2. Dale Van Harlingen Sergey Frolov, Micah Stoutimore, Martin Stehno University of Illinois at Urbana-Champaign Valery Ryazanov Vladimir Oboznov, Vitaly Bolginov, Alexey Feofanov Institute of Solid State Physics, Chernogolovka, Russia 10 th International Vortex Workshop --- January 14, 2005 --- Mumbai, India Current-Phase Relations and Spontaneous Vortices in SFS  -Josephson junctions and arrays Supported by the National Science Foundation and the U. S. Civilian Research Development Fund I 

3.  -Josephson junction 0-junction minimum energy at 0 I   -junction minimum energy at  I  Spontaneously-broken symmetry Spontaneous circulating current for  L >1 in zero applied magnetic flux I = I c sin(  +  ) = -I c sin  E = E J [1 - cos(  +  )] = E J [1 + cos  ] E  E  negative critical current   -- 22 -2  0

4. THEORYEXPERIMENT Klapwijk, 1999 Ryazanov, 2000 Testa, 2003 + - + - Van Harlingen, 1993 YBCO d-wave corner SQUIDs Non-equilibrium SNS junctions SFS junctions d-wave grain boundary junctions Not (yet) observed A.F. Volkov (1995) non-equilibrium Andreev states Yurii Barash (1996) zero-energy bound states Vadim Geshkenbein (1987) --- p-wave Tony Leggett (1992) --- d-wave directional phase shift Lev Bulaevskii (1978) tunneling via magnetic impurities Alex Buzdin (1982) tunneling w/ exchange interaction  F S x S _ + _ + _ + _ + NOT a  -junction The History of  junctions

5. FF  p p E   2E ex Order parameter oscillations SF interface: Exchange energy-induced oscillations of the proximity-induced order parameter Proximity decay  x SC FM Exchange energy Fermi velocity

6.  F S x S  F S x S 0-state  -state SFS Josephson junctions: dependence of free energy on ferromagnetic barrier thickness 0  0  ~ nd ~ (n+½) d

7. Variation of critical current with barrier thickness Quasiclassical Usadel equations: Buzdin et al., Kontos et al.

8. Variation of critical current with temperature Control transition by temperature via coherence length: d = 24nm 23nm 22nm 21nm 20nm

9. Si Step 1: Deposit Base Nb layer Step 2: Deposit CuNi + protective Cu Step 3: Define SiO window Step 4: Deposit Top wiring Nb layer Si Window Junctions (Chernogolovka)Trilayer Junctions (Urbana) Step 1: Deposit Nb-CuNi-Nb trilayer Step 2: Etch top Nb, backfill with SiO 2 Step 3: Deposit Top wiring Nb layer 5  m x 5  m to 50  m x 50  m 2  m x 2  m to 20  m x 20  m SFS junction fabrication

10. Critical current measurements: SFS Junctions

11. SQUID potentiometer measurement R N ~ 10 -5  I c R N ~ 10 -10 V

12. Current-Phase Relation Measurement dc SQUID technique: J.R. Waldram et al., Rev. Phys. Appl. 10, 7 (1975) SQUID I  Null SQUID current --- measure I and  ~ 

13.  - junction in an rf-SQUID Simulation: I Measurement: Hysteretic when  L > 1  L varied by changing I c (T) or L CPR is accessible for  L < 1    I  M L ICIC SQUID detector  65432106543210 L=L=

14. Near the 0-  crossover temperature Study region near crossover for which -1 <  < 1 I  Simulation

15.  00 Temperature: rf SQUID curves Slight shift die to a background magnetic field ~ 1-10 mG

16. Current-Phase Relation measurements Extracted from rf SQUID characteristics: 0-  crossover is sharp I c = 0 at the crossover temperature T  CPR is sinusoidal No distortions due to sin(2  )

17. Why do we expect a sin(2  ) component ? What is the right experiment to probe sin(2  Theoretical predictions: Radovic et al. Chtchelkatchev et al. Hekkila et al. Golubov et al. Suggestive experiments: Ryazanov et al. (arrays) Baselmans et al. (SNS SQUIDs) Current-phase relation measurements Critical current diffraction patterns: extra structure in junctions higher harmonics in SQUIDs/arrays Shapiro steps (microwave irradiated) --- subharmonic steps High frequency rf SQUID structure Absence of first-order term makes it possible to observe second-order Josephson tunneling Interaction of 0 and  states at crossover – competing energies

18. Secondary Josephson Harmonics ? Results of data fitting :  < 5 % I c goes to 0 at T , contrary to predictions of large sin 2   I c resolution ~ 10 nA Shapiro steps: only integer steps Diffraction patterns: Fraunhofer

19. Critical current vs. temperature Critical current does not vanish --- this suggests sin(2  ) term in CPR

20. Shapiro steps Half-integer Shapiro steps --- consistent with sin(2  ) term in CPR Half-integer steps only occur near T  where critical current vanishes Suggests coexisting “0” and “  ” states that entangle near degeneracy

21. Critical current diffraction patterns Junction barrier is not uniform near T 

22. Average film thickness 24nm Linear thickness variation of 0.4nm Effect of sloped barrier thickness variation T = 2.6K T = 2.8K T = 3.0K T (K) I c (nA) y (  m)   

