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Title: Defect motion and lattice pinning barriers in Josephson-junction ladders

Abstract

We study the motion of domain wall defects in a fully frustrated Josephson-junction ladder system, driven by small applied currents. For small system sizes, the energy barrier E{sub B} to the defect motion is computed analytically via symmetry and topological considerations. More generally, we perform numerical simulations directly on the equations of motion, based on the resistively-shunted junction model, to study the dynamics of defects, varying the system size. Coherent motion of domain walls is observed for large system sizes. In the thermodynamical limit, we find E{sub B}=0.1827 in units of the Josephson coupling energy.

Authors:
;  [1];  [2];  [3];  [1];  [4]
  1. Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747 (Korea, Republic of)
  2. Laboratoire de Physique Theorique, Universite Louis Pasteur, 67084 Strasbourg (France)
  3. Department of Physics, Keimyung University, Daegu 704-701 (Korea, Republic of)
  4. (Korea, Republic of)
Publication Date:
OSTI Identifier:
20787821
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevB.73.014504; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; COMPUTERIZED SIMULATION; COUPLING; DEFECTS; DOMAIN STRUCTURE; ELECTRIC CURRENTS; EQUATIONS OF MOTION; JOSEPHSON EFFECT; JOSEPHSON JUNCTIONS; MAGNETIC FLUX; SYMMETRY; TOPOLOGY; WALLS

Citation Formats

Kang, H., Lim, Jong Soo, Fortin, J.-Y., Choi, J., Choi, M. Y., and Korea Institute for Advanced Study, Seoul 130-722. Defect motion and lattice pinning barriers in Josephson-junction ladders. United States: N. p., 2006. Web. doi:10.1103/PHYSREVB.73.0.
Kang, H., Lim, Jong Soo, Fortin, J.-Y., Choi, J., Choi, M. Y., & Korea Institute for Advanced Study, Seoul 130-722. Defect motion and lattice pinning barriers in Josephson-junction ladders. United States. doi:10.1103/PHYSREVB.73.0.
Kang, H., Lim, Jong Soo, Fortin, J.-Y., Choi, J., Choi, M. Y., and Korea Institute for Advanced Study, Seoul 130-722. Sun . "Defect motion and lattice pinning barriers in Josephson-junction ladders". United States. doi:10.1103/PHYSREVB.73.0.
@article{osti_20787821,
title = {Defect motion and lattice pinning barriers in Josephson-junction ladders},
author = {Kang, H. and Lim, Jong Soo and Fortin, J.-Y. and Choi, J. and Choi, M. Y. and Korea Institute for Advanced Study, Seoul 130-722},
abstractNote = {We study the motion of domain wall defects in a fully frustrated Josephson-junction ladder system, driven by small applied currents. For small system sizes, the energy barrier E{sub B} to the defect motion is computed analytically via symmetry and topological considerations. More generally, we perform numerical simulations directly on the equations of motion, based on the resistively-shunted junction model, to study the dynamics of defects, varying the system size. Coherent motion of domain walls is observed for large system sizes. In the thermodynamical limit, we find E{sub B}=0.1827 in units of the Josephson coupling energy.},
doi = {10.1103/PHYSREVB.73.0},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}
  • We present simulation results on the dynamics of 1D Josephson ladder arrays at zero temperature in the presence of uniform magnetic fields when dc plus ac currents are applied. For a frustration [ital f]=[ital p]/[ital q], the dynamics of the array can be described by the reduced equations for only [ital q] variables, if the initial configuration is assumed to be invariant under the [ital q]-lattice translation. When dc plus ac currents are injected, fractional Shapiro steps are found at time-averaged voltage [l angle][ital V][r angle]=([ital n]/[ital q])([h bar][omega]/2[ital e]) with [ital n] an integer and [omega] the external drivingmore » frequency. If the ladder array is wound into an [ital annular] geometry, we can have defects in the vortex configuration depending on the initial random-phase configuration which cannot evolve into [ital q]-periodic states, and these defects are shown to smear the Shapiro steps. The dynamic resistance on the smeared Shapiro step is proportional to the number density of the defects.« less
  • A pinning force acting upon a periodic fluxon chain in a long Josephson junction with a commensurable periodic lattice of local inhomogeneities is calculated by means of a perturbation theory. The pinning force for a single fluxon is also calculated. Dynamics of a chain and of a single fluxon are also studied. The experimental part of the paper reports results of measurements of a critical bias current {ital I}{sub {ital c}} versus external magnetic field {ital H}. The measurements have been performed for long overlap Nb-NbO{sub {ital x}}-Pb junctions {ital I}{sub {ital c}}({ital H}) curve were observed at multiple valuesmore » of {ital H}. Agreement between the theory and experiment for different spatial periods of the fluxon chain is satisfactory.« less
  • This paper considers a Josephson junction array with the geometry of a ladder and anisotropy in the Josephson couplings. The ground-state problem for the ladder corresponds to the one for the one-dimensional chiral {ital XY} model in a twofold anisotropy field, which allows for a rigorous characterization of the ground-state phase diagram and the relevant elementary excitations for the system. The approach to equilibrium, which we study using Langevin dynamics, shows slow relaxation, typical of systems whose energy landscape in the configuration space consists of a wealth of metastable states, dynamically disconnected.
  • Both critical current and Shapiro steps in Josephson ladders are found to show effects of vortex exclusion below a critical magnetic field. Vortices are excluded even though the flux itself is {ital not} screened out. When current is injected perpendicular to the ladder edges, the critical current is unchanged from its {ital f}=0 value up to a penetration field of {ital f}{sub {ital c}1{perpendicular}}{approx_equal}0.12 flux quanta per plaquette. Similarly, there are only integer Shapiro steps below a critical {ital c}1{perpendicular}{asterisk}, where vortices first penetrate. A narrower critical current plateau also appears to form near {ital f} =1/2. No such plateausmore » occur when current is injected in the parallel direction. We attribute the exclusion in the perpendicular geometry to screening currents which flow along the edges of the ladder. {copyright} {ital 1996 The American Physical Society.}« less
  • We have numerically studied dynamical behaviors of Josephson-junction ladders consisting of [ital N][sub [ital p]] plaquettes, where the 2([ital N][sub [ital p]]+1) superconducting islands are coupled by resistively shunted Josephson junctions with negligible capacitance. When a ladder is subjected to a current of the form [ital I][sub dc]+[ital I][sub ac]sin([omega][ital t]) in the [10] direction the dc [ital I]-[ital V] curve, in the presence of a transverse external magnetic field, becomes a devil's staircase for [ital N][sub [ital p]]=1, and exhibits hysteresis and a transition to chaos for [ital N][sub [ital p]][ge]2. We have identified the symmetric state,'' where themore » phase variables of the junctions satisfy symmetry relations and motion of the system is constrained to the phase space of smaller dimension than the original one. The dynamic behavior of each junction in the ladder depends very sensitively on whether the number of the plaquettes in a ladder is odd or even. However, the averaged dc [ital I]-[ital V] curves of the whole ladders with [ital N][sub [ital p]][ge]3 turn out similar to one another, enabling one to understand the dynamical behavior of a large ladder from that of a three-plaquette ladder.« less