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arXiv:cond-mat/0508138 · Europhysics Letters (EPL)

Dissipate locally, couple globally: A sharp transition from decoupling to infinite range coupling in Josephson arrays with on-site dissipation

Sumanta Tewari, John Toner

Published Mar 14, 2006• 5 citations
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Abstract

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.

DOI
10.1209/epl/i2005-10528-9

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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 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 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 $I\text{\ensuremath{-}}V$ characteristics. This may be the simplest and most natural example of a floating phase.
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 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.
Based on the two-band free-energy functional, we have investigated phase transitions of a three-dimensional granular superconductor through the Monte Carlo method and finite-size scaling analysis. In the ordered lattices for this superconductor consisting of Josephson-coupled grains, we obtain an intermediate phase above the critical intraband coupling strength while maintaining a constant interband coupling coefficient. This phase is distinct from both the low-temperature superconducting phase and the high-temperature normal phase, characterized by the absence of long-range phase coherence solely for the first band. This numerical prediction can be confirmed through magnetic susceptibility calculations, and the phase diagram is qualitatively consistent with the mean-field theoretical analysis. Additionally, we have considered the effects of interband interaction between the nearest-neighbor grains and random disorders in diluted lattices with three different site occupancies. When the occupation probability exceeds the percolation threshold, the results are qualitatively similar to those of ordered lattices, and the intermediate phase likewise appears by adjusting the intraband Josephson coupling coefficient. In contrast, below the percolation threshold, such a phase does not exist because the long-range phase coherence for both bands disappears.
We present a study of quantum phase analysis of inhomogeneous and homogeneous arrays of superconducting quantum dots (SQD). We observe the existance of Josephson decouple (JD) phase only at the half filling for inhomogeneous array of SQD due to the fluctuation of Josephson couplings over the sites at half filling. In JD phase superconductivity disappears even in the absence of Coulomb blockade phase. We also observe that fluctuation of on-site Coulomb charging energy produces the relevant coupling term that yields Coulomb blockade gapped phase. The presence of nearest-neighbor and next-nearest-neighbor Coulomb interaction yields the same physics for inhomogeneous and homogeneous SQD.