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Volume 23, Issue 5
Schrödinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube

Hiroaki Niikuni

DOI: 10.4208/cicp.120715.080517a

Commun. Comput. Phys., 23 (2018), pp. 1434-1475.

Published online: 2018-04

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  • Abstract

Throughout this paper, we study the spectrum of a periodic Schrödinger operator on a zigzag super carbon nanotube, which is a generalization of the zigzag carbon nanotube. We prove that its absolutely continuous spectrum has the band structure. Moreover, we show that its eigenvalues with infinite multiplicities consisting of the Dirichlet eigenvalues and points embedded in the spectral band for some corresponding Hill operator. We also give the asymptotics for the spectral band edges.

  • Keywords

Carbon nanotube, zigzag nanotube, supergraphene, quantum graph, spectral gap, band structure, Floquet–Bloch theory, Hill operator.

  • AMS Subject Headings

34L05, 34L15, 34B45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-1434, author = {Hiroaki Niikuni}, title = {Schrödinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {5}, pages = {1434--1475}, abstract = {

Throughout this paper, we study the spectrum of a periodic Schrödinger operator on a zigzag super carbon nanotube, which is a generalization of the zigzag carbon nanotube. We prove that its absolutely continuous spectrum has the band structure. Moreover, we show that its eigenvalues with infinite multiplicities consisting of the Dirichlet eigenvalues and points embedded in the spectral band for some corresponding Hill operator. We also give the asymptotics for the spectral band edges.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120715.080517a}, url = {http://global-sci.org/intro/article_detail/cicp/11222.html} }
TY - JOUR T1 - Schrödinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube AU - Hiroaki Niikuni JO - Communications in Computational Physics VL - 5 SP - 1434 EP - 1475 PY - 2018 DA - 2018/04 SN - 23 DO - http://doi.org/10.4208/cicp.120715.080517a UR - https://global-sci.org/intro/article_detail/cicp/11222.html KW - Carbon nanotube, zigzag nanotube, supergraphene, quantum graph, spectral gap, band structure, Floquet–Bloch theory, Hill operator. AB -

Throughout this paper, we study the spectrum of a periodic Schrödinger operator on a zigzag super carbon nanotube, which is a generalization of the zigzag carbon nanotube. We prove that its absolutely continuous spectrum has the band structure. Moreover, we show that its eigenvalues with infinite multiplicities consisting of the Dirichlet eigenvalues and points embedded in the spectral band for some corresponding Hill operator. We also give the asymptotics for the spectral band edges.

Hiroaki Niikuni. (2018). Schrödinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube. Communications in Computational Physics. 23 (5). 1434-1475. doi:10.4208/cicp.120715.080517a
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