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There has been an increasing interest in the fundamental physical properties of strain-induced nano-architectures [1] possessing non-trivial topology [2]. In the present talk, interplay of topological and geometrical effects is theoretically discussed for a special class of three-dimensional (3D) semiconductor Möbius nanorings including an inhomogeneous twist. For those systems, the Laplace-Beltrami operator is derived taking into consideration the effective inhomogeneity of the space metric. A resulting change of the kinetic energy of an electron in a 3D Möbius ring is demonstrated to constitute ~ 0.001 to 0.01 of the electron energy in a conventional ring rolled up from the same semiconductor film. An interplay between the electron energy reduction (because it avoids the region of a high kinetic energy) and the energy rise (due to the size quantization in the untwisted region) leads to a continuous transition of the electron ground state from delocalized, when the untwisted region is small in comparison with the circumference of the ring, to effectively localized, when the untwisted region becomes sufficiently large. A clear manifestation of this transition is provided by the Aharonov-Bohm effect in a 3D Möbius ring. This effect is estimated to be detectable through observation of persistent currents as a function of the magnetic flux threading inhomogeneous Möbius rings.
Acknowledgement I gratefully acknowledge fruitful creative interactions with O. G. Schmidt. References [1] O. G. Schmidt and K. Eberl, Nature 410, 168 (2001). [2] S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, and N. Hatakenaka, Nature 417, 397 (2002). |
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