Superconductor-to-normal transitions in dissipative chains of mesoscopic grains and nanowires

Abstract

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed and the results are applied to nanowires. It is shown that in one dimensional arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase ͑FSC͒, each grain acts superconducting, and the coupling to the dissipative conduction is important. In the SC Ã phase, the dissipation is irrelevant at long wavelengths. The transition between these two phases is driven by quantum phase slip dipoles, and is primarily local, with continuously varying critical exponents. In contrast, the transition from the SC Ã phase to the normal metallic phase is a Kosterlitz-Thouless transition with global character ͑i.e., determined by the field behavior at large wavelengths͒. Most interesting is the transition from the FSC phase directly to the normal phase: this transition, which has mixed local and global characteristics, can be one of three distinct types. The corresponding segments of the phase boundary come together at bicritical points. The zero-temperature phase diagram, as well as the finite-temperature scaling behavior are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.

Sharp Superconductor-Insulator Transition in Short Wires

“…Schmid [7] and Chakravarty [8] showed that a JJ undergoes a SIT as a function of the junction's shunt resistance, R s , with a critical resistance of R Q , and that the resistance across the junction obeys the power law R T / T 2 R Q =R s ÿ1 . The theory was later extended to JJ arrays and SC wires [9][10][11]. Within these theories, a similar power-law temperature dependence of the resistance at low temperature prevails.…”

Dissipation-driven phase transitions in superconducting wires

“…I, these topological excitations produce finite resistivity at T Ӷ T c and are believed to be the origin of destruction of superconductivity in narrow wires 30,33 and in dissipative Josepshon junctions arrays. 10,11 It can be shown 2 that defining a field ͑x͒, such that ٌ͑x͒ϵ⌸͑x͒, the generation of topological defects in the field ͑x͒ can be described by a term…”

“…1,2 On the other hand, dissipation counteracts fluctuations effects, decreasing the lower critical dimension. [3][4][5][6] Some physical realizations of dissipative low-dimensional systems are the well-known resistively shunted Josephson junctions arrays, where the effect of local ohmic dissipation has been intensively studied, [7][8][9][10][11] superconducting grains embedded in metallic films, [12][13][14][15] and Luttinger liquids coupled to dissipative baths. [16][17][18] Narrow superconducting wires with diameter d Ӷ 0 ͑where 0 is the bulk superconducting coherence length͒ are low-dimensional systems in which strong fluctuations of the order parameter affect low-temperature properties.…”

Dynamics of superconducting nanowires shunted with an external resistor

“…Advances in fabricating ultra-narrow superconducting nanowires has greatly boosted the interest in studying phase slippage in quasi-one-dimensional superconductors 2 . There has been an intense activity to establish the existence of quantum phase slips (QPS) related to macroscopic quantum tunneling (MQT) [3][4][5][6][7][8][9][10][11] and to study quantum phase transitions between possibly superconducting, metallic and insulating phases in nanowires 4,[12][13][14][15][16][17] . A dissipation-controlled quantum phase transition [18][19][20][21][22][23][24][25] has been predicted in junctions of superconducting nanowires.…”