of NxM arrays of SNS Josephson junctions; these steps occur at N times the single junction voltage. Both integer and fractional giant steps are observed as a function of temperature, external magnetic field, and rf current. The fractional steps occur at multiples of l/q times the giant Shapiro step voltage and are seen at well defined values of the applied field, p/q flux quantum per placquette. We also observe a fractional step at 1/2 integer voltages, even in zero applied field. These fractional steps decrease in size if random site disorder is introduced to the array. The interaction of high frequency radiation with superconducting tunnel junctions has been extensively investigated since the 1960's. We report the experimental observation of giant Shapiro steps in planar arrays of Josephson junctions. For single junctions, Shapiro steps, steps in the I-V characteristics, occur at voltages nhv /2e, where v is the frequency of the incident signal and n = 1,2,3,.. is the order of the step. We have observed giant Shapiro steps in NxN square and NxM triangular arrays of coupled SNS junctions at normalized voltages n = 2eV/Nhv, where N is the number of junctions along the current direction. These giant steps are indicative of phase locking throughout the entire array. In addition to these integer giant steps, we observe, in magnetic fields equal to p/q flux quantum per plaquette (p and q are integers), steps in the I-V curve at normalized voltages n = p/q. Such giant steps and tractional giant steps were recently observed by Benz et al. l . We also observe fractional giant steps at half-integer values in zero applied field. The giant Shapiro steps are observed in square arrays of Nb/ Au junctions as well as in triangular arrays of Pb/Sn junctions. The Nb/Au junctions consist of niobium crosses (10 IJ.m long and 1.2 IJ.m wide) with an underlaid gold film forming the normal metal barrier 0.4 IJ.ms across; the arrays had 299
crosses on a side. The Pb/Sn arrays consist of hexagonal lead islands, 12 IJ.m across, with an islandisland separation of 1 IJ.m; a tin overlayer fills this separation forming the normal metal barrier. We fabricated a series of triangular arrays with widths ranging from 200 islands to 1 island; all are 1000 islands long. The dc properties of both sets of arrays were extensively analyzed2• We measure Ide vs. Vde , and dVdcldIde vs. Vde , as a function of temperature, external magnetic field, and frequency and amplitude of rf current, while a ramped dc current is applied to the array (Ide caries from 0 to several Ie)' In Fig. 1, we plot dV/dI vs. V for a square array, at T = 4.2K (T < TKT' where T KT is the Kosterlitz-Thouless temperature), v = 90MHz, and in zero magnetic field. The Shapiro steps are seen as dips in the dynamic resistance, dV/ dI, occurring at normalized voltages n = 1,2,3,... We observe these giant steps in the square arrays to frequencies as high as 500MHz. We also observe these steps in the Pb/Sn arrays; however, for the narrow Pb/Sn arrays, the amplitude and the number of observable steps is less than for the square arrays for the same ratio of Ire/Ie. If we apply two separate rf signals, we clearly observe giant steps at the usual sum and difference frequencies (i.e. voltages) expected for frequency mixing in non-linear systems. For all arrays, a necessary condition for the
" Supported by U.S.A.F. Office of Scientific Research, Grant No. F33615-85-C-0108. Supported by the National Science Foundation, Grant No. DMR-8821167. 0921-4526/90/$03.50
© 1990 -
Elsevier Science Publishers B.V. (North-Holland)
1572
H.C. Lee et al.
observation of the giant steps is that ITf ~ Ie. The giant steps are also observed, although much reduced in amplitude, at temperatures far above T KT' even at temperatures near the transition temperature of the bulk superconductor. In addition to the integer order giant steps, we observe half-integer steps in both square and the triangular arrays, also seen in Fig. 1. We observe these half-integer steps in zero magnetic field, as well as in applied fields. Larger value half-integer steps (3/2, 5/2, 7/2) appear as the rf current is increased in zero field. When the rf current is increased the integer peaks sharpen and the half-integer peaks' position shifts by approximately 5% and their shape sharpens. For fixed rf current, but changing magnetic fields, the integer peaks remain virtually unchanged while the amplitude of the half-integer peaks varies cyclically with the applied field. In a magnetic field we observe steps at fractional normalized voltages (p/g), where q = 3 and p = 1,2,4,5,... in the square arrays, Fig. 2, at T = 3.4K and v = 60MHz. These 1/3 steps appear when the external magnetic field is p/3 flux quanta per placquette. These steps are much smaller than the integer steps but are approximately equal in size to the 1/2 steps at this field. The size of 1/3 steps increases with decreasing temperature. We observe some structure in the dynamic resistance at normalized voltages near (1/5) for fields of 1/5 flux quantum per placquette, but no well defined "dips" are seen. We hope that additional measurements at lower temperatures may resolve these features. We have not observed 1/3 or 1/5 steps in any of the triangular arrays that we have studied. We also studied a "site percolated" square array with junctions at only 90% of the available lattice sites. For the same sample temperature and Irf/I e ratio used for the 100% arrays, the size of the integer steps and the half-integer steps is substantially reduced (by a factor of approximately 4). We have not observed the 1/3 steps in this array, but that may be partly due to temperature effects.
