Abstract
A model system consisting of a mesoscopic superconducting grain coupled by Josephson junctions to two macroscopic superconducting electrodes is studied. We focus on the effects of Ohmic dissipation caused by resistive shunts and superconducting-normal charge relaxation within the grain. As the temperature is lowered, the behavior crosses over from uncoupled Josephson junctions, similar to situations analyzed previously, to strongly interacting junctions. The crossover temperature is related to the energy-level spacing of the grain and is of the order of the inverse escape time from the grain. In the limit of zero temperature, the two-junction system exhibits five distinct quantum phases, including a novel superconducting state with localized Cooper pairs on the grain but phase coherence between the leads due to Cooper pair cotunneling processes. In contrast to a single junction, the transition from the fully superconducting to fully normal phases is found to be controlled by an intermediate-coupling fixed point whose critical exponents vary continuously as the resistances are changed. The model is analyzed via two-component sine-Gordon models and related Coulomb gases that provide effective low-temperature descriptions in both the weak and strong Josephson coupling limits. The complicated phase diagram is consistent with symmetries of the two component sine-Gordon models, which include weak- to strong-coupling duality and permutation triality. Experimental consequences of the results and potential implications for superconductor to normal transitions in thin wires and films are discussed briefly.
Highlights
Understanding the effects of dissipation on quantum phase transitions has proved to be a challenging problem in many contexts including quantum Hall transitions[1] and quantum critical points in antiferromagnets.[2]
We suggest that our results may be relevant for understanding some puzzling experimental results on superconductorto-normal transitions in thin wires and films
Eration of cotunneling processes in which a Cooper pair moves between the leads, but with both junctions individually insulating. The circuit describing this case is depicted in Fig. 5͑c, with the cotunneling process described as two current sources forcing the same current through both Josephson junctions
Summary
Understanding the effects of dissipation on quantum phase transitions has proved to be a challenging problem in many contexts including quantum Hall transitions[1] and quantum critical points in antiferromagnets.[2]. The primary purpose of this paper is to begin to reconcile these two approaches by studying a deceptively simple system: two resistively shunted Josephson junctions coupled in series through a superconducting grain This system, in addition to its intrinsic interest,[53] provides a simple paradigm for the competing effects of dissipation and quantum fluctuations on superconductivity. In some regimes of parameter space, the superconductor-to-normal transition between the two macroscopic leads is determined by the total shunting resistance of the system, rather than individual resistances of the junctions, while in other regimes its location depends on the strengths of the Josephson couplings as well as the shunting resistances In this latter case, the corresponding critical behavior becomes very different from the single junction case. The renormalization group analysis of the two-component sineGordon model and the relations to classical Coulomb gasses are given in Appendixes Dweak coupling, and Estrong coupling
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