Physics of Quantum Rings by Vladimir M. Fomin

Author:Vladimir M. Fomin
Language: eng
Format: epub, pdf
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(9.48)

where a 0 is a “cutoff” radius. For a 3D exciton in a strong magnetic field this radius a 0 equals the magnetic length a H . In our case a 0 is obviously related to the size (width or thickness) of the ring.

Besides the ground state, a 1D exciton has the hydrogen series of energy levels E n =−μe 4/2ε 2 ħ 2 n 2, n=1,2,3,…. All these levels form (approximately!) the set of allowed values for the eigenvalue w in (9.45) provided that the effective Bohr radius a B =εħ 2/e 2 μ is much smaller than the distance 2πa to the next well in the Coulomb energy U c . For the QRs reported up till now the condition a B ≪a is very well satisfied, and we may solve (9.45) in the tight-binding approximation.

Any solution of the type (9.46) corresponds to the energy

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