Abstract
We investigate the mechanical resonance characteristics of semiconductor rolled-up tubes containing a high-mobility two-dimensional electron gas (HM2DEG) by optical and electrical means. The observed mode frequencies are in an excellent agreement with the theoretically calculated frequencies for the ground bending and excited bending and axial modes. The effect of the curvature is to increase the frequencies of the ground bending modes and the axial wave modes, while decreasing the frequencies of the first excited bending modes. We find significant splitting of the bending and twisting modes by the residual stress effects due to axial shear relaxation in $z$-dependent modes. The HM2DEG interacts with the mechanical motion due to Eddy currents and embedded impedances. A prominent asymmetry appears in the vibration amplitude with respect to the direction of the magnetic field. This originates from the broken symmetry of the HM2DEG on the curved surfaces.
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