Abstract
We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on its physical parameter values. The former case is dominated by a Cooper-pair superfluid, while the quantum case is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and mean-field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one is in the quantum-fluctuations-dominated regime, we derive a duality transformation between the charge and vortex-dominated arrays that involves a gauge vector field which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.
Similar content being viewed by others
REFERENCES
For a recent reviews of superconducting networks see Proceedings of the 2nd CTP Workshop on Statistical Physics: KT Transition and Superconducting Arrays, D. Kim, J. S. Chung, and M. Y. Choi, eds. (Min Eum Sa, Seoul, Korea, 1993). Macroscopic quantum phenomena and coherence in superconducting networks, C. Giovannella and M. Tinkham, eds. (World Scientific Co., Singapore, 1995). Proceedings of the ICTP Workshop on Josephson Junction Arrays, H. Cerdeira and S. R. Shenoy, eds., Physica B 222, (1996). Mesoscopic superconductivity, Proceedings of a NATO Workshop, F. W. Hekking, G. Schön, and D. V. Averin, eds., Physica B 203, 1994. “1997 Euroschool, Siena, Italy, Superconductivity in Networks and Mesoscopic Structures,” C. Giovannella and C. Lambert, eds. (AIP, 1998).
“Vortex dynamics in artificially fabricated superconducting networks” H. S. J. van der Zant, Ph.D. Thesis (Delft, 1991) and H. S. J. van der Zant, H. S. J. Elion, W. J. and J. E. Mooij, Phys. Rev. B 54:10081 (1996). P. Lafarge, M. Matters, and J. E. Mooij, Phys. Rev. B 54:7380 (1996).
T. S. Tighe, A. T. Johnson, and M. Tinkham, Phys. Rev. B 44:10986 (1991).
P. Delsing, C. D. Chen, and T. Claeson, Phys. Rev. B 50:3959 (1994). C. D. Chen, Y. Cai, Phys. Rev. B 51:15645 (1995). P. Delsing, C. D. Chen, and D. B. Haviland, Physica B 194:993 (1994). C. D. Chen, P. Delsing, and C. D. Cleason, Physica Scripta T 42:182 (1992).
M. Matters, J. J. Versluys, and J. E. Mooij, Phys. Rev. Lett. 78:2469 (1997). R. Therrien, T. R. Ho, C. Kurdak, A. J. Rimberg, J. Clarke, K. L. Campman, and A. C. Gossard, Bull. Am. Phys. Soc. 43:55 (1998). C. Kurdak, A. J. Rimberg, T. R. Ho, R. Therrien, J. Clarke, and J. D. Walker, Bull. Am. Phys. Soc. 43:55 (1998).
C. Rojas and J. V. José, Phys. Rev. B 54:12361 (1996).
“Quantum phase transitions in arrays of ultrasmall Josephson junctions and chaotic scattering”, C. Rojas, Ph.D. thesis, Northeastern University (1995).
J. V. José, Phys. Rev. B 29:2836 (1984), L. Jacobs, J. V. José, M. A. Novotny, and A. M. Goldman, Phys. Rev. B 38:4562 (1988); L. Jacobs, J. V. José, M. A. Novotny, and A. M. Goldman, Europhys. Lett. 3:1295 (1987); L. Jacobs, J. V. José, and M. A. Novotny, Phys. Rev. Lett. 53:2177 (1984).
L. L. Sohn, J. Romijn, E. van der Drift, W. J. Elion, and J. E. Mooij, Physica B 194–196:125 (1994).
H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore, 1989).
W. J. Elion, M. Matters, and J. E. Mooij, Nature 371:594 (1994).
R. Fazio and G. Schön, Phys. Rev. B 43:5307 (1991).
J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16:1217 (1977).
A. Stern, Phys. Rev. B 50:10092 (1994).
C. Rojas, J. V. José, and A. M. Tikofsky, Bull. Am. Phys. Soc. 40; p. 68, B11-7 (1995).
Ya. M. Blanter and G. Schön, Phys. Rev. B 53:14534 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
José, J.V. Duality in Two Capacitively Coupled Layered Arrays of Ultrasmall Josephson Junctions. Journal of Statistical Physics 93, 943–964 (1998). https://doi.org/10.1023/B:JOSS.0000033171.04828.d6
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000033171.04828.d6