Enumeration of Moire Patterns of a Hexagonal Twisted Bilayer and Intercalated Transition Metals in Twisted h-BN

TL;DR

This paper classifies moire patterns in twisted hexagonal bilayers using a real-space method and explores how intercalated transition metals influence the energy and magnetic properties of twisted h-BN bilayers.

Contribution

It introduces a classification scheme for moire patterns in twisted hexagonal bilayers and analyzes the effects of intercalated transition metals on their structural and magnetic properties.

Findings

Moire patterns are classified by fundamental transformations involving coprime integers.

The number of lattice coincidence areas is given by (n-m)^2.

Intercalated transition metals favor aligned or anti-aligned configurations with high magnetization.

Abstract

A real-space method using generating integers is used to classify the possible moire patterns for two equal hexagonal lattices. The result is that the rotations that take (n,m) to (m,n) with n,m relatively prime form the fundamental moire transformations, and the number of lattice coincidence areas within each supercell is given by (n-m)^2. The scheme may be extended to cases where the lattice constants differ. Additionally, we consider a system with a transition metal between the layers of a twisted bilayer of h-BN. We find that the lowest energy configurations for such an arrangement are those at aligned and anti-aligned sites of the moire pattern, depending on the transition metal, and the low-symmetry sites possess high magnetization.