An $O(N)$ $Abinitio$ Calculation Scheme for Large-Scale Moiré Structures

Abstract

We present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for ground state is performed with $O(N)$ Krylov subspace method implemented in OpenMX. Secondly, the crystal momentum dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures at the first magic angle ($\theta =1.08^{\circ }$) and other three larger ones with satisfied accuracy on affordable costs. The band structures are in good agreement with those from tight binding models, continuum models, plane-wave pseudo-potential based $abinitio$ calculations, and the experimental observations. This efficient two-step method is to play a crucial role in other twisted two-dimensional materials, where the band structures are much more complex than graphene and the effective model is hard to be constructed.

References in corpus (5)

• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta \sim 1.08^{\circ }$
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2
• Multifaceted moiré superlattice physics in twisted WSe${}_2$ bilayers

Cited by in corpus (5)

• Truncated atomic plane wave method for the subband structure calculations of Moiré systems
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions