Path integral quantum Monte Carlo simulation of a parabolic quantum dot

In this paper we present a numerical simulation for a two-dimensional parabolic quantum dot (2D-PQD) using path integral Monte Carlo (PIMC). We model a typical GaAs quantum dot (QD) which is centered in a square plane of size ~(5 nm)². We calculate the energy of the quantum dot system in terms of temperature and number of confined electrons, with and without electron-electron interaction. We also calculate QD energy and electron density for the QD confining up to 20 electrons. Moreover, we describe the effect of electron-electron interaction and confining potential on electron distribution. We also compare electron density in both weak and strong interaction regimes. Then, we investigate shell-filling and formation of Wigner molecule structure in strong interaction regime. Finally, we study the effect of external magnetic field on QD energy and electron density. We demonstrate the compression of Wigner molecule and shell combination under applied magnetic field.