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We analyze theoretically the electron energy spectrum and the magnetization of an electron in a strained ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ self-assembled quantum ring (SAQR) with realistic parameters, determined from the cross-sectional scanning-tunneling microscopy characterization of that nanostructure. The SAQRs have an asymmetric indium-rich craterlike shape with a depression rather than an opening at the center. Although the real SAQR shape differs strongly from an idealized circular-symmetric open ring structure, the Aharonov-Bohm oscillations of the magnetization survive.

physical review b

Theory of electron energy spectrum and Aharonov-Bohm effect in self-assembled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">In</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Ga</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">As</mml:mi></mml:mrow></mml:math>quantum rings in GaAs

Theory of electron energy spectrum and Aharonov-Bohm effect in self-assembledInxGa1−xAsquantum rings in GaAs