# Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects

## TL;DR

This paper presents an improved recursive Green's function method that efficiently handles disordered quasi-one-dimensional systems with realistic defects, significantly reducing computational complexity.

## Contribution

An enhanced RGF algorithm that accelerates calculations in disordered systems by leveraging the renormalization decimation scheme, reducing complexity from system length to defect density.

## Key findings

- Computational complexity scales linearly with defect number.
- Algorithm reduces calculation time for defective carbon nanotubes.
- Memory requirements are optimized for systems with realistic defects.

## Abstract

We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computational complexity scales linearly with the number of defects, instead of linearly with the total system length for the conventional approach. We show that the scaling of the calculation time of the Green's function depends on the defect density of a random test system. Furthermore, we discuss the calculation time and the memory requirement of the whole transport formalism applied to defective carbon nanotubes.