Abstract
The phase diagram of a two-dimensional Josephson array of mesoscopic objects (superconducting granules, superfluid helium in a porous medium, traps with Bose-condensed atoms, etc.) is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number n 0 of the sites in the system (the “number of Cooper pairs” per granule, the number of atoms in a trap, etc.) leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on n 0. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in n 0 within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum path-integral Monte Carlo calculations.
Similar content being viewed by others
References
F. J. Nacker and J. Dupont-Roc, Phys. Rev. Lett. 67, 2966 (1991).
J. D. Reppy, J. Low Temp. Phys. 67, 207 (1992).
H. S. J. van der Zant, F. C. Fritschy, J. E. Mooij et al., Phys. Rev. Lett. 69, 2971 (1992); J. E. Mooij, R. Fazio, G. Schön et al., Phys. Rev. Lett. 65, 645 (1990).
V. G. Gantmakher, V. M. Teplinskii, and V. N. Zverev, JETP Lett. 62, 887 (1995).
A. F. Hebard and M. A. Paalanen, Phys. Rev. Lett. 65, 927 (1990).
A. L. Dobryakov, Yu. E. Lozovik, A. A. Puretzky et al., Appl. Phys. A 54, 100 (1992).
Yu. M. Mucharsky, A. Loshak, K. Schwab et al., Czech. J. Phys. 46, 115 (1996); S. V. Pereverzev, A. Loshak, S. Backhaus et al., Nature (London) 388, 449 (1997).
M. N. Anderson, J. R. Ensher, M. R. Mathews et al., Science 269, 198 (1995).
C. C. Bradley, C. A. Sackoff, J. J. Tollett et al., Phys. Rev. Lett. 75, 1687 (1995).
K. B. Davis, M.-O. Mewes, M. R. Andrew et al., Phys. Rev. Lett. 75, 3969 (1995).
M. R. Andrews, C. G. Towsend, J.-J. Miesner et al., Science 275, 637 (1997).
Yu. E. Lozovik, submitted to Physica E (Amsterdam); Yu. E. Lozovik and O. L. Berman, Zh. Éksp. Teor. Fiz. 111, 1879 (1997) [JETP 84, 1027 (1997)]; Yu. E. Lozovik, O. L. Berman, and V. G. Tsvetus, JETP Lett. 66, 355 (1997).
B. J. Kim and M. Y. Choi, Phys. Rev. B 52, 3624 (1995); B. J. Kim, J. Kim, M. Y. Choi et al., Phys. Rev. B 56, 395 (1997).
C. Bruder, R. Fazio, A. P. Kampf et al., Phys. Scr. T 42, 159 (1992).
I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, Adv. Phys. 10, 165 (1961).
G. T. Zimanyi, P. A. Crowell, R. T. Scalettar et al., Phys. Rev. B 50, 6515 (1994).
M. P. A. Fisher and G. Grinstein, Phys. Rev. Lett. 60, 208 (1988); M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989); M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Phys. Rev. Lett. 64, 587 (1990).
M. C. Cha, M. P. A. Fisher, S. M. Girvin et al., Phys. Rev. B 44, 6883 (1991).
A. P. Kampf and G. T. Zimanyi, Phys. Rev. B 47, 279 (1993).
W. Knauth, N. Trivedi, and D. Ceperley, Phys. Rev. Lett. 67, 2703 (1991); W. Krauth and N. Trivedi, Europhys. Lett. 14, 627 (1991).
V. A. Kashurnikov, A. V. Krasavin, and B. V. Svistunov, JETP Lett. 64, 99 (1996).
A. V. Otterlo and K. H. Wagenblast, Phys. Rev. Lett. 72, 3598 (1994); E. Roddick and D. Stroud, Phys. Rev. B 51, 8672 (1995).
A. I. Belousov, S. A. Verzakov, and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 113, 261 (1998) [JETP 86, 146 (1998)]; A. I. Belousov and Yu. E. Lozovik, JETP Lett. 66, 686 (1997).
S. Doniach, Phys. Rev. B 24, 5063 (1981).
V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics, Reidel, Dordrecht (1983).
J. J. Alvarez and C. A. Balseiro, Solid State Commun. 98, 313 (1996).
P. Olsson, Phys. Rev. B 52, 4511 (1995).
A. Blaer and J. Han, Phys. Rev. A 46, 3225 (1992).
G. G. Batrouni, B. Larson, R. T. Scalettar et al., Phys. Rev. B 48, 9628 (1993).
P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
M. Jacobs, J. V. Jose, M. A. Novotny et al., Phys. Rev. B 38, 4562 (1988).
S. L. Sondhi, S. M. Girvin, J. P. Carini et al., Rev. Mod. Phys. 69, 315 (1997).
A. I. Belousov and S. G. Akopov, J. Phys. C 14, L31 (1981); S. G. Akopov and Yu. E. Lozovik, J. Phys. C 15, 4403 (1982).
A. I. Belousov and Yu. E. Lozovik, Solid State Commun. 100, 421 (1996); A. I. Belousov and Yu. E. Lozovik, Fiz. Tverd. Tela (St. Petersberg) 39, 1513 (1997) [Phys. Solid State 39, 1345 (1997)]; S. A. Verzakov and Yu. E. Lozovik, Fiz. Tverd. Tela (St. Petersberg) 39, 818 (1997) [Phys. Solid State 39, 724 (1997)].
F. F. Assaad, W. Hanke, and D. J. Scalapino, Phys. Rev. B 50, 12 835 (1994).
D. Marx and P. Nielaba, J. Chem. Phys. 102, 4538 (1995).
Author information
Authors and Affiliations
Additional information
Zh. Éksp. Teor. Fiz. 114, 591–604 (August 1998)
Rights and permissions
About this article
Cite this article
Belousov, A.I., Berzakov, S.A. & Lozovik, Y.E. Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential. J. Exp. Theor. Phys. 87, 322–328 (1998). https://doi.org/10.1134/1.558662
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.558662