Parity-Dependent Moir\'e Superlattices in Graphene/h-BN Heterostructures: A Route to Mechanomutable Metamaterials

TL;DR

This study reveals how the parity of layers in graphene/h-BN heterostructures influences their superlattice patterns and mechanical properties, enabling the design of mechanically tunable metamaterials.

Contribution

It uncovers the parity-dependent superlattice patterns and mechanical behaviors in graphene/h-BN stacks, providing a new route for designing mechanomutable metamaterials.

Findings

Odd layers produce flamingo-like superlattice patterns.

Even layers exhibit hexagonal or rectangular superlattices.

Superlattice patterns and mechanical properties depend on layer parity.

Abstract

The superlattice of alternating graphene/h-BN few-layered heterostructures is found to exhibit strong dependence on the parity of the number of layers within the stack. Odd-parity systems show a unique flamingo-like pattern, whereas their even-parity counterparts exhibit regular hexagonal or rectangular superlattices. When the alternating stack consists of seven layers or more, the flamingo pattern becomes favorable, regardless of parity. Notably, the out-of-plane corrugation of the system strongly depends on the shape of the superstructure resulting in significant parity dependence of its mechanical properties. The predicted phenomenon originates in an intricate competition between moir\'e patterns developing at the interface of consecutive layers. This mechanism is of general nature and is expected to occur in other alternating stacks of closely matched rigid layered materials as demonstrated for homogeneous alternating junctions of twisted graphene and h-BN. Our findings thus allow for the rational design of mechanomutable metamaterials based on Van der Waals heterostructures.