Boundary layer model for vortex fingers in type-II superconductors

Abstract

Propagating fingerlike patterns in type-II superconductors are studied through a boundary layer model that takes into account the coupling with the temperature of the sample. By formulating an approach based on an interfacial description for a domain of vortices, we determine the shape-preserving fronts and study the properties and scale of the patterns, such as the fingers' shape and width. We show that the formation and the characteristics of these instabilities are strictly related to the local overheating of the material and depend on the substrate temperature, in agreement with the experiments and suggestions from linear stability calculations. The dynamics of vortices in type-II superconductors exhibits a wide variety of instabilities of thermomagnetic origin.1 Beyond phenomena such as avalanches and flux jumps, recent experiments have revealed interesting out-ofequilibrium patterns involving the formation of ramified dendritic or finger-shaped domains of vortices in Nb and MgB 2 thin films and dropletlike patterns in NbSe 2 single crystals. [2][3][4][5][6] It is generally accepted that the nonuniform penetration of the magnetic flux is a thermomagnetic effect due to the local overheating produced by the dissipative motion of vortices. As a consequence of the increased local temperature, the pinning barrier is lowered, leading to a large-scale flux invasion and to a final nonuniform magnetic flux distribution. 7The thermomagnetic nature of the instability underlying the evolution of a flat front between the vortex and the superconducting states into narrow fingers and dendrites has been proposed in some recent theoretical models, [8][9][10] augmented by numerical simulations and linear stability analysis. However, the shapes of the fingers, their remarkably well-defined widths between 20 and 50 m, and their dependence on the substrate temperature were not obtained explicitly in this earlier work. In this paper we concentrate particularly on these finger-type growth forms and propose that they are self-organized propagating shapes with a relatively high temperature and mobility at the tip and a low temperature and mobility on the sides.A detailed analysis for the shape of the fingers requires a more tractable mathematical model than the ones proposed previously. In particular, the formulation of an interfacial description for the vortex front is an effective and simple method to study the problem in its essential features. Local growth models have proven to be a useful tool to analyze front propagation in other physical systems, such as dendrites in crystal growth, and also magnetic flux penetration in type-I superconductors.11-14 The sharp interface limit is appropriate when the vortex density and temperature change rapidly in a layer whose thickness is thin in comparison to the radius of the curvature of the front.In the case of a type-II superconductor, the coarse-grained density of vortices can be represented by a continuous field that decays near the interface with the vortex-free superconducting state...

Dendritic and uniform flux jumps in superconducting films

“…The last prediction has also been obtained in the boundary layer model allowing calculation of the exact finger shape. 30 The first and the second predictions have already been confirmed experimentally. 10,12 As for the last one, the T dependence of the finger width has not yet been studied.…”

Onset of Dendritic Flux Avalanches in Superconducting Films

“…However, why such avalanches should develop into dendritic patterns is a topic under vivid discussion, and several competing theories were recently proposed. They include a stability analysis taking into account the complicating non-local electrodynamics of thin film superconductors [18,19], a boundary layer model assuming shape-preserving fronts [20], and a shock wave approach [21], all leading to substantially different predictions. In this work we report on the first experi- In the sum image the grey tone regions are those of repeated behavior, whereas colors show where there is no or only partial overlap.…”

Intrinsic thermoelectric power of group VB metals

“…10 Like other members, niobium having bcc structure (a=0.3300 nm) with space group Im-3m and jungle-gym type of Fermi surface (FS) has been proven to be an interesting transition metal (TM) for its superconducting and electrical properties. [12][13][14][15][16][17][18][19][20][21] However, its thermoelectric power (S) is relatively poorly understood. 12,13,15,22 Carter et al 13 reported S =0 below its T c and large value of 30 μV/K near 70K.…”