Qualitative analysis of trapped Dirac fermions in graphene
arXiv:1405.2535 · doi:10.1016/j.aop.2014.06.020
Abstract
We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.
17 pages, analysis of the systems with the non-vanishing mass corrected
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- Coherent states for graphene under the interaction of crossed electric and magnetic fields
- Complex Supersymmetry in Graphene
- Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump
- Energy spectra of graphene quantum dots induced between Landau levels
- Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
- On the existence of eigenvalues of a one-dimensional Dirac operator
- Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles