Fractal vortices in disordered superconductors

Abstract

We measure the low-frequency magnetic response χ = χ′ + iχ″ of halogenated ceramics YBa 2Cu 3O 7−δF x as functions of x, AC field amplitude H 0 and temperature T. The field of first flux penetration displays scaling behaviour: H 1( x, T) = H 1( x, 0) (1 − T/ T c ) ζ , with T c the coherence temperature and ζ = 2.7 ± 0.2; in all cases H 1 ⪢ H c1 expected for the ideal material. A model where deviations from stoichiometry are assumed to result in local critical temperatures T c( r ), is described. Superconductivity is due to regions where T< T c( r ) with concentration p(T). The coherence temperature is defined by p( T c) = p c, the percolation threshold. Critical exponents appear to be related to percolation exponents, in particular ν = 2 ν p/3 β p≅ 1.33, in agreement with the experimental value found in granular superconductors. Expressions are found for the magnetic fields observed in Euclidean space while being due to currents restricted to fractal percolation clusters. The free energy of the resulting fractal vortices accounts for the experimental value of the exponent in the temperature dependence of H 1( T).