Flux noise in high-temperature superconductors

Spontaneously created vortex-antivortex pairs are the predominant source of flux noise in high-temperature superconductors. In principle, flux noise measurements allow to check theoretical predictions for both the distribution of vortex-pair sizes and for the vortex diffusivity. In this paper the flux-noise power spectrum is calculated for the highly anisotropic high-temperature superconductor ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$, both for bulk crystals and for ultrathin films. The spectrum is basically given by the Fourier transform of the temporal magnetic-field correlation function. We start from a Berezinskii-Kosterlitz-Thouless-type theory and incorporate vortex diffusion, intrapair vortex interaction, and annihilation of pairs by means of a Fokker-Planck equation to determine the noise spectrum below and above the superconducting transition temperature. We find white noise at low frequencies ω and a spectrum proportional to 1/${\mathrm{\omega }}^{3\mathrm{/}2}$ at high frequencies. The crossover frequency between these regimes strongly depends on temperature. The results are compared with earlier results of computer simulations.