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arXiv · 1601.06607

Spectral gaps of Dirac operators describing graphene quantum dots

Rafael D. Benguria·Søren Fournais·Edgardo Stockmeyer·Hanne Van Den Bosch
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Abstract

The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to $|Ω|^{-1/2}$, where $Ω\subset \mathbb{R}^2$ is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.

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Rafael D. Benguria, Søren Fournais, Edgardo Stockmeyer, Hanne Van Den Bosch. 2017-04-20. Spectral gaps of Dirac operators describing graphene quantum dots. https://doi.org/10.1007/s11040-017-9242-4

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