Electron confinement into ring structures within an external magnetic field

The energy spectrum of an electron confined within a circular ring in the p resence of an external magnetic field (perpendicular to the plane of confin ement) is studied exactly through the solution of the corresponding Schrodi nger equation. The results show that for strong spatial confinement (weak f ields) the degeneracy of the energy spectrum is completely removed, while i n the case of strong magnetic confinement the spectrum shows the infinite-f old degeneracy, typical of Landau states, as expected. In between, in spite that all degeneracy is lifted due to spatial confinement, Landau condensat ion can occur, i.e., the energy levels can be very close to each other. Mor eover, for a given ratio between spatial and magnetic confining lengths, th e magnetic flux can be quantized, while electron's currents appear to flow in the "wrong" direction. The conditions for the quantization of the flux a re established and the possible consequences discussed.