Upper Critical Field of a Percolating Superconductor

Percolation and Superconductivity

“…Our understanding of these materials is based upon the distinction between the homogeneous and the inhomogeneous limit, as first introduced by Deutscher et al 37 The boundary between the two regimes is defined by the condition ~s = ~P' where ~s is the effective superconducting coherence length of the medium, and not the superconducting coherence length of the pure superconductor:-As explained by de Gennes in this volume, the erroneous condition ~s = ~p leads to incorrect theoretical results.…”

“…Hcz(T) still has a linear variation near Tc , but the slope dHcz/dT varies more slowly with Pn. 37 The critical field anisotropy decreases with Pn'…”

Spin-Glass State of a Randomly Diluted Granular Superconductor

“…Here, b is a positive constant which depends on the bond occupation probability p. Magnetic field fluctuations can be included in this model by the addition of the magnetic energy term and an integration over A a (x): (7) where g = {iir^k^T)' 1 and jx 0 is the bare magnetic permeability of the composite. We will refer to the models with and without electromagnetic fluctuations as model I and model II.…”

“…The presence of the field A suppresses order in those modes for which S k^0 so that at the glass transition p s vanishes. In the weakfield limit {A -* 0), the implicit dependence of i// k on A may be neglected and it may be shown 5 that the divergence of X as p -• p c is governed by the conductivity exponent: X~2(p -p c ) 1 . This equation implies that k 2 /^-\p-p c \ (~t~2v) is always large near threshold 1 * for d ^ 3 0 = 3 and y = j in mean-field theory and / = 1.85 and i/ = 0.85 in 3d).…”

“…Such systems have received considerable theoretical 1 " 5 and experimental attention. 1,6 Recent numerical studies have suggested that disordered systems in the presence of a sufficiently strong magnetic field may freeze into a state in which the condensate wave function exhibits spin-glass-type order among the superconducting grains. 5 In this Letter, we examine the properties of a randomly diluted granular superconductor near percolation in the low-temperature limit, and discuss the conditions under which a transition to a thermodynamic state of spin-glass superconducting order may occur.…”