The Ginzburg-Landau (GL) and Schrödinger equations with a nonuniform magnetic flux density (Formula presented) admit a class of internally orthogonal solutions with (Formula presented) the gradient of the logarithm of the order parameter (Formula presented) (wave function magnitude) orthogonal to (Formula presented) the gradient of the gauge invariant phase. Constrained cases with (Formula presented) are minimum energy solutions, referred to as tracking solutions. For the macroscopic GL model virtually all solutions are in the internally orthogonal class. In two dimensions, we find multifluxoid quantum vortex, dot and wall nucleation, and surface tracking solutions for (Formula presented) with (Formula presented) For the microscopic Schrödinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.
|Number of pages||8|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - Jan 1 2000|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics