Phase transition in a chain of quantum vortices
Abstract
We consider interacting vortices in a quasionedimensional 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 onedimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex and the longrange interaction between the vortices leads to the existence of a specific commensurateincommensurate transition in a onedimensional 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 abovementioned 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.
 Publication:

Physical Review B
 Pub Date:
 January 1999
 DOI:
 10.1103/PhysRevB.59.1383
 arXiv:
 arXiv:condmat/9809118
 Bibcode:
 1999PhRvB..59.1383B
 Keywords:

 74.50.+r;
 64.70.Rh;
 05.30.Jp;
 Tunneling phenomena;
 point contacts weak links Josephson effects;
 Commensurateincommensurate transitions;
 Boson systems;
 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 14 pages, 7 eps figures