# Accuracy of effective mass equation for a single and double cylindrical quantum dot

## TL;DR

This paper evaluates the accuracy of various effective mass equations in modeling spectral and spin features of single and double cylindrical quantum dots, comparing them to the 8 band k.p model.

## Contribution

It systematically assesses the precision of simplified effective mass equations against a comprehensive 8 band k.p model for quantum dot systems.

## Key findings

- g-factor is accurately reproduced by effective mass equations
- Spectral splitting is less accurately modeled
- Spin-orbit induced spin mixing is poorly approximated

## Abstract

In this contribution we study the accuracy of various forms of electron effective mass equation in reproducing spectral and spin-related features of quantum dot systems. We compare the results of the standard 8 band k.p model to those obtained from effective mass equations obtained by perturbative elimination procedures in various approximations for a cylindrical quantum dot or a system of two such dots. We calculate the splitting of electronic shells, the electron g-factor and spin-orbit induced spin mixing and show that for a cylindrical dot the g-factor is reproduced very exactly, while for the two other quantities the effective mass equation is much less accurate.