As mentioned, our observations of the integer giant Shapiro steps and the 1/3 steps are in agreement with the reported observations of Betz et al. (Ref. 1). Lee et al. 3 have predicted that one should observe fractional steps at normalized voltages of 1/2, 1/3, 1/4 and 1/5 in the appropriate magnetic field. We did not observe any fractional steps at 1/4; they are possibly there at 1/5. Their theory also predicts that 1/2 fractional steps should be present at magnetic fields that show the 1/3 and 1/5 fractional steps. We essentially see 1/2 steps at all fields. There is disagreement between our data and the calculation of Lee et al. as to the size of the integer steps at these fields values as well; they predict very small integer steps while we observe very large integer steps. The existence of the large 1/2 fractional giant Shapiro steps in zero magnetic field has not been explained, nor has the observed changes in the step position and size with changes in rf current and external magnetic field. It has been suggested4 that the zero field 1/2 step could be due to driving bound vortices periodically through the junction with the rf current; the substantial rf power dependence of these steps in zero field lends some support to this speculation. ACKNOWLEDGMENTS We would like to acknowledge the assistance of the Cornell Nanofabrication Facility in preparing our samples. REFERENCES (1) S. P. Benz, M. S. Rzchowski, M. Tinkham, and C. J. Lobb, Phys. Rev. Lett. 64, 693 (1990). (2) D. L. Harris, Ph.D. thesis, Ohio State University and to be published; K.S. Brown, R. S. Newrock, D. B. Mast, and L. Bortner, to be published. (3) K. H. Lee, D. Stroud, and J. S. Chung, Phys. Rev. Lett. 64, 962, (1990). (4) Bruce Patton, private communication.
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OBSERVATION OF INTEGER AND FRACTIONAL GIANT SHAPIRO STEPS IN ARRAYS OF SNS JOSEPHSON JUNCTIONS H. C. LEE, D. B. MAST, R. S. NEWROCK, L. BORTNER, K. BROWN, and F. P. ESPOSITO Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA' D. C. HARRIS and J. C. GARLAND Department of Physics, Ohio State University, Columbus, OH 43210, USA" We observe giant Shapiro steps in the I-V curves of NxM arrays of SNS Josephson junctions; these steps occur at N times the single junction voltage. Both integer and fractional giant steps are observed as a function of temperature, external magnetic field, and rf current. The fractional steps occur at multiples of l/q times the giant Shapiro step voltage and are seen at well defined values of the applied field, p/q flux quantum per placquette. We also observe a fractional step at 1/2 integer voltages, even in zero applied field. These fractional steps decrease in size if random site disorder is introduced to the array. The interaction of high frequency radiation with superconducting tunnel junctions has been extensively investigated since the 1960's. We report the experimental observation of giant Shapiro steps in planar arrays of Josephson junctions. For single junctions, Shapiro steps, steps in the I-V characteristics, occur at voltages nhv /2e, where v is the frequency of the incident signal and n = 1,2,3,.. is the order of the step. We have observed giant Shapiro steps in NxN square and NxM triangular arrays of coupled SNS junctions at normalized voltages n = 2eV/Nhv, where N is the number of junctions along the current direction. These giant steps are indicative of phase locking throughout the entire array. In addition to these integer giant steps, we observe, in magnetic fields equal to p/q flux quantum per plaquette (p and q are integers), steps in the I-V curve at normalized voltages n = p/q. Such giant steps and tractional giant steps were recently observed by Benz et al. l . We also observe fractional giant steps at half-integer values in zero applied field. The giant Shapiro steps are observed in square arrays of Nb/ Au junctions as well as in triangular arrays of Pb/Sn junctions. The Nb/Au junctions consist of niobium crosses (10 IJ.m long and 1.2 IJ.m wide) with an underlaid gold film forming the normal metal barrier 0.4 IJ.ms across; the arrays had 299
crosses on a side. The Pb/Sn arrays consist of hexagonal lead islands, 12 IJ.m across, with an islandisland separation of 1 IJ.m; a tin overlayer fills this separation forming the normal metal barrier. We fabricated a series of triangular arrays with widths ranging from 200 islands to 1 island; all are 1000 islands long. The dc properties of both sets of arrays were extensively analyzed2• We measure Ide vs. Vde , and dVdcldIde vs. Vde , as a function of temperature, external magnetic field, and frequency and amplitude of rf current, while a ramped dc current is applied to the array (Ide caries from 0 to several Ie)' In Fig. 1, we plot dV/dI vs. V for a square array, at T = 4.2K (T < TKT' where T KT is the Kosterlitz-Thouless temperature), v = 90MHz, and in zero magnetic field. The Shapiro steps are seen as dips in the dynamic resistance, dV/ dI, occurring at normalized voltages n = 1,2,3,... We observe these giant steps in the square arrays to frequencies as high as 500MHz. We also observe these steps in the Pb/Sn arrays; however, for the narrow Pb/Sn arrays, the amplitude and the number of observable steps is less than for the square arrays for the same ratio of Ire/Ie. If we apply two separate rf signals, we clearly observe giant steps at the usual sum and difference frequencies (i.e. voltages) expected for frequency mixing in non-linear systems. For all arrays, a necessary condition for the
" Supported by U.S.A.F. Office of Scientific Research, Grant No. F33615-85-C-0108. Supported by the National Science Foundation, Grant No. DMR-8821167. 0921-4526/90/$03.50
© 1990 -
Elsevier Science Publishers B.V. (North-Holland)
1572
H.C. Lee et al.