23. Arrays of  -Josephson junctions Motivation: 1.Observe spontaneous currents and vortices 2.Opportunity to explore non-uniform frustration 3.Opportunity to tune through  -transition to measure uniformity of junctions and variation of vortex size a

24. Cluster Mask 2 x 2 6 x 6 3 x 3 1 x N

25. Cluster Designs 2 x 2 6 x 6 fully-frustrated checkerboard-frustrated fully-frustrated unfrustrated checkerboard-frustrated 30  m

26. Scanning SQUID Microscopy (SSM) x-y scan hinge Square arrays Triangle arrays YBCO films 10  m 100  m Spatial resolution: 10  m Flux sensitivity: 10 -6  0 MoGe films

27. Array images: magnetic field-induced vortices Single vortex f  0 f = 0.03 f = 0.33 f = 0.50 f = 0.66

28.  -junction array images: spontaneous currents zero magnetic field 3 x 3 1 x 20 6 x 6

29. What determines the current pattern? 1.Distribution of frustrated cells --- to maintain phase coherence, each much generate (approximately)  0 /2 flux quantum 2.Disorder in cell areas (small) and critical currents (substantial) 3.Thermal fluctuations during cooling --- closely-spaced metastable states 6 x 6

30. TT T = 1.7K T = 4.2K T = 2.75K Scanning SQUID Microscope images T IcIc

31. Checkerboard frustrated Fully frustrated 2 x 2 arrays: spontaneous vortices

32. 2 x 2 arrays --- simulations of vortex configurations all 0-JJ all  -JJ

33. 1D-chain arrays --- simulations of vortex configurations

34. T, K ICIC 1 2 3 4 6x6 checkerboard frustrated cluster: Magnetic field applied (to enhance contrast of SC lines)

35. T, K ICIC 1 2 3 4 6x6 checkerboard frustrated cluster: Zero magnetic field

36. 6x6 checkerboard frustrated cluster: Zero Field Vortices appear at T . (difficult to determine T  precisely since diverges) Resolution improves as I c increases --- limits for ~ a

37. T, K ICIC 1 2 3 4 6x6 checkerboard frustrated cluster: Magnetic field applied (to enhance contrast of SC lines)

38. Conclusions Measuring Current-Phase Relation (CPR) of SFS junctions Observe transition between 0-junction and  -junction states Mixed evidence for any sin 2  in the CPR in the 0-  crossover region Considering effects of barrier inhomogeneities Imaging arrays of  -junctions by Scanning SQUID Microscopy Observe spontaneous vortices Studying crossover region Develop trilayer process --- materials and fabrication issues Engineer superconducting flux qubit incorporating a  -junction Measure 1/f noise from magnetic domain dynamics on SFS junctions Measure CPR in non-equilibrium  -SNS junctions Work in Progress

40. 1. Provides natural and precisely-degenerate two-level system Advantages of  -junction flux qubits J E  Precisely-degenerate two-level system with no flux bias Spontaneous circulating current in rf SQUID 2. Decouple qubit from environment since no external field needed (always need some field bias to counteract stray fields and to control qubit state, but does reduce size of fields needed)

41. 1.Controllability/reproducibility of 0-  transition point and critical currents in multiple-qubit circuits  determines tunneling rate 2.Enhancing normal state resistance of  -junction  determines decoherence due to quasiparticle dissipation 3. Low frequency magnetic noise in SFS junction barriers  source of decoherence Challenges for  -junction flux qubits Approach: trilayer junction technology Approach: SIFIS and SFIFS structures Approach: barrier material engineering

42. Decoherence from 1/f magnetic domain switching noise 1/f critical current noise modulates tunneling barrier height Fluctuation of the tunneling frequency causes phase noise  decoherence since  is different for each successive point of a distribution measurement t  ICIC  ~  I c Magnetic domain switching causes critical current noise MODEL S S F SIMULATION

43. Secondary Josephson Harmonics Results of data fitting :  < 5 % I c goes to 0 at T , contrary to predictions of large sin 2  Current  Simulation  = 0.5 I c resolution ~ 10 nA

44. 1.Existence of Josephson sin(2  ) component 2.Effect of barrier inhomogeneities and fluctuations Clustering of magnetic atoms  junction aging effects Interface conduction  reduction of current density  Barrier thickness variations  non-uniform current densities Ferromagnetic domain noise  decoherence in qubits 3.SFS arrays --- magnetic imaging of spontaneous vortices 4.Implementation of  -junctions in superconducting flux qubits Key Issues

45. BSCCO grain boundary junctions Possible origin: second-order Josephson coupling  non-sinusoidal current-phase relation … I(  ) = I c1 sin(  ) + I c2 sin(2  ) (cancellation of tunneling into + and – lobes) Zero-field peak in critical current has ½ width of finite field peaks _ + _ + _ + _ +

46. Evidence for sin(2  ) in SNS ballistic  -junctions Baselmans et al., PRL 2002 NS S E Andreev levels V

47. Suggests sin(2  ) component

48.  I    I = = vortex Observe half-integer Shapiro steps in a dc SQUID near  0 /2

49. Another SFS junction – 4x4  m

50. Shapiro step maximum amplitude Half-integer steps only occur near T  where critical current vanishes Suggests coexisting “0” and “  ” states that entangle near degeneracy