Ripples and Warping of Graphene: A Theoretical Study

By Umesh V. Waghmare

Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur, India

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We use first-principles density functional theory based analysis to understand formation of ripples in graphene and related 2-D materials. For an infinite graphene, we show that ripples are linked with a low energy branch of phonons that exhibits quadratic dispersion at long wave-lengths. Many modes in this branch become unstable as a function of compressive strain and rippling occurs in a way similar to a structural phase transition. We use a simple model to develop understanding of this phenomenon.

At the nanoscale, we find that Stone-Wales (SW) defects play an interesting role. Such defects lead to stresses in a graphene nano-ribbon (GNR) that are relieved through its deformation or reconstruction at the edges. Due to a markedly anisotropic interaction among the SW defects, the resulting localized deformation depends sensitively on the orientation of an SW defect with respective to the edge of the GNR.


Umesh Waghmare Umesh Waghmare received his B. Tech. degree in Engineering Physics in 1990 from the Indian Institute of Technology, Bombay. He received his M.S. and M. Phil. degrees in Applied Physics in 1994 and his Ph. D. in 1996, all from Yale University. Umesh’s career started as a post-doctoral fellow in the Department of Physics at Harvard University from June 1996 to May 1999. From June 1999 to May 2000, he was a visiting scholar in the Department of Chemistry and Chemical Biology and from June 1999 to June 2000, was a research associate in the Department of Physics, both at Harvard University. In May 2000, he was a faculty fellow; in 2005, an Associate Professor; and in 2009 became a Professor within the Jawaharial Nehru Centre for Advance Scientific Research (JNCASR). He has received several academic and professional honors. His research interests within his group has three-fold goals: (1) understand aspects of chemical bonding and microscopic couplings that are essential to the specific properties of a material; (2) obtain information about the atomistic structure and electronic states that may be hard to access experimentally; and (3) design new materials or modify existing materials to yield desired properties, or narrow down the choices of new materials for design by experiments.


Work is done in collaboration with K. P. S. S. Hembram, Sandeep Kumar, Somnath Bhowmick and Professor C. N. R. Rao.

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  • Umesh V. Waghmare (2010), "Ripples and Warping of Graphene: A Theoretical Study,"

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