observation of the giant steps is that ITf ~ Ie. The giant steps are also observed, although much reduced in amplitude, at temperatures far above T KT' even at temperatures near the transition temperature of the bulk superconductor. In addition to the integer order giant steps, we observe half-integer steps in both square and the triangular arrays, also seen in Fig. 1. We observe these half-integer steps in zero magnetic field, as well as in applied fields. Larger value half-integer steps (3/2, 5/2, 7/2) appear as the rf current is increased in zero field. When the rf current is increased the integer peaks sharpen and the half-integer peaks' position shifts by approximately 5% and their shape sharpens. For fixed rf current, but changing magnetic fields, the integer peaks remain virtually unchanged while the amplitude of the half-integer peaks varies cyclically with the applied field. In a magnetic field we observe steps at fractional normalized voltages (p/g), where q = 3 and p = 1,2,4,5,... in the square arrays, Fig. 2, at T = 3.4K and v = 60MHz. These 1/3 steps appear when the external magnetic field is p/3 flux quanta per placquette. These steps are much smaller than the integer steps but are approximately equal in size to the 1/2 steps at this field. The size of 1/3 steps increases with decreasing temperature. We observe some structure in the dynamic resistance at normalized voltages near (1/5) for fields of 1/5 flux quantum per placquette, but no well defined "dips" are seen. We hope that additional measurements at lower temperatures may resolve these features. We have not observed 1/3 or 1/5 steps in any of the triangular arrays that we have studied. We also studied a "site percolated" square array with junctions at only 90% of the available lattice sites. For the same sample temperature and Irf/I e ratio used for the 100% arrays, the size of the integer steps and the half-integer steps is substantially reduced (by a factor of approximately 4). We have not observed the 1/3 steps in this array, but that may be partly due to temperature effects.
As mentioned, our observations of the integer giant Shapiro steps and the 1/3 steps are in agreement with the reported observations of Betz et al. (Ref. 1). Lee et al. 3 have predicted that one should observe fractional steps at normalized voltages of 1/2, 1/3, 1/4 and 1/5 in the appropriate magnetic field. We did not observe any fractional steps at 1/4; they are possibly there at 1/5. Their theory also predicts that 1/2 fractional steps should be present at magnetic fields that show the 1/3 and 1/5 fractional steps. We essentially see 1/2 steps at all fields. There is disagreement between our data and the calculation of Lee et al. as to the size of the integer steps at these fields values as well; they predict very small integer steps while we observe very large integer steps. The existence of the large 1/2 fractional giant Shapiro steps in zero magnetic field has not been explained, nor has the observed changes in the step position and size with changes in rf current and external magnetic field. It has been suggested4 that the zero field 1/2 step could be due to driving bound vortices periodically through the junction with the rf current; the substantial rf power dependence of these steps in zero field lends some support to this speculation. ACKNOWLEDGMENTS We would like to acknowledge the assistance of the Cornell Nanofabrication Facility in preparing our samples. REFERENCES (1) S. P. Benz, M. S. Rzchowski, M. Tinkham, and C. J. Lobb, Phys. Rev. Lett. 64, 693 (1990). (2) D. L. Harris, Ph.D. thesis, Ohio State University and to be published; K.S. Brown, R. S. Newrock, D. B. Mast, and L. Bortner, to be published. (3) K. H. Lee, D. Stroud, and J. S. Chung, Phys. Rev. Lett. 64, 962, (1990). (4) Bruce Patton, private communication.
-:1 ..Q
- - "=-:rl
0\r~ 'v
\
fa!.
'---
\ __ ,
o
_~~_,_~
2/32/22/3
1
2eV/Nhf Figure 2
I
~_~J
4/33/2