An improved Green's function algorithm applied to quantum transport in carbon nanotubes

TL;DR

This paper presents an improved Green's function algorithm based on the renormalization-decimation method, optimized for large quasi-one-dimensional systems like carbon nanotubes, enabling efficient quantum transport calculations in complex structures.

Contribution

An enhanced RDA algorithm that efficiently handles very long and disordered systems by subdividing the unit cell and reducing computation time, applicable to large-scale quantum transport problems.

Findings

Reduced calculation time for large systems

Effective handling of disordered and defect-laden structures

Successful application to chiral carbon nanotubes

Abstract

The renormalization-decimation algorithm (RDA) of L\'opez Sancho et al. is used in quantum transport theory to calculate bulk and surface Green's functions. We derive an improved version of the RDA for the case of very long quasi one-dimensional unit cells (in transport direction). This covers not only long unit cells but also supercell-like calculations for structures with disorder or defects. In such large systems, short-range interactions lead to sparse real-space Hamiltonian matrices. We show how this and a corresponding subdivision of the unit cell in combination with the decimation technique can be used to reduce the calculation time. Within the resulting algorithm, separate RDA calculations of much smaller effective Hamiltonian matrices must be done for each Green's function, which enables the treatment of systems too large for the common RDA. Finally, we discuss the performance properties of our improved algorithm as well as some exemplary results for chiral carbon nanotubes.