Electronic Structure of Multiple Dots

TL;DR

This paper investigates the electronic states of multiple quantum dots using spin density functional theory and exact diagonalization, revealing how exchange interactions and magnetic flux influence their ground states and electronic properties.

Contribution

It combines realistic SDFT calculations with exact diagonalization to analyze electron states in double and triple quantum dots, highlighting flux-dependent exchange interactions.

Findings

Transition from singlet to triplet ground state in double dots.

Quasi-periodic fluctuation of exchange interaction J in triple dots with magnetic field.

Electronic structure variations with flux quanta in triple dots.

Abstract

We calculate, via spin density functional theory (SDFT) and exact diagonalization, the eigenstates for electrons in a variety of external potentials, including double and triple dots. The SDFT calculations employ realistic wafer profiles and gate geometries and also serve as the basis for the exact diagonalization calculations. The exchange interaction J between electrons is the difference between singlet and triplet ground state energies and reflects competition between tunneling and the exchange matrix element, both of which result from overlap in the barrier. For double dots, a characteristic transition from singlet ground state to triplet ground state (positive to negative J) is calculated. For the triple dot geometry with 2 electrons we also find the electronic structure with exact diagonalization. For larger electron number (18 and 20) we use only SDFT. In contrast to the double dot case, the triple dot case shows a quasi-periodic fluctuation of J with magnetic field which we attribute to periodic variations of the basis states in response to changing flux quanta threading the triple dot structure.