Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene

TL;DR

This paper introduces a hybrid Chebyshev polynomial method combined with complex absorbing potentials to efficiently and accurately compute quantum conductance in large mesoscopic systems, exemplified by twisted bilayer graphene.

Contribution

It develops a novel hybrid approach for quantum conductance calculations that overcomes previous limitations, enabling analysis of very large systems with high accuracy.

Findings

Moiré effects significantly influence conductance in twisted bilayer graphene.

Interlayer scattering and twist-angle disorder are crucial for understanding transport properties.

The method efficiently handles systems with over two million atomic sites.

Abstract

In recent years, Chebyshev polynomial expansions of tight-binding Green's functions have been successfully applied to the study of a wide range of spectral and transport properties of materials. However, the application of the Chebyshev approach to the study of quantum transport properties of noninteracting mesoscopic systems with leads has been hampered by the lack of a suitable Chebyshev expansion of Landaeur's formula or one of its equivalent formulations in terms of Green's functions in Keldysh's perturbation theory. Here, we tackle this issue by means of a hybrid approach that combines the efficiency of Chebyshev expansions with the convenience of complex absorbing potentials to calculate the conductance of two-terminal devices in a computationally expedient and accurate fashion. The versatility of the approach is demonstrated for mesoscopic twisted bilayer graphene (TBG) devices with up to $2.3\times10^6$ atomic sites. Our results highlight the importance of moir\'e effects, interlayer scattering events and twist-angle disorder in determining the conductance curves in devices with a small twist angle near the TBG magic angle $\theta_m \approx 1.1^\circ$.