Phase Transitions in Dissipative Josephson Chains
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PHASE TRANSITIONS IN DISSIPATIVE JOSEPHSON CHAINS
P.A. BOBBERT,* R. FAZIO,* GERD SCHON,* and GT. ZIMANYI,** * Department of Applied Physics, Delft University of Technology, 2628 CJ Delft, The Netherlands ** Department of Physics, University of California, Davis CA 95616
ABSTRACT We study the zero temperature phase transitions of a chain of Josephson junctions, taking into account the quantum fluctuations due to the charging energy and the effects of an Ohmic dissipation. We map the problem onto a generalized Coulomb gas model, which then is transformed into a sine-Gordon field theory. Apart from the expected dipole unbinding transition, which describes a transition between globally superconducting and resistive behavior, we find a quadrupole unbinding transition at a critical strength of the dissipation. This transition separates two superconducting states characterized by different local properties. 1.Introduction In the last years the interest in the properties of mesoscopic tunnel junctions, junction arrays and granular superconductors has been growing. With modern lithographic techniques it is possible to fabricate regular arrays of Josephson junctions which show a transition between a globally superconducting and a resistive state. In 2-dimensional classical arrays this transition is of the Kosterlitz-Thouless-Berezinskii (KTB) type [1], and occurs at a critical temperature TKTB below the superconducting transition temperature of the individual islands. It has been recognized [2] that in these systems quantum effects induced by the charging energy of the metallic islands can play an important role. When the geometrical capacitance of the islands is of the order of picofarad the Coulomb energy Ec = e2 /2C may exceed the Josephson energy Ei. In this case the quantum fluctuations lower the coherent transition temperature TKTB, and below a critical value of the ratio EjiEc global phase coherence is prevented even at T = 0. Bradley and Doniach [3] mapped the quantum Josephson chain on a (1+1)-dimensional classical XY model. The coherent transition in this case is again of the KTB type. A series of experiments, both on granular superconductors [4] and arrays of Josephson junctions [5] showed an additional feature: The low temperature properties of the network depend strongly on the normal sheet resistance R of the system. Only below a critical value of R of the order of h/4e2 • 6.5kgl the system reaches a globally superconducting state. The experiments suggest that this is a simple independent, universal value. It is the purpose of this paper to work out in more detail the properties of the phase transitions in a chain of Josephson junctions. Based on the above considerations we include quantum fluctuations through a charging energy term and the dissipation by assuming that the junctions are shunted by Ohmic resistors Rs and that the quasiparticle contribution can be disregarded.
Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
358
TI. The model The model is defined by the following action
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