Differential Geometry Applied to Rings and Möbius Nanostructures

Chapter
Part of the NanoScience and Technology book series (NANO)

Abstract

Nanostructure shape effects have become a topic of increasing interest due to advancements in fabrication technology. In order to pursue novel physics and better devices by tailoring the shape and size of nanostructures, effective analytical and computational tools are indispensable. In this chapter, we present analytical and computational differential geometry methods to examine particle quantum eigenstates and eigenenergies in curved and strained nanostructures. Example studies are carried out for a set of ring structures with different radii and it is shown that eigenstate and eigenenergy changes due to curvature are most significant for the groundstate eventually leading to qualitative and quantitative changes in physical properties. In particular, the groundstate in-plane symmetry characteristics are broken by curvature effects, however, curvature contributions can be discarded at bending radii above 50 nm. In the second part of the chapter, a more complicated topological structure, the Möbius nanostructure, is analyzed and geometry effects for eigenstate properties are discussed including dependencies on the Möbius nanostructure width, length, thickness, and strain.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Benny Lassen
    • 1
  • Morten Willatzen
    • 1
    • 2
  • Jens Gravesen
    • 3
  1. 1.Mads Clausen InstituteUniversity of Southern DenmarkSønderborgDenmark
  2. 2.Department of Photonics EngineeringTechnical University of DenmarkKgs. LyngbyDenmark
  3. 3.Department of MathematicsTechnical University of DenmarkKgs. LyngbyDenmark

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