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arXiv:cond-mat/0407308 · Physical Review B

Floating phase in a dissipative Josephson junction array

Sumanta Tewari, John Toner, Sudip Chakravarty

Published Aug 16, 2005• 18 citations
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Abstract

We show that dissipative Josephson junction arrays, an extended system, have an unusual ``floating'' metal phase in which the states of local $(0+1)$-dimensional elements (single junctions) can slide past each other despite arbitrary range spatial couplings among them. The zero-temperature metal-to-superconductor quantum phase transition is controlled in any dimension by a locus of critical points fixed only by the local lattice topology. Our theory can be tested by measuring $I\text{\ensuremath{-}}V$ characteristics. This may be the simplest and most natural example of a floating phase.

DOI
10.1103/physrevb.72.060505

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Physical review. B, Condensed matter•Aug 1, 1993•80 citations
We show that dissipative Josephson junction arrays, an extended system, have an unusual ``floating'' metal phase in which the states of local (0+1)(0+1)(0+1)-dimensional elements (single junctions) can slide past each other despite arbitrary range spatial couplings among them. The zero-temperature metal-to-superconductor quantum phase transition is controlled in any dimension by a locus of critical points fixed only by the local lattice topology. Our theory can be tested by measuring I\ensuremath-VI\text{\ensuremath{-}}VI\ensuremath-V characteristics. This may be the simplest and most natural example of a floating phase.
We study the nature of correlations within, and the transition into, the floating phase of dissipative Josephson junction arrays. Order parameter correlations in this phase are long-ranged in time, but only short-ranged in space. A perturbative renormalization group analysis shows that, in arbitrary spatial dimension, the transition is controlled by a continuous locus of critical fixed points determined entirely by the local topology of the lattice. This may be the most natural example of a line of critical points existing in arbitrary dimensions.
We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase $\ensuremath{\theta}$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\ensuremath{\Delta}\ensuremath{\theta}$, not in $\ensuremath{\theta}$. Significantly, the most ordered state therefore does not have three-dimensional (3D) XYXYXY ordering. Rather, it features two-dimensional (2D) spin waves coexisting with temporally disordered phases $\ensuremath{\theta}$. There is also an intermediate phase featuring quasi-long-range spatial order in $\ensuremath{\theta}$ coexisting with a gas of instantons in $\ensuremath{\Delta}\ensuremath{\theta}$. We briefly discuss possible experimental signatures of such a state, which may be viewed as a local metal and a global superconductor. The most disordered state has phase disorder in all spatio-temporal directions, and may be characterized as a gas of proliferated vortices coexisting with a gas of $\ensuremath{\Delta}\ensuremath{\theta}$ instantons. The phase transitions between these phases are discussed. The transition from the most ordered state to the intermediate state is driven by proliferation of instantons in $\ensuremath{\Delta}\ensuremath{\theta}$. The transition from the intermediate state to the most disordered state is driven by the proliferation of spatial point vortices in the background of a proliferated $\ensuremath{\Delta}\ensuremath{\theta}$-instanton gas, and constitutes a Berezinskii-Kosterlitz-Thouless phase transition. The model also features a direct phase transition from the most ordered state to the most disordered state, and this transition is neither in the 2D XYXYXY nor in the 3D XYXYXY universality class. It comes about via a simultaneous proliferation of point vortices in two spatial dimensions and $\ensuremath{\Delta}\ensuremath{\theta}$ instantons, with a complicated interplay between them. The results are compared to, and differ in a fundamental way from, the results that are found in dissipative quantum rotor systems. The difference originates with the difference in the values that the fundamental degrees of freedom can take in the latter systems compared to dissipative Josephson junction arrays.
The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent z≈2z\approx 2z≈2. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.
We study the T=0 normal to superconducting transition of Josephson arrays with {\it on-site} dissipation. A perturbative renormalization group solution is given. Like the previously studied case of {\it bond} dissipation (BD), this is a "floating" to coupled (FC) phase transition. {\it Unlike} the BD transition, at which {\it only} nearest-neighbor couplings become relevant, here {\it all} inter-grain couplings, out to {\it infinitely} large distances, do so simultaneously. We predict, for the first time in an FC transition, a diverging spatial correlation length. Our results show the robustness of floating phases in dissipative quantum systems.
We present a cluster algorithm for resistively shunted Josephson junctions or similar physical systems, which dramatically improves sampling efficiency, and apply it to the superconductor-to-metal transition in a single junction. Measuring the temperature dependence of the zero bias resistance, we confirm that the critical point does not depend on the strength of the Josephson coupling. However, we find that the correlation exponents vary continuously along the phase boundary, indicating that the Schmid-Bulgadaev transition is a line of fixed points.
We study the superconductor-insulator transition of a two-dimensional Bose-Hubbard model, considering as a specific example, an array of Josephson junctions. Within a coarse-graining approach we derive an effective free-energy functional from which we determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-insulating lobes. The phase boundaries of some of these lobes display reentrant behavior as a function of temperature. Next, we evaluate the electromagnetic-response functions of the system. The real part of the longitudinal conductivity is characterized by an excitation gap, whereas the imaginary part describes a capacitor. In an ideal system, under certain conditions a universal conductance is found at the transition. If we add low-frequency dissipation to the model a different value of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively differing results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system.