Zero-energy states in triangular and trapezoidal graphene structures

Details Zero-energy states in triangular and trapezoidal graphene structures Zero-energy states in triangular and trapezoidal graphene structures

2009-10-21

arxiv.org/abs/0910.4121v1

Phys. Rev. B 81, 033403 (2010)

Physics

Condensed Matter

Materials Science

4 pages, 4 figures

Scientific paper

We derive analytical solutions for the zero-energy states of degenerate shell obtained as a singular eigenevalue problem found in tight-binding (TB) Hamiltonian of triangular graphene quantum dots with zigzag edges. These analytical solutions are in agreement with previous TB and density functional theory (DFT) results for small graphene triangles and extend to arbitrary size. We also generalize these solutions to trapezoidal structure which allow us to study bowtie graphene devices.

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