Collective excitations in Quantum Dot

TL;DR

This paper analytically investigates various collective excitations in finite-electron quantum dots at zero magnetic field, analyzing their energies under different interactions using sum-rule approaches.

Contribution

It introduces an analytical framework for calculating collective excitation energies in quantum dots considering multiple interaction types and excitation modes.

Findings

Analytical expressions for excitation energies derived

Dependence of energies on system size and parameters analyzed

Different interaction types influence excitation spectra distinctively

Abstract

We investigate different types of collective excitations in a quantum dot containing finite number of electrons at zero magnetic field. To estimate the excitation energies analytically we follow the energy weighted sum-rule approach. We consider the most general multipole excitation with angular momentum l, and the breathing mode excitation (monopole excitation) of a large quantum dot, for three different types of effective electron-electron interaction. These are the logarithmic interaction, the short range pseudopotential and the coulomb interaction. The ground state density of the many-body system is calculated within Thomas-Fermi approximation. The analytical results for the collective excitation energies and their dependence on the system size and other external parameters are discussed in detail.