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Curvature-Induced Energy Band Tilting in Finite-Length Carbon Nanotubes
Umeå University, Faculty of Science and Technology, Department of Physics.
2011 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The near-Fermi-energy energy band structure of carbon nanotubes is given by cross-sections of the graphene Dirac cones near the K and K' points. Using second-order perturbation theory and a nearest-neighbor approximated tight-binding model, curvature-induced corrections to the graphene-based effective model are derived. In addition to the already known Dirac-point shift, the curvature is shown to cause not only a warping of the Dirac cone, tantamount to a slight compression and a correction to the overall Fermi velocity, but also a tilting of the Dirac cone and the associated nanotube energy bands. This tilting results in a velocity asymmetry for left- and right-going waves and two different kinds of excitations, allowing for varying degeneracy in the same sample. Previous experiments have shown irregularities in the level degeneracy and should be reconsidered in this context.

Abstract [sv]

Energibandstrukturen för kolnanorör ges av tvärsnitt av grafens Dirac-koner nära K- och K'-punkterna. Medelst andra ordningens störningsteori och en tight-binding-modell med närmaste-granne-approximationen härleds de kurvaturinducerade korrektionerna till den grafenbaserade effektiva modellen. Utöver det redan kända Dirac-punkt-skiftet så visas kurvaturen orsaka inte bara en förvrängning av Dirac-konen, liktydigt med en mild kompression och en korrektion till den övergripande fermihastigheten, utan också en lutning av Dirac-konen och de associerade nanorörsenergibanden. Denna lutning resulterar i en hastighetsasymmetri för vänster- och högergående vågor och två olika sorters excitationer, vilket tillåter för varierande degeneration i samma prov. Tidigare experiment har visat oregelbundenheter i nivådegenerationen och bör omprövas i denna kontext.

Place, publisher, year, edition, pages
2011. , 84 p.
Keyword [en]
carbon nanotubes, graphene, Dirac cone, condensed matter, velocity asymmetry, tilting
Keyword [sv]
kolnanorör, grafen, Dirac-kon, kondenserade materien, hastighetsasymmetri, lutning
National Category
Condensed Matter Physics
URN: urn:nbn:se:umu:diva-49673OAI: diva2:456463
Subject / course
Examensarbete i teknisk fysik
Educational program
Civilingenjörsprogrammet i teknisk fysik
2011-11-11, Universitetsklubben, Umeå universitet, Umeå, 15:40 (English)
Physics, Chemistry, Mathematics
Available from: 2011-11-14 Created: 2011-11-14 Last updated: 2011-11-14Bibliographically approved

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Vikström, Anton
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