Discrete differential geometry and the properties of conformal two-dimensional materials
Abstract
Two-dimensional materials were first isolated no longer than ten years ago, and a comprehensive understanding of their properties under non-planar shapes is still being developed. Strictly speaking, the theoretical study of the properties of graphene and other two-dimensional materials is the most complete for planar structures and for structures with small deformations from planarity. The opposite limit of large deformations is yet to be studied comprehensively but that limit is extremely relevant because it determines material properties near the point of failure. We are exploring uses for discrete differential geometry within the context of graphene and other two-dimensional materials, and these concepts appear promising in linking materials properties to shape regardless of how large a given material deformation is. A brief account of additional contributions arising from our group to two-dimensional materials that include graphene, stanene and phosphorene is provided towards the end of this manuscript.
Keywords
Cite
@article{arxiv.1506.03534,
title = {Discrete differential geometry and the properties of conformal two-dimensional materials},
author = {Salvador Barraza-Lopez},
journal= {arXiv preprint arXiv:1506.03534},
year = {2015}
}
Comments
Submitted on December 30, 2014 as an invited contribution to an upcoming issue on Advances in Graphene Science and Engineering. Editors: Jeanie Lau (UC-Riverside), Roland Kawakami (Ohio State) and Arthur Epstein (Ohio State). Accepted version of the manuscript, with small changes with respect to the previously posted one