Monte Carlo simulations of thermal fluctuations in moderately damped Josephson junctions: Multiple escape and retrapping, switching- and return-current distributions, and hysteresis

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 5, 2008, Pages

  Fenton, J C ^a   Warburton, P A ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50849106121     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.054526     Document Type: Article

References (28)

1. T. Fulton and L. Dunkleberger, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.9.4760 9, 4760 (1974).
2. R. Kautz and J. Martinis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.9903 42, 9903 (1990).
3. A. Franz, Y. Koval, D. Vasyukov, P. Müller, H. Schneidewind, D. Ryndyk, J. Keller, and C. Helm, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.014506 69, 014506 (2004).
4. J. Kivioja, T. Nieminen, J. Claudon, O. Buisson, F. Hekking, and J. Pekola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.247002 94, 247002 (2005).
5. V. Krasnov, T. Bauch, S. Intiso, E. Hürfeld, T. Akazaki, H. Takayanagi, and P. Delsing, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.157002 95, 157002 (2005).
6. J. Männik, S. Li, W. Qiu, Q. Chen, V. Patel, S. Han, and J. Lukens, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.220509 71, 220509 (2005).
7. E. Ben-Jacob, D. Bergman, B. Matkowsky, and Z. Schuss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.2805 26, 2805 (1982).
8. Y. Chen, M. Fisher, and A. Leggett, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.341527 64, 3119 (1988).
9. R. Cristiano and P. Silvestrini, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.336490 59, 1401 (1986).
10. J. Fenton and P. Warburton (unpublished).
11. This period would be set by the details of an experiment-see Sec. 4.
12. M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, Singapore, 1996).
13. The McCumber parameter βc ≡ Q2 is also sometimes used to characterize the damping.
14. H. Kramers, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/S0031-8914(40) 90098-2 7, 284 (1940).
15. J. Fenton, M. Korsah, C. Grovenor, and P. Warburton, Physica C PHYCE6 0921-4534 10.1016/j.physc.2007.04.156 460-462, 1470 (2007).
16. Note that the numerator is the total probability of there having been no switch as the current ramps from 0 to I, so that the quotient represents the average probability per unit current of there having been no switch.
17. See also the discussion in Sec. 3.
18. The counterintuitive nature of the accompanying decrease in the width with increasing temperature has previously been highlighted by Krasnov in Refs..
19. V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.11.104 11, 104 (1963).
20. Note that, even above T high, zero voltage is expected for I< IEI and so the low-bias phase-diffusion voltage remains zero.
21. Y. Ivanchenko and L. Zil'berman, Sov. Phys. JETP 28, 1272 (1969). 0038-5646
22. H. Zappe, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1662354 44, 1371 (1973).
23. Additionally, in a theoretical paper, Chen (Ref.) showed that close to the fluctuation-free return current, the voltage departs from V=IR. However, we neglect that dependence here.
24. M. Castellano, G. Torrioli, F. Chiarello, C. Cosmelli, and P. Carelli, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.371704 86, 6405 (1999).
25. The distribution was scaled by dividing by the total probability of a switch following a single escape event.
26. V. Krasnov, T. Golod, T. Bauch, and P. Delsing, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.224517 76, 224517 (2007).
27. For an escape event involving n retraps before eventual escape in a time Δt, the average time for each escape is Δt/ (n+1), implying an equal probability of each escape event in that average time. However, the probabilities of the first n escapes were set (Ref.) to 1, with the (n+1) th escape being assigned the probability ΓΔt/ (n+1). More rigorously, the escape rate could have been expressed by integrating over all possible values of the time te for each escape, subject to the constraint te =Δt.
28. J. Männik (private communication).