One-dimensional Mott localization of quantum vortices in Josephson-junction arrays

Oudenaarden, Alexander van; Leeuwen, Bas van; Robbens, M.P.M.; Mooij, J. E.

doi:10.1103/physrevb.57.11684

Cited by 12 publications

(22 citation statements)

References 19 publications

(16 reference statements)

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“…Our theory explains consistently the main experimental observations reported in this paper and in Ref. 9: ͑1͒ the cusplike dependence of the activation energy on the magnetic field in the commensurate phase; ͑2͒ the large value of this activation energy ͑compared to E J and E C ), and ͑3͒ oscillations of the resistance with the applied magnetic field, with a period corresponding to one flux quantum through the entire array, in the incommensurate phase. We conclude with a discussion in Sec.…”

Section: Introductionsupporting

confidence: 89%

“…Indeed, in the experiment a cusplike dependence of the resistance activation energy on ͉BϪB 0 ͉ was observed ͑see Ref. 9 and Sec. VI of this paper͒.…”

Section: Introductionmentioning

confidence: 82%

“…VI we will further refine the estimate ͑31͒ for the specific geometry of the experiment. 9 In the above consideration, we have completely ignored the existence of Abrikosov vortices in the contacts. This is acceptable only if their currents do not overlap with the currents created by Josephson vortices.…”

Section: Compressible Vortex Chainmentioning

confidence: 99%

“…Commensurability effects in a chain of quantum vortices were investigated in the recent experiments of van Oudenaarden et al 9 There a number of two-dimensional arrays with various ratios E C /E J , and various widths of the order of ten cells were studied. All arrays were quasi-one-dimensional in fact, their length varying between 100 and 1000 cells.…”

Section: Introductionmentioning

confidence: 99%

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Phase transition in a chain of quantum vortices

et al. 1999

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We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array. We find the dependence of the resistance activation energy on the magnetic field and parameters of the Josephson array. This energy consists of the above-mentioned gap, and also of a boundary pinning term, which is different in the commensurate and incommensurate phases. The developed theory allows us to explain quantitatively the available experimental data. ͓S0163-1829͑99͒00402-6͔

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Section: Introductionsupporting

confidence: 89%

“…Indeed, in the experiment a cusplike dependence of the resistance activation energy on ͉BϪB 0 ͉ was observed ͑see Ref. 9 and Sec. VI of this paper͒.…”

Section: Introductionmentioning

confidence: 82%

Section: Compressible Vortex Chainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase transition in a chain of quantum vortices

et al. 1999

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“…Longer ranger interactions have been found to be important in experiments [7][8][9] . We now include nearestneighbor interactions by setting V = 0.4.…”

Section: Nearest-neighbor Interactionmentioning

confidence: 99%

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

2000

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We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG). For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.

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Quantum phase transitions and vortex dynamics in superconducting networks

2001

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Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of lowcapacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) Superconductor-Insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum-vortex experiments and theoretical treatments of their quantum dynamics.

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One-dimensional Mott localization of quantum vortices in Josephson-junction arrays

Cited by 12 publications

References 19 publications

Phase transition in a chain of quantum vortices

Phase transition in a chain of quantum vortices

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

Quantum phase transitions and vortex dynamics in superconducting networks

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