Vorticity quantum numbers for confined electrons

The eigenstates of a confined particle in an applied magnetic field are characterized by vorticity quantum numbers, defined in a conventional way as gradient of phase integrals on the contour along the boundary line of the sample. The energy spectrum of the problem can be rationalized in terms of diabatic states corresponding to definite vorticity numbers in the whole range of applied fields. The vorticity number of a given state equals the sum of winding numbers of separate, spatially resolved vortices. The vortex patterns evolution shows some surprising similarities with mesoscopic superconductors.status: publishe