# Instability of a lattice semifluxon in a current-biased 0-π array of Josephson junctions

11 Citations (Scopus)

### Abstract

We consider a one-dimensional parallel biased array of small Josephson junctions with a discontinuity point characterized by a phase jump of $\pi$ in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the discontinuity point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases $2\pi$ fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.
Original language Undefined 092507 4 Physical Review B (Condensed Matter and Materials Physics) 69 9 https://doi.org/10.1103/PhysRevB.69.092507 Published - 2004

### Keywords

• calculation
• molecular physics
• EWI-13976
• Mathematical analysis
• IR-47553
• METIS-218130

### Cite this

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title = "Instability of a lattice semifluxon in a current-biased 0-π array of Josephson junctions",
abstract = "We consider a one-dimensional parallel biased array of small Josephson junctions with a discontinuity point characterized by a phase jump of $\pi$ in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the discontinuity point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases $2\pi$ fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.",
keywords = "calculation, molecular physics, EWI-13976, Mathematical analysis, IR-47553, METIS-218130",
author = "H. Susanto and {van Gils}, {Stephanus A.}",
year = "2004",
doi = "10.1103/PhysRevB.69.092507",
language = "Undefined",
volume = "69",
pages = "092507",
journal = "Physical review B: Covering condensed matter and materials physics",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "9",

}

In: Physical Review B (Condensed Matter and Materials Physics), Vol. 69, No. 9, 2004, p. 092507.

TY - JOUR

T1 - Instability of a lattice semifluxon in a current-biased 0-π array of Josephson junctions

AU - Susanto, H.

AU - van Gils, Stephanus A.

PY - 2004

Y1 - 2004

N2 - We consider a one-dimensional parallel biased array of small Josephson junctions with a discontinuity point characterized by a phase jump of $\pi$ in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the discontinuity point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases $2\pi$ fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.

AB - We consider a one-dimensional parallel biased array of small Josephson junctions with a discontinuity point characterized by a phase jump of $\pi$ in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the discontinuity point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases $2\pi$ fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.

KW - calculation

KW - molecular physics

KW - EWI-13976

KW - Mathematical analysis

KW - IR-47553

KW - METIS-218130

U2 - 10.1103/PhysRevB.69.092507

DO - 10.1103/PhysRevB.69.092507

M3 - Article

VL - 69

SP - 092507

JO - Physical review B: Covering condensed matter and materials physics

JF - Physical review B: Covering condensed matter and materials physics

SN - 2469-9950

IS - 9

ER -