Generalized multi-terminal decoherent transport: Recursive algorithms and applications to SASER and giant magnetoresistance

TL;DR

This paper extends the D'Amato-Pastawski model to multi-terminal decoherent transport, introduces recursive algorithms for Green's function evaluation, and applies these methods to SASER and giant magnetoresistance problems.

Contribution

It provides a matrix formulation and recursive algorithms for multi-terminal decoherent transport, enabling advanced analysis of nanodevices beyond previous two-terminal models.

Findings

Decoherence effects in SASER models analyzed.

Classical limit of GMR derived from spin-dependent Hamiltonian.

Recursive algorithms efficiently compute transport properties.

Abstract

Decoherent transport in mesoscopic and nanoscopic systems can be formulated in terms of the D'Amato-Pastawski (DP) model. This generalizes the Landauer-B\"{u}ttiker picture by considering a distribution of local decoherent processes. However, its generalization for multi-terminal setups is lacking. We first review the original two-terminal DP model for decoherent transport. Then, we extend it to a matrix formulation capable of dealing with multi-terminal problems. We also introduce recursive algorithms to evaluate the Green's functions for general banded Hamiltonians as well as local density of states, effective conductances and voltage profiles. We finally illustrate the method by analyzing two problems of current relevance. 1) Assessing the role of decoherence in a model for phonon lasers (SASER). 2) Obtaining the classical limit of Giant Magnetoresistance from a spin-dependent Hamiltonian. The presented methods should pave the way for computationally demanding calculations of transport through nanodevices, bridging the gap between fully coherent quantum schemes and semiclassical ones.