Topology-Induced Critical Current Enhancement in Josephson Networks

Transcription

1 Topology-Indued Critial Current Enhanement in Josephson Networks P.Silvestrini 1, R. Russo 1,2, V.Corato 1, B. Ruggiero 2,1, C.Granata 2, S. Rombetto 2,#, M.Russo 2, M. Cirillo 3, A. Trombettoni 4 and P.Sodano 4, 1 Dipartimento d Ingegneria dell Informazione, Seonda Università di Napoli, Aversa, Italy 2 Istituto di Cibernetia E. Caianiello del CNR, Pozzuoli, Italy 3 Dipartimento di Fisia and INFM, Università di Roma Tor Vergata, 173 Roma, Italy 4 Dipartimento di Fisia, Università di Perugia, 6123 Perugia, Italy and Sezione I.N.F.N.-Perugia Progetto Lagrange, Fondazione C.R.T. e Fondazione I.S.I., Dipartimento di Fisia, Politenio di Torino, Corso Dua degli Abruzzi 24, 124 Torino, Italy PACS: 74..+r, 3.67Lx, 8.2.Cp Abstrat: We investigate the properties of Josephson juntion networks with inhomogeneous arhiteture. The networks are shaped as square omb planar latties on whih Josephson juntions link superonduting islands arranged in the plane to generate the pertinent topology. Compared to the behavior of referene linear arrays, the temperature dependenies of the Josephson urrents of the branhes of the network exhibit relevant differenes. The observed phenomena evidene new and surprising behavior of superonduting Josephson arrays as well as remarkable similarities with bosoni juntion arrays.

2 Marosopi Quantum Coherene ours in a variety of physial systems suh as Bose-Einstein ondensates of atomi gases (1-3), superfluid Helium (4,), superondutors (6,7), solid-state mesosopi systems (8-12) and old atoms in optial latties (13-1). In this area, Josephson Juntion Networks (JJN) are by now the prototype of a versatile solid-state system, whih - by ating on a few ontrol parameters - may be used for the engineering of a variety of marosopially quantum states (16-19). Very often the JJN that have attrated attention for modelling of superondutive systems have been planar arrays obtained by losing superonduting loops by point Josephson juntions (16). This kind of arrays have been very helpful and provided muh physial insight, for example, in the physis of granular superondutors; series arrays of juntions instead have provided important and useful devies in superondutive eletronis (7). In this paper we shall provide experimental evidene for the fat that in JJN with non-onventional arhiteture, ontaining no superondutive loops and made by different branhes in whih the juntions are series-onneted, the network s topology (i.e. the way in whih the superonduting islands of the array are oupled together by the Josephson juntions) plays a key role in determining new and unexpeted properties of the array. We have fabriated JJN with omb-like topology (see Fig.1) using a reliable niobium trilayer tehnology (2). The individual Josephson juntions forming the array have a x or 4x4 µm 2 area and ritial urrent densities ranging from 3 to A/m 2, resulting in a relatively large apaitane (C 2pF) and Josephson ritial urrent I µa (see Fig.2a). In this limit one an safely neglet the 2 h harging energy E with respet to the Josephson energy E j : E = e 2C, E j = I and E /E j <.1 2e (being e the eletron harge and h the Plank onstant). In Fig. 1b we show an optial image of a fabriated sample; in the photo we an see the square-omb network on whih we have evidened the loalization of the Bakbone Array (BBA) and the Central Finger Array (CFA). Beside the omb network, we have fabriated referene linear arrays alled RBA (Referene Bakbone Array) and RFA (Referene Finger Array) loalized very lose to the omb struture; the arrays are omposed of superonduting islands onneted to eah other in series through Josephson juntions. The omparison between the ritial urrents in the referene arrays and the ones observed in the bakbone and finger arrays of the square omb is a relevant tool for our investigation. The Current-Voltage (I-V) harateristis were reorded by supplying a bias urrent to all the juntions of the arrays by means of ontat pads loated at the ends of the individual arrays (BBA, RFA et.). For

