Differential geometry applied to rings and möbius nanostructures

Benny Lassen, Morten Willatzen*, Jens Gravesen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review


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. 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. In the final part of the chapter, we derive the phonon equations-of-motion of thin shells applied to 2D graphene using a differential geometry formulation.

Original languageEnglish
Title of host publicationPhysics of quantum rings
EditorsVladimir M. Fomin
PublisherSpringer VS
Publication date1. Jan 2018
Edition2. udg.
ISBN (Print)9783319951584
ISBN (Electronic)9783319951591
Publication statusPublished - 1. Jan 2018
SeriesNanoScience and Technology


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