8 - Variational calculations in two dimensions: quantum dots

Summary

Introduction

Two-dimensional few-electron systems have been the focus of extensive theoretical and experimental investigation. Recent advances in nanofabrication techniques have enabled experiments with 2D quantum dots having highly controlled parameters such as electron number, size, shape, confinement strength, and magnetic field. The possibility of fabricating these “artificial atoms” with tunable properties is a fascinating new development in nanotechnology. The principal motivations for these investigations are the variety of possible applications in quantum computing [298], spintronics [261], information storage [199], and nanoelectronics [15, 159, 315].

Theoretical calculations of quantum dot systems are based on the effective mass approximation [42, 131, 130, 350, 205, 101, 233, 356, 184, 139, 35, 127]. In these models the electrons move in an external confining potential and interact via the Coulomb interaction. The apparent similarity of “natural” atoms and quantum dots have motivated the application of sophisticated theoretical methods borrowed from atomic physics and quantum chemistry to calculate the properties of quantum dots. Parabolically confined 2D quantum dots have been studied by several different well-established methods: exact diagonalization techniques [131, 205], Hartree–Fock approximations [101, 233, 356], and density functional approaches [184, 139]. Quantum Monte Carlo (QMC) techniques have also been used for 2D [35, 127, 255, 85] as well as 3D structures. The strongly correlated low-electronicdensity regime has received much attention owing to the intriguing possibility of the formation of Wigner molecules [356, 85].