Projects per year
Abstract
We study a 3D GinzburgLandau model in a halfspace which is expected to capture the key features of surface superconductivity for applied magnetic fields between the second critical field HC2 and the third critical field HC3. For the magnetic field in this regime, it is known from physics that superconductivity should be essentially restricted to a thin layer along the boundary of the sample. This leads to the introduction of a GinzburgLandau model on a halfspace. We prove that the nonlinear GinzburgLandau energy on the halfspace with constant magnetic field is a decreasing function of the angle ν that the magnetic field makes with the boundary. In the case when the magnetic field is tangent to the boundary (ν = 0), we show that the energy is determined to leading order by the minimization of a simplified 1D functional in the direction perpendicular to the boundary. For nonparallel applied fields, we also construct a periodic problem with vortex lattice minimizers reproducing the effective energy, which suggests that the order parameter of the full GinzburgLandau model will exhibit 3 dimensional vortex structure near the surface of the sample.
Original language  English 

Article number  12 
Journal  Mathematical Physics Analysis and Geometry 
Volume  22 
Issue  2 
Number of pages  33 
ISSN  13850172 
DOIs  
Publication status  Published  2019 
Keywords
 3D vortices
 Calculus of variation
 Estimate of eigenvalue
 GinzburgLandau equations
 Magnetic Schrodinger operator
 Partial differential equations
 Superconductivity
 Surface concentration
 Surface superconductivity
Fingerprint
Dive into the research topics of 'Concentration Behavior and Lattice Structure of 3D Surface Superconductivity in the Half Space'. Together they form a unique fingerprint.Projects
 1 Finished

Semiclassical Quantum Mechanics
Fournais, S. (PI), Madsen, P. (Participant), Mikkelsen, S. (Participant), Miqueu, J.P. C. (Participant) & Bley, G. (Participant)
01/07/2015 → 31/12/2020
Project: Research