Two-dimensional electron system on a curved surface with a constant radius

Abstract

Two topics of two-dimensional electron systems on a curved surface with a constant radius are studied in this dissertation: the binding energies and impurity states of a single donor and the oscillator strength property in the system in the presence of an electric field. For both, we solve the Schrödinger equation for energy levels and eigenfunctions by using a finite difference approach within the scope of the effective-mass approximation. Then those results are brought to calculate the binding energies and the oscillator strength. The impacts of donor positions, curvature, and system size on the binding energies are discussed. We observe that when the radius of such a system is less than the effective Bohr radius, the binding energy increase considerably. Additionally, by changing the direction of an external electric field, it is possible to efficiently manipulate the values of a donor's binding energies at certain places. The effect of tilt angles can enhance the oscillator strength along the x-direction, and the electric field on the -x-direction considerably upgrades the oscillator strength along the y-direction, especially when the curvature is numerous.

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