• 文献标题:   Ripples in Graphene: A Variational Approach
  • 文献类型:   Article
  • 作  者:   FRIEDRICH M, STEFANELLI U
  • 作者关键词:  
  • 出版物名称:   COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • ISSN:   0010-3616 EI 1432-0916
  • 通讯作者地址:   Univ Munster
  • 被引频次:   0
  • DOI:   10.1007/s00220-020-03869-z EA OCT 2020
  • 出版年:   2020

▎ 摘  要

Suspended graphene samples are observed to be gently rippled rather than being flat. In Friedrich et al. (Z Angew Math Phys 69:70, 2018), we have checked that this nonplanarity can be rigorously described within the classical molecular-mechanical frame of configurational-energy minimization. There, we have identified all ground-state configurations with graphene topology with respect to classes of next-to-nearest neighbor interaction energies and classified their fine nonflat geometries. In this second paper on graphene nonflatness, we refine the analysis further and prove the emergence of wave patterning. Moving within the frame of Friedrich et al. (2018), rippling formation in graphene is reduced to a two-dimensional problem for one-dimensional chains. Specifically, we show that almost minimizers of the configurational energy develop waves with specific wavelength, independently of the size of the sample. This corresponds remarkably to experiments and simulations.