B(H) constitutive relations near Hc1 in disordered superconductors

Abstract

We provide a self-contained account of the B vs. H constitutive relation near H c1 in Type II superconductors with various types of quenchedvalid in the absence of disorder and thermal fluctuations, changes significantly in the presence of disorder. Moreover, the constitutive relations will depend strongly on the type of disorder. In the presence of point disorder, B ∼ (H − H c1 ) 3/2 in three-dimensional (thick) superconductors, as shown by Nattermann and Lipowsky. In two-dimensional (thin film) superconductors with point disorder, B ∼ (H − H c1 ). In the presence of parallel columnar disorder, we find that B ∼ exp[−C 3 /(H − H c1 )] in three dimensions, whileIn the presence of nearly isotropically splayed disorder, we find that B ∼ (H − H c1 ) 3/2 in both two and three dimensions.

Vortex wandering among splayed columnar defects

“…It affects, e.g., the constitutive relation B(H) just above the H c1 -line, where a balance between magnetic field, pinning energy, and repulsive interactions gives B ∼ (H − H c1 ) β , with β = dζ/(1−ω). 11,7 This relation was recently measured in experiments in a (1+1) dimensional geometry for samples with point disorder, 12 confirming the prediction β = 1. Furthermore, the non-linear current-voltage (IV) characteristics at low temperatures and currents is determined by the depinning of single flux lines from the defects.…”

“…6 The properties of individual flux lines in such disordered environments are just beginning to be investigated. 7 In this paper we focus on the scaling properties of a single flux line in a sample with many randomly tilted columnar defects. We consider the flux line as it enters the superconducting sample on one side at some arbitrary but fixed position (taken to be the origin), and leaves on the opposite.…”

“…While the single vortex pinning from point disorder and parallel columnar defects has received much attention, the case with splayed columnar disorder has only been addressed quite recently, 7 and only for the special case of a "nearly" isotropic distribution of splay angles. There it was argued that, for very wide angle distributions, the problem would reduce to a flux line in a disorder landscape with long range spatial transverse correlations but no correlations along the magnetic field.…”

Influence of spatial variations in the lower critical field on the equilibrium field penetration into superconductors

“…For the case ӷ 1, the best fit is obtained when the value of the numerical parameter ␣ is in the range of 2-3. 38 Although B͑H͒ in the irradiated and pristine materials are in general different, 25,39 we shall show below that our main experimental findings can be understood within the simplest approximation: the induction curves of the pristine and irradiated material exhibit the same B͑H͒ forms that differ only in their lower critical field values H c1 pr and H c1 cd in Eq. ͑4͒.…”

“…The introduction of CDs is expected to decrease the free energy of a vortex line [18][19][20][21] and consequently to reduce H c1 . [22][23][24][25] CDs are very effective in pinning vortices when oriented along the field direction and are usually used to enhance pinning and critical currents. [26][27][28][29] Here, however, we use the CDs for the purpose of reducing H c1 .…”