Abstract
We discuss the phase diagram of regular networks of quantum mechanical Josephson junctions in one and two dimensions for different choices of the Coulomb interaction between pairs. In a particular case this is equivalent to a quantum interface with lateral tunneling along the boundary. Using a functional integral approach the partition function is transformed into that of classical roughening or Coulomb gas problems. It is shown, in particular, that the structure of the phase diagram depends crucially on the form of the Coulomb interaction and that with dissipative interactions both globally and locally superconducting phases are possible. The relation of our results to recent experiments on granular superconducting films and ideal Josephson junction arrays is discussed briefly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Leggett, A.J.: In: Chance and matter. Les Houches 1986. Souletie, J., Vannimenus, J., Stora, R. (eds.). Amsterdam: North Holland 1987
Orr, B.G., Jaeger, H.M., Goldman, A.M.: Phys. Rev. B32, 7586 (1985)
Orr, B.G., Jaeger, H.M., Goldman, A.M., Kuper, C.G.: Phys. Rev. Lett.56, 378 (1986)
Jaeger, H.M., Haviland, D.B., Goldman, A.M., Orr, B.G.: Phys. Rev. B34, 4920 (1986)
Note that φ is periodic andn discrete like angle and angular momentum around a fixed axis and thus the commutation relation should more properly be written as [eiφ,n]=−eiφ.
Hertz, J.A.: Phys. Rev. B14, 4978 (1976)
Zwerger, W.: In: Festkörperprobleme/Advances in Solid State Physics. Vol. 29, p. 19. Braunschweig: Vieweg 1989
Fisher, M.P.A., Lee, D.H.: Phys. Rev. B39, 2756 (1989)
Bradley, R.M., Doniach, S.: Phys. Rev. B30, 1138 (1984)
Fradkin, E.: Phys. Rev. B28, 5338 (1983)
Zwerger, W.: Europhys. Lett.9, 421 (1989)
Iordansky, S.V., Korshunov, S.E.: J. Low Temp. Phys.58, 425 (1985)
Fisher, M.P.A., Grinstein, G.: Phys. Rev. Lett.60, 208 (1988)
Mühlschlegel, B., Scalapino, D.J., Denton, R.: Phys. Rev. B6, 1767 (1972)
The corresponding offdiagonal elements of the inverse capacitance matrix are negative thus violating the generally valid requirement (C −1) ll′ >=0. However due to the neutrality condition\(\sum\limits_t {n_t = 0} \) it is always possible to add a constant to (C −1) ll′ such thatC −1 is a matrix with only positive elements
Fisher, D.S., Weeks, J.D.: Phys. Rev. Lett.50, 1077 (1983)
Fisher, M.P.A.: Phys. Rev. B36, 1917 (1987)
Ferrell, R.A., Mirhashem, B.: Phys. Rev B37, 648 (1988)
Zwerger, W.: J. Low Temp. Phys.72, 291 (1988)
Villain, J.: Phys. (Paris)36, 581 (1976). Note that the form (27) is used even if ɛE J→0 which guarantees a sensible continuum limit later on
Chui, S.T., Weeks, J.D.: Phys. Rev. B14, 4978 (1976)
Note that the potentialv(τ) in [11] differs by a minus sign from the one used here
Zittartz, J.: Z. Phys. B — Condensed Matter and Quanta31, 89 (1978)
This argument neglects screening by the other charges with a factor ε -10 , however in the present case the critical value α c =1 is known exactly from duality arguments, see [25, 26]
Schmid, A.: Phys. Rev. Lett.51, 1506 (1983)
Fisher, M.P.A., Zwerger, W.: Phys. Rev. B32, 6190 (1985)
Zwerger, W.: Phys. Rev. B35, 4737 (1987)
Korshunov, S.E.: Europhys. Lett.9, 107 (1989)
Note that in [11] the factor was given incorrectly as 2 π instead of 8/π
Nelson, D.R., Kosterlitz, J.M.: Phys. Rev. Lett.39, 1201 (1977)
Note that the Josephson coupling has to be nonzero, however, since otherwise the scale\(\tau _0 = \frac{{\alpha \hbar }}{{2\pi E_J }}\) for the logarithmic interaction would be infinite
Dasgupta, C., Halperin, B.I.: Phys. Rev. Lett.47, 1556 (1981)
Note that the vector potential A in [8] is related to our h byA x-hy andA y=−hx in the gaugeA τ=0
Chakravarty, S., Ingold, G.L., Kivelson, S., Zimanyi, G.: Phys. Rev. B37, 3283 (1988)
Zaikin, A.D.: Physica B152, 251 (1988)
For a recent review see: Minnhagen, P.: Rev. Mod. Phys.59, 1001 (1987)
Shugard, W.J., Weeks, J.D., Gilmer, G.H.: Phys. Rev. Lett.41, 1399 (1978)
Geerligs, L.J., Peters, M., de Groot, L.E.M., Verbruggen, A., Mooij, J.E.: Phys. Rev. Lett.63, 326 (1989)
Eckern, U., Ambegaokar, V., Schön, G.: Phys. Rev. B30, 6419 (1984)
Chakravarty, S., Kivelson, S., Zimanyi, G., Halperin, B.I.: Phys. Rev. B35, 7256 (1987)
Haviland, D.B., Liu, Y., Goldman, A.M.: Phys. Rev. Lett.62, 2180 (1989)
Author information
Authors and Affiliations
Additional information
Dedicated to Professor W. Brenig on the occasion of his 60th birthday
Rights and permissions
About this article
Cite this article
Zwerger, W. Josephson-junction networks and roughening problems. Z. Physik B - Condensed Matter 78, 111–123 (1990). https://doi.org/10.1007/BF01317363
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01317363