Differential geometry applied to rings and möbius nanostructures

Benny Lassen, Morten Willatzen*, Jens Gravesen

*Kontaktforfatter for dette arbejde

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingBidrag til bog/antologiForskningpeer review

Resumé

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.

OriginalsprogEngelsk
TitelPhysics of quantum rings
RedaktørerVladimir M. Fomin
ForlagSpringer VS
Publikationsdato1. jan. 2018
Udgave2. udg.
Sider499-533
ISBN (Trykt)9783319951584
ISBN (Elektronisk)9783319951591
DOI
StatusUdgivet - 1. jan. 2018
NavnNanoScience and Technology
ISSN1434-4904

Fingeraftryk

differential geometry
eigenvectors
curvature
rings
computational geometry
radii
ring structures
graphene
equations of motion
physical properties
formulations
fabrication
physics
symmetry
geometry

Citer dette

Lassen, B., Willatzen, M., & Gravesen, J. (2018). Differential geometry applied to rings and möbius nanostructures. I V. M. Fomin (red.), Physics of quantum rings (2. udg. udg., s. 499-533). Springer VS. NanoScience and Technology https://doi.org/10.1007/978-3-319-95159-1_16
Lassen, Benny ; Willatzen, Morten ; Gravesen, Jens. / Differential geometry applied to rings and möbius nanostructures. Physics of quantum rings. red. / Vladimir M. Fomin. 2. udg. udg. Springer VS, 2018. s. 499-533 (NanoScience and Technology).
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Lassen, B, Willatzen, M & Gravesen, J 2018, Differential geometry applied to rings and möbius nanostructures. i VM Fomin (red.), Physics of quantum rings. 2. udg. udg, Springer VS, NanoScience and Technology, s. 499-533. https://doi.org/10.1007/978-3-319-95159-1_16

Differential geometry applied to rings and möbius nanostructures. / Lassen, Benny; Willatzen, Morten; Gravesen, Jens.

Physics of quantum rings. red. / Vladimir M. Fomin. 2. udg. udg. Springer VS, 2018. s. 499-533 (NanoScience and Technology).

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingBidrag til bog/antologiForskningpeer review

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AU - Gravesen, Jens

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N2 - 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.

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Lassen B, Willatzen M, Gravesen J. Differential geometry applied to rings and möbius nanostructures. I Fomin VM, red., Physics of quantum rings. 2. udg. udg. Springer VS. 2018. s. 499-533. (NanoScience and Technology). https://doi.org/10.1007/978-3-319-95159-1_16