Electronic States and Light Absorption in a Cylindrical Quantum Dot Having Thin Falciform Cross Section

TL;DR

This paper investigates the energy levels and light absorption properties of a cylindrical quantum dot with a thin falciform cross section, providing analytical solutions and revealing oscillatory behaviors and selection rules.

Contribution

It introduces an analytical model for the energy spectrum and absorption characteristics of a novel quantum dot shape using the adiabatic approximation.

Findings

Energy spectrum derived analytically

Oscillatory dependence of wave function amplitude

Calculated absorption coefficient and edge frequencies

Abstract

Energy level structure and direct light absorption in a cylindrical quantum dot, having thin falciform cross section, are studied within the framework of the adiabatic approximation. An analytical expression for the energy spectrum of the particle is obtained. For the one-dimensional fast subsystem, an oscillatory dependence of the wave function amplitude on the cross section parameters is revealed. For treatment of the slow subsystem, parabolic and modified Poschl-Teller effective potentials are used. It is shown that the low-energy levels of the spectrum are equidistant. In the strong quantization regime, the absorption coefficient and edge frequencies are calculated. Selection rules for the corresponding quantum transitions are obtained.