Transmission from reverse reaction coordinate mappings

TL;DR

This paper introduces a method to map the transport properties of fermionic chains to a single quantum dot system with structured reservoirs, simplifying calculations and enabling optimization of transmission.

Contribution

It presents a novel mapping technique that relates fermionic chain transport to quantum dot transmission with structured spectral densities, both analytically and numerically.

Findings

Analytical calculation of transmission for short chains.

Optimization of transmission through the mapping.

Numerical demonstration with Su-Schrieffer-Heeger chain.

Abstract

We point out that the transport properties of non-interacting fermionic chains tunnel-coupled to two reservoirs at their ends can be mapped to those of a single quantum dot that is tunnel-coupled to two transformed reservoirs. The parameters of the chain are mapped to additional structure in the spectral densities of the transformed reservoirs. For example, this enables the calculation of the transmission of quantum dot chains by evaluating the known transmission of a single quantum dot together with structured spectral densities. We exemplify this analytically for short chains, which allows to optimize the transmission. In addition, we also demonstrate that the mapping can be performed numerically by computing the transmission of a Su-Schrieffer-Heeger chain.