Intrinsic Rippling Enhances Static Non-Reciprocity in Graphene Metamaterials

TL;DR

This paper reveals that intrinsic out-of-plane ripples in graphene significantly enhance static non-reciprocal mechanical responses in graphene metamaterials, highlighting potential for symmetry-breaking applications in 2D materials.

Contribution

It demonstrates that intrinsic ripples in graphene can greatly amplify static non-reciprocity, a phenomenon previously underexplored in atomically-thin materials.

Findings

Ripples enable multiple orders of magnitude increase in non-reciprocal response.

Interplay between ripples and stress fields affects displacement transmission.

Graphene metamaterials can be used for symmetry-breaking applications.

Abstract

In mechanical systems, Maxwell-Betti reciprocity means that the displacement at point B in response to a force at point A is the same as the displacement at point A in response to the same force applied at point B. Because the notion of reciprocity is general, fundamental, and is operant for other physical systems like electromagnetics, acoustics, and optics, there is significant interest in understanding systems that are not reciprocal, or exhibit non-reciprocity. However, most studies of non-reciprocity have occurred in bulk-scale structures for dynamic problems involving time reversal symmetry. As a result, little is known about the mechanisms governing static non-reciprocal responses, particularly in atomically-thin two-dimensional materials like graphene. Here, we use classical atomistic simulations to demonstrate that out of plane ripples, which are intrinsic to graphene, enable significant, multiple orders of magnitude enhancements in the statically non-reciprocal response of graphene metamaterials. Specifically, we find that a striking interplay between the ripples and the stress fields that are induced in the metamaterials due to their geometry impact the displacements that are transmitted by the metamaterial, thus leading to a significantly enhanced static non-reciprocal response. This study thus demonstrates the potential of two-dimensional mechanical metamaterials for symmetry-breaking applications.