Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots

@article{Benguria2017SpectralGO,
  title={Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots},
  author={Rafael D. Benguria and S{\o}ren Fournais and Edgardo Stockmeyer and Hanne Van Den Bosch},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2017},
  volume={20},
  pages={1-12}
}
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⊂ℝ2${\Omega } \subset \mathbb {R}^{2}$ is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in… CONTINUE READING

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