Coulombically Interacting Electrons in a One-dimensional Quantum Dot

TL;DR

This paper investigates the spectral properties and excitations of up to four Coulombically interacting electrons in a finite one-dimensional quantum dot, revealing insights into their ground state, excitations, and charge distributions.

Contribution

It provides a numerical analysis of few-electron systems in a 1D quantum dot, highlighting limitations of capacitance models and explaining excitation modes.

Findings

Ground state energy varies with electron number and system length

Lowest excitations are vibrational and tunneling modes

Limits of dilute and dense electron arrangements are discussed

Abstract

The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.