# The Distribution of Superconductivity Near a Magnetic Barrier

@article{Assaad2019TheDO, title={The Distribution of Superconductivity Near a Magnetic Barrier}, author={W. Assaad and Ayman Kachmar and Mikael Persson-Sundqvist}, journal={Communications in Mathematical Physics}, year={2019}, volume={366}, pages={269-332} }

We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In the regime of large Ginzburg–Landau parameter and strong magnetic field, we study the concentration of the minimizing configurations along this discontinuity by computing the energy of the minimizers and their weak limit in the sense of distributions.

## 17 Citations

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## References

SHOWING 1-10 OF 58 REFERENCES

SUPERCONDUCTIVITY IN DOMAINS WITH CORNERS

- Physics
- 2007

We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the…

Effects of Boundary Curvature on Surface Superconductivity

- Physics
- 2015

We investigate, within 2D Ginzburg-Landau theory, the ground state of a type-II superconducting cylinder in a parallel magnetic field varying between the second and third critical values. In this…

The influence of magnetic steps on bulk superconductivity

- Physics
- 2015

We study the distribution of bulk superconductivity in presence of an applied magnetic field, supposed to be a step function, modeled by the Ginzburg-Landau theory. Our results are valid for the…

Decay of superconductivity away from the magnetic zero set

- Physics
- 2016

We establish exponential bounds on the Ginzburg–Landau order parameter away from the curve where the applied magnetic field vanishes. In the units used in this paper, the estimates are valid when the…

The distribution of 3D superconductivity near the second critical field

- Physics, Mathematics
- 2015

We study the minimizers of the Ginzburg–Landau energy functional with a uniform magnetic field in a three dimensional bounded domain. The functional depends on two positive parameters, the…

Surface Superconductivity in Presence of Corners

- Physics, Mathematics
- 2016

We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the…

The Ginzburg–Landau Functional with Vanishing Magnetic Field

- Physics, Mathematics
- 2014

We study the infimum of the Ginzburg–Landau functional in a two dimensional simply connected domain and with an external magnetic field allowed to vanish along a smooth curve. We obtain energy…

On the Ginzburg–Landau Functional in the Surface Superconductivity Regime

- Physics, Mathematics
- 2014

We present new estimates on the two-dimensional Ginzburg–Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime,…

Energy and vorticity of the Ginzburg-Landau model with variable magnetic field

- Physics, MathematicsAsymptot. Anal.
- 2015

An accurate asymptotic formula is determined for the minimize energy of the Ginzburg-Landau functional and it is shown that the energy minimizers have vortices.