3 the data aquisition we used an experimental set-up filtered from the external noise, as tested in similar Josephson juntion measurements. The ritial urrent of the referene arrays show a good uniformity as well as a modulation to zero in a magneti field (see inset Fig.2b); these behaviors (7) represent an important indiation in favor of the good quality of our fabriation proess. In Fig. 2 we show the I-V harateristis of the BBA (blak line) of the network ompared with the referene array, RBA (red line), at two different temperatures. Sine the juntions are urrent-biased in series, the voltage readout aross the whole array shall be the sum of the individual juntion voltages. The swithes of the first juntions in series are enlarged in the inset of Fig.2a; the inset shows how the number of juntions in the array an be determined by ounting the number of voltage jumps ontributing to the gap voltage sum of the series onnetion. It is worth notiing that eah voltage jump is roughly 2.7 mv, orresponding to the gap value of a single juntion: we stress that the juntions whih are not swithed to the gap voltage are still in the superonduting (zero voltage) state. Fig. 2a shows that the Josephson ritial urrent of the BBA is systematially higher than the referene one. At T=4.2K, the ritial urrent differene between BBA and RBA is of the order of few perents, and, thus, it is not so signifiant; it ould be asribed to fabriation tehnology margins and related unertainties (although we shall see in the following our unertainties are lower, see figure 4). In Fig. 2b we show, that, at a temperature of 1.2K, the ritial urrent of eah juntion in the RBA array (red line in figure) inreases as expeted from the BCS-based Ambegaokar-Baratoff temperature dependene of the Josephson urrents (7), whereas most of the juntions in the BBA show a ritial urrent raising signifiantly above this expeted BCS behavior. The two urves are almost idential from to mv that is the sum of swithes to the gap voltage of about 18 Juntions. There are18jjs in BBA that have the same ritial urrent than 18JJs in the RBA. The remaining 4JJs of the BBA (that are still in the zero voltage state) have a ritial urrent higher than the orresponding JJs in the RFA. Upon inreasing the bias urrent also these juntions swith to the gap voltage manifesting a larger I in omparison to the linear array. In partiular after the swithing from the superonduting state to the gap branh of approximately 32 JJs (orresponding to about 9mV), the differene in ritial urrent between the remaining JJs in BBA and RBA is about 1%. There are, then, 4 JJs whih are still in the superonduting state with a ritial urrent about 1% higher than the ones in the referene array. We believe that some juntions in the BBA do not display the urrent rise most likely beause our square ombs have a finite size and the juntions with low ritial urrents are loated at the edge of the omb. From the data shown in Fig. 2b we an quantitatively estimate the ritial urrent enhanement in the

4 BBA RBA I I BBA introduing the parameter F defined as F =, resulting in about 1% at T=1.2 K. RBA I BBA RBA Here, ( I ) I is the average value of the ritial urrent of BBA (RBA) and it is omputed exluding the first 2JJs (the juntion having a lower I, similar to the RFA due to the finite size of the square omb). This estimate, repeated for all our samples, provides an average result for the enhanement fration F of 13% with a % satter around the average. Although the satter around the average an be asribed to unertainties in fabriation and measurements, a differene of average ritial urrent between the BBA and the RBA of 13% an only be attributed to new effets indued by the network topology. In Fig.3 we display the I-V urves for the CFA of the network and its linear referene array RFA. In Fig. 3a we observe (similarly to what we see in Fig. 2a) that the Josephson urrent of the CFA does not differ signifiantly from the RFA at T= 4.2 K. In Fig. 3b, instead, we show that, at T=1.2K, the ritial urrents of juntions in the CFA undergo a non uniform variation. Moreover, we see that, at T=1.2K, most of the juntions in the CFA have ritial urrent values lower than the RFA: thus, lowering the temperature, leads to opposite behaviors for the BBA and for the CFA. Most of the juntions in the CFA show an inrease of the ritial urrent smaller than the one expeted from the Ambegaokar- Baratoff equation; in addition, a few juntions have a ritial urrent at 1.2K lower than the lowest reorded at 4.2K. We note that, instead, the RFA follows the Josephson urrent inrease predited by the BCS theory for a linear hain. From the omparison between Fig. 2b and Fig. 3b we an say that the topology indues in the network a new temperature behavior, namely: at low temperature, I, inreases along the bakbone diretion while it dereases along the fingers of the omb. The data presented are well representative of a behavior that has been observed in all the ten samples whih we measured and haraterized. From the reported evidenes we have no doubt left that the observed effets are due to the peuliar topology of the network. However, as a further hek of the reliability of our measurements we performed an additional experimental test. The goal of this test is to provide a measurement of the BBA and CFA when these are isolated from the remainder of the network; for this purpose, using lithographi tehniques, we removed in three samples all the fingers from the omb network. Remeasuring the Josephson urrents in these samples after the utting proess, we find again that the urrent of the RBA follows the BCS preditions at all temperatures (from 4.2K to 1.2K) but now the

5 same happens the isolated BBA whose harateristi remains always idential to the one of the RBA (see Fig.4). Thus, the reorded differenes of the Josephson ritial urrent between the BBA and RBA disappear when the BBA is isolated from the surrounding network a result very well evidened in Fig. 4. After the fingers removal, the ritial urrent of both arrays (RBA and BBA) displays no signifiant differenes both at 4.2K and 1.2 K: the different behaviors exhibited by the BBA and RBA shown in Fig. 2b an be solely attributed to the omb topology. We also applied the same lithographi proedure to the CFA obtaining similar results: measuring the I-V urves of the finger isolated from its surrounding we find that the temperature behavior of CFA is idential to that of the referene array. Our experiments show remarkable similarities with behaviors expeted to be observed for the systems of ultraold atoms, arranged in inhomogeneous omb-shaped optial latties, analyzed in refs.18,19. An aurate quantitative explanation of the data presented in this paper should be sought within the framework of other theories/models speifi of the superonduting state provided that one is able to takle arefully the new effets indued by the existene of the hidden spetrum in a omb-graph. We thank F. P. Manini and M. Rasetti for stimulating and useful disussions, as well as E. Esposito for the help in setting the ryogeni failities at the Seonda Università di Napoli. Work partially supported by the M.I.U.R. National Projet JOSNET (grant n.2427) REFERENCES: 1. E. A. Donley, et al., Nature 412, 29 (21). 2. J.R. Anglin, W. Ketterle, Nature 416, 211 (22). 3. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999). 4. A.J. Leggett, Rev. Mod. Phys. 71, S318 (1999).. A.J. Leggett, Rev. Mod. Phys. 76, 999 (24). 6. J.R. Shrieffer, ( Wesley, Menlo Park, U.S.A., 1988); P.G. De Gennes, (Advaned Books Classis, Westview Press, U.S.A.,1999). 7. A. Barone, G. Paternò, Physis and Appliations of the Josephson Effet (Wiley, New York, 1982); T. Van Duzer and C. W. Turner, Priniples of Superondutive Devies and Ciruits (Elsevier, NY 1998)

6 8. Chioresu, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Siene 299, 1869 (23). 9. D. Vion, et al. Siene 296, 886 (22).. J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, J. E. Lukens, Nature 46, 43 (2). 11. Y. Yu, S. Han, X. Chu, S.I. Chu, Z. Wang, Siene 296, 889 (22). 12. J. M. Martinis, S. Nam, J. Aumentado, C. Urbina, Phys. Rev. Lett 89, (22). 13. D. Jaksh, C. Bruder, J. Cira, C. W. Gardiner, P. Zoller, Phys.Rev.Lett. 81, 38 (1998). 14. F.S. Cataliotti, et al. Siene 293, 843 (21). 1. M. Greiner, O. Mandel, T. Esslinger, T. W. Hansh, I. Bloh, Nature 41, 39 (22). 16. R. Fazio, H. van der Zant, Phys. Rep. 3, 23 (21). 17. Y. Makhlin, G. Shoen, A. Shnirman, Rev. Mod. Phys., 73, 37 (21). 18. R. Burioni et al., Europhys. Lett. 2, (2); R. Burioni, D. Cassi, M. Rasetti, P. Sodano, A. Vezzani, J. Phys. B 34, 4697 (21). 19. G. Giusiano, F. P. Manini, P. Sodano, A. Trombettoni, Int. Jour. Mod. Phys. B 18, 691 (24); I. Brunelli, G. Giusiano, F. P. Manini, P. Sodano, A. Trombettoni, J. Phys. B 37, S27 (24). 2. C. Granata, et al. Appl. Phys. Lett. 8, 292 (22). See also referene 9 ited therein. 21. B. Ruggiero, et al., Phys. Rev. B 7, 134 (1998).

7 Figure 1 (Color online) a) Shemati drawing of a square omb array. The superonduting islands (full retangles in the figure) are onneted to eah other in series through Josephson juntions JJ (rosses in the drawing). A entral array named bakbone array (BBA) is onneted to linear arrays (fingers) perpendiular to it; there are no onnetions between fingers, exept through the BBA. The blak urve skethed in the figure represents the qualitative behavior of the ground eigenstate of the boson hopping Hamiltonian, having the maximum on the bakbone(18,19). b) Optial mirosope pitures of a fabriated sample. The Central Finger Array is referred as CFA. Linear arrays used as referenes (RBA and RFA) loated very lose to the juntion network are also shown. In the inset the detail of a BBA region is well visible. Figure 2 (Color online) Current-voltage harateristis for the BBA (blak urve) and RBA (red urve) inluding JJ with area A=xµm 2 a) measured at T= 4.2 K and b) measured at T=1.2 K. The x-axis represents the measured voltage of the series array of 72 juntions. The inset of Fig.2a shows a magnifiation of the ritial urrent swithing of the first juntions in the xµm 2 array whereas the inset in Fig. 2b reports the magneti pattern of the two arrays (irles and squares) showing a modulation to zero for both arrays (blak line is the theoretial sinx/x behavior) Figure 3 (Color online) Current-voltage harateristis for the Central Finger array, CFA (blak urve), and the referene arrays, RFA (red urve), with juntion area A= xµm 2 a) measured at T=4.2 K and b) measured at T=1.2 K. The insets show a magnifiation of the ritial urrent swithing of the first juntions in the xµm 2 CFA at the T=4.2K and T=1.2K. Note the at 1.2K the lowest I s of CFA are lower than the lowest I s reorded at 4.2K on the same array. Figure 4 (Color online) Current-voltage harateristis of the same hip shown in Fig. 2 after removing the fingers from the omb network. The blak urves represent the BBA after it has been isolated from the remainder of the network, and the red urve represents the RBA response during the same measurement run. a) I-V urves measured at T= 4.2K and b) at T=1.2K.

8 FIGURE 1

9 a) JJ JJ b) Normalized Current Solenoid Current (ma) 1 2 FIGURE 2

10 1 a) 8. 1 JJ 8. JJ b) JJ JJs FIGURE 3

11 2 2 1 a) b) 1 2 FIGURE 4