Linear response quantum transport through interacting multi-orbital nanostructures

TL;DR

This paper reviews quantum transport techniques in nanoelectronics, introduces an improved NRG-based method for calculating ac conductance in interacting nanostructures, and derives effective models for low-temperature conductance, demonstrated on complex quantum dot systems.

Contribution

It develops a new numerical scheme for ac conductance calculation and derives analytical low-energy models, enhancing accuracy and physical understanding in quantum transport studies.

Findings

Improved NRG-based method for ac conductance calculation.

Analytical expressions for low-temperature conductance.

Benchmarking on complex quantum dot systems.

Abstract

Nanoelectronics devices, such as quantum dot systems or single-molecule transistors, consist of a quantum nanostructure coupled to a macroscopic external electronic circuit. Thermoelectric transport between source and drain leads is controlled by the quantum dynamics of the lead-coupled nanostructure, through which a current must pass. Strong electron interactions due to quantum confinement on the nanostructure produce nontrivial conductance signatures such as Coulomb blockade and Kondo effects, which become especially pronounced at low temperatures. In this work we first provide a modern review of standard quantum transport techniques, focusing on the linear response regime, and highlight the strengths and limitations of each. In the second part, we develop an improved numerical scheme for calculation of the ac linear electrical conductance through generic interacting nanostructures, based on the numerical renormalization group (NRG) method, and explicitly demonstrate its utility in terms of accuracy and efficiency. In the third part we derive low-energy effective models valid in various commonly-encountered situations, and from them we obtain simple analytical expressions for the low-temperature conductance. This indirect route via effective models, although approximate, allows certain limitations of conventional methodologies to be overcome, and provides physical insights into transport mechanisms. Finally, we apply and compare the various techniques, taking the two-terminal triple quantum dot and the serial multi-level double dot devices as nontrivial benchmark systems.