Improved performance in quantum transport calculations: A divide-and-conquer method based on S-matrices

TL;DR

This paper introduces an exact divide-and-conquer algorithm for calculating scattering matrices in tight-binding structures, significantly improving the efficiency of quantum transport property computations in mesoscopic systems.

Contribution

The paper presents a novel recursive divide-and-conquer method for computing scattering matrices, outperforming existing algorithms in various lattice structures.

Findings

Significant speed-up over previous methods

Effective in square, triangular, and honeycomb lattices

Enables accurate transport calculations in mesoscopic systems

Abstract

We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer formula. The method is exact, and by analyzing the performance of the algorithm in square, triangular and honeycomb lattices, we show a significant improvement in comparison to other state-of-the-art recursive and non-recursive methods.