A Transfer Hamiltonian approach in self-consistent field regime for transport in arbitrary quantum dot arrays

TL;DR

This paper introduces a transfer Hamiltonian-based method for modeling electron transport in quantum dot arrays, incorporating interactions and self-consistent potentials, validated against complex models.

Contribution

It presents a scalable, matrix-formulated transfer Hamiltonian approach for self-consistent electron transport in arbitrary quantum dot arrays, enabling analysis of larger systems.

Findings

Successfully reproduces known transport effects

Qualitatively agrees with complex theoretical models

Validates the model across various quantum dot configurations

Abstract

A transport methodology to study the electron transport between quantum dots arrays based in Transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are introduced by transition rates and capacitive couplings. The effects of the local potential are computed within the self-consistent field regime. The model has been developed and expressed in a matrix form in order to make it extendable to larger systems. Transport through several quantum dot configurations have been studied in order to validate the model. Despite the simplicity of the model, well-known effects are satisfactorily reproduced and explained. The results qualitatively agree with other results obtained using more complex theoretical approaches.