### Abstract

In a layered high-T
_{c} superconductor an Abrikosov vortex line perpendicular to the layers can be considered as a stack of coupled two-dimensional 'pancake' vortices (2DV) with cores residing inside the superconducting layers. When the in-plane penetration length λ
_{ab}EQλ is smaller than the Josephson length λ
_{J}=λ
_{c}d/(d: layer period) the interaction between 2DV is via a magnetic pair force which is complicated but exactly known. We calculate linear and nonlinear ac responses for this model including randomly distributed pinning centers. In detail, the thermally averaged shift S
_{n}(t) of a 2DV inlayer n under the influence of a finite external ac current in the frequency range up to 1 GHz is computed from coupled Fokker-Planck equations for the distribution functions of 2DV positions. In the adiabatic approximation, the Fokker-Planck equations can be cast into a nonlinear differential equation for a continuous shift function S(z, t) using a gradient expansion. The constitutive equation for S(z,t) is solved perturbatively for the linear ac response and for the mixing current at frequency 2ω-1$/-ω-2$/ from two external currents at frequencies ω-1$/ and ω-2$/ ≈2ω-1$/ due to a third order process. This pseudo-harmonic mixing probes the nonlinearity of the intervortex force and its interplay with pinning. Explicit results for the film geometry are given for the surface impedance Z
_{3} and the mixing current amplitude δ
_{j}
^{(3)} as functions of external frequencies, crossover frequency ω-1$/ ∝ n
_{i}dω-D$/ (measuring the pinning), and diffusion frequency W
_{D} of free 2DV.

Original language | English |
---|---|

Title of host publication | Journal De Physique. IV : JP |

Publisher | Publ by Editions de Physique |

Pages | 79-82 |

Number of pages | 4 |

Volume | 3 |

Edition | 2 |

Publication status | Published - Jul 1993 |

Event | Proceedings of the International Workshop on Electronic Crystals (ECRYS 93) - Carry-le-Rouet, Fr Duration: 2 Jun 1993 → 4 Jun 1993 |

### Other

Other | Proceedings of the International Workshop on Electronic Crystals (ECRYS 93) |
---|---|

City | Carry-le-Rouet, Fr |

Period | 2.6.93 → 4.6.93 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal De Physique. IV : JP*(2 ed., Vol. 3, pp. 79-82). Publ by Editions de Physique.

**AC response of Abrikosov vortices in layered superconductors.** / Artemenko, S. N.; Kramer, C.; Wonneberger, W.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Journal De Physique. IV : JP.*2 edn, vol. 3, Publ by Editions de Physique, pp. 79-82, Proceedings of the International Workshop on Electronic Crystals (ECRYS 93), Carry-le-Rouet, Fr, 2.6.93.

}

TY - CHAP

T1 - AC response of Abrikosov vortices in layered superconductors

AU - Artemenko, S. N.

AU - Kramer, C.

AU - Wonneberger, W.

PY - 1993/7

Y1 - 1993/7

N2 - In a layered high-T c superconductor an Abrikosov vortex line perpendicular to the layers can be considered as a stack of coupled two-dimensional 'pancake' vortices (2DV) with cores residing inside the superconducting layers. When the in-plane penetration length λ abEQλ is smaller than the Josephson length λ J=λ cd/(d: layer period) the interaction between 2DV is via a magnetic pair force which is complicated but exactly known. We calculate linear and nonlinear ac responses for this model including randomly distributed pinning centers. In detail, the thermally averaged shift S n(t) of a 2DV inlayer n under the influence of a finite external ac current in the frequency range up to 1 GHz is computed from coupled Fokker-Planck equations for the distribution functions of 2DV positions. In the adiabatic approximation, the Fokker-Planck equations can be cast into a nonlinear differential equation for a continuous shift function S(z, t) using a gradient expansion. The constitutive equation for S(z,t) is solved perturbatively for the linear ac response and for the mixing current at frequency 2ω-1$/-ω-2$/ from two external currents at frequencies ω-1$/ and ω-2$/ ≈2ω-1$/ due to a third order process. This pseudo-harmonic mixing probes the nonlinearity of the intervortex force and its interplay with pinning. Explicit results for the film geometry are given for the surface impedance Z 3 and the mixing current amplitude δ j (3) as functions of external frequencies, crossover frequency ω-1$/ ∝ n idω-D$/ (measuring the pinning), and diffusion frequency W D of free 2DV.

AB - In a layered high-T c superconductor an Abrikosov vortex line perpendicular to the layers can be considered as a stack of coupled two-dimensional 'pancake' vortices (2DV) with cores residing inside the superconducting layers. When the in-plane penetration length λ abEQλ is smaller than the Josephson length λ J=λ cd/(d: layer period) the interaction between 2DV is via a magnetic pair force which is complicated but exactly known. We calculate linear and nonlinear ac responses for this model including randomly distributed pinning centers. In detail, the thermally averaged shift S n(t) of a 2DV inlayer n under the influence of a finite external ac current in the frequency range up to 1 GHz is computed from coupled Fokker-Planck equations for the distribution functions of 2DV positions. In the adiabatic approximation, the Fokker-Planck equations can be cast into a nonlinear differential equation for a continuous shift function S(z, t) using a gradient expansion. The constitutive equation for S(z,t) is solved perturbatively for the linear ac response and for the mixing current at frequency 2ω-1$/-ω-2$/ from two external currents at frequencies ω-1$/ and ω-2$/ ≈2ω-1$/ due to a third order process. This pseudo-harmonic mixing probes the nonlinearity of the intervortex force and its interplay with pinning. Explicit results for the film geometry are given for the surface impedance Z 3 and the mixing current amplitude δ j (3) as functions of external frequencies, crossover frequency ω-1$/ ∝ n idω-D$/ (measuring the pinning), and diffusion frequency W D of free 2DV.

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M3 - Chapter

VL - 3

SP - 79

EP - 82

BT - Journal De Physique. IV : JP

PB - Publ by Editions de Physique

ER -