Zero-energy states in triangular and trapezoidal graphene structures

TL;DR

This paper derives analytical solutions for zero-energy states in triangular and trapezoidal graphene structures, extending previous computational results and enabling the study of bowtie graphene devices.

Contribution

It