Investigation of Classical Bohr-Sommerfeld Quantization on Cylindrical Surfaces Under High Magnetic Fields
In this work, the edge state energies of the two dimensional electron system ,which is subjected to a high perpendicular magnetic field, is investigated in the presence of the certain boundary conditions within semiclassical approximation. The eigenvalues of the energy of the system which is equivalent to one dimensional harmonic problem is related to Maslov index. Same problem is calculated semi-analytical and semi-numerical for a cylindrical surface. The formation condition of the incompressible strips are investigated for both quantum point concats and quantum Hall bar which is defined on a cylindrical surface by numerical modeling. The width and the location of the incompressible strips are obtained for a spinless particle called Landau levels and a spin particle called Zeeman gap. The observation conditions of Aharonov-Bohm phase are predicted at the value of the magnetic field where the incompressible strips are formed as a closed loop.
