Tag Archives: Alejandro A. Pacheco Sanjuan

The geometry of graphene at the University of Arkansas (US)

The University of Arkansas (US) has announced the development of a new mathematical framework useful for studying graphene according to a May 5, 2014 news item on Nanowerk,

Scientists studying graphene’s properties are using a new mathematical framework to make extremely accurate characterizations of the two-dimensional material’s shape.

“The properties of two-dimensional materials depend on shape,” said Salvador Barraza-Lopez, an assistant professor of physics at the University of Arkansas. “And this mathematical framework allows you to make extremely accurate characterizations of shape. This framework is a novel tool to understand shape in materials that behave as atom-thin membranes.”

A May 5, 2014 University of Arkansas news release, which originated the news item, provides more details,

The mathematical framework being used is known as discrete differential geometry, which is the geometry of two-dimensional interlaced structures called meshes. When the nodes of the structure, or mesh points, correspond with atomic positions, discrete differential geometry provides direct information on the potential chemistry and on the electronic properties of two-dimensional materials, Barraza-Lopez said.

The application of discrete differential geometry to understand two-dimensional materials is an original interdisciplinary development, he said.

“Since two-dimensional materials can be easily visualized as meshes, we asked ourselves how these theories would look if you express them directly in terms of the positions of the atoms, bypassing entirely the common continuum approximation,” Barraza-Lopez said. …

Two papers have been produced about this work,

Quantitative Chemistry and the Discrete Geometry of Conformal Atom-Thin Crystals by Alejandro A. Pacheco Sanjuan, Mehrshad Mehboudi, Edmund O. Harriss, Humberto Terrones, and Salvador Barraza-Lopez. ACS Nano, 2014, 8 (2), pp 1136–1146 DOI: 10.1021/nn406532z Publication Date (Web): January 8, 2014

Copyright © 2014 American Chemical Society

Graphene’s morphology and electronic properties from discrete differential geometry by Alejandro A. Pacheco Sanjuan, Zhengfei Wang, Hamed Pour Imani, Mihajlo Vanević, and Salvador Barraza-Lopez. Phys. Rev. B 89, 121403(R) – Published 6 March 2014 DOI: http://dx.doi.org/10.1103/PhysRevB.89.121403

©2014 American Physical Society

Both papers are behind paywalls.