Abstract
We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.
Original language | English |
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Article number | 1450018 |
Journal | Reviews in Mathematical Physics |
Volume | 26 |
Issue number | 10 |
DOIs | |
Publication status | Published - 22 Nov 2014 |
Externally published | Yes |
Keywords
- Dirac operator
- Graphene
- Spectrum
- Zigzag and armchair boundary conditions
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics