An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

TL;DR

This paper introduces an extended plane wave framework that significantly reduces computational costs and improves the accuracy of electronic structure calculations for twisted bilayer 2D materials, especially at small twist angles.

Contribution

The authors develop a novel extended plane wave method with tensor-product basis and cutoff techniques, enabling efficient and accurate electronic structure calculations for twisted bilayer systems.

Findings

Reproduced flat bands in bilayer graphene at magic angle.

Reduced Hamiltonian matrix size by about 100 times.

Framework is more extendable and computationally efficient than traditional models.

Abstract

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle ($\sim 1.05^{\circ}$). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations.