Quantum Dot-Ring Nanostructure - A Comparison Of Different Approaches

It has been shown recently that a nanostructure composed of a quantum dot (QD) surrounded by a quantum ring (QR) possesses a set of very unique characteristics that make it a good candidate for future nanoelectronic devices. Its main advantage is the ability to easily tune transport properties on demand by so-called "wavefunction engineering". In practice, the distribution of the electron wavefunction in the nanostructure can be controlled by, e.g., electrical gating. In order to predict some particular properties of the system, one has to know the exact wavefunctions for different shapes of the confining potential that defines the structure.In this paper, we compare three different methods that can be used to determine the energy spectrum, electron wavefunctions and transport properties of the system under investigation. In the first approach, we utilize the cylindrical symmetry of the confining potential and solve only the radial part of the Schrodinger equation; in the second approach, we discretize the Schrodinger equation in two dimensions and find the eigenstates with the help of the Lanczos method; in the third approach, we use package Kwant to solve a tight-binding approximation of the original system. To study the transport properties in all these approaches, we calculate microscopically the strength of the coupling between the nanosystem and leads. In the first two approaches, we use the Bardeen method, in the third one calculations are performed with the help of package Kwant.