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Updated: Sep 13, 2026

Resonance Fluorescence of an InGaAs Quantum Dot in a Planar Cavity Using Orthogonal Excitation and Detection
Published on: October 13, 2017
Electronic Energy Levels in Quantum Dots with Weakly Modulated Spherical-Harmonic Surfaces
Roman Leshko1, Olha Leshko2, Taras Monastyrskyi1
1Department of Physics and Information Systems, Drohobych Ivan Franko State Pedagogical University, Stryiska Str, Drohobych, Lviv Region, 82100, Ukraine.
Abstract:
The precise control of quantum dot (QD) geometry is crucial for tailoring their optoelectronic properties, yet an exact analytical description of non-spherical nanoparticles remains mathematically challenging. In this work, we present a comprehensive theoretical framework to calculate the electronic energy spectra of QDs with arbitrary weakly modulated spherical-harmonic surfaces. Utilizing the perturbation theory up to the second order, we derive analytical expressions for the energy corrections. The important feature of our approach is the explicit incorporation of Wigner 3j-symbols, which establishes selection rules based on the spatial and axial symmetries of the surface corrugations. The model is validated through numerical calculations for a GaAs QD under various geometric configurations, including spheroidal, pear-shaped, and multi-harmonic shapes. The proposed analytical tool offers deep physical insights into the quantum confinement effect in realistically corrugated nanocrystals, providing a computationally efficient platform for the shape-engineering of semiconductor nanomaterials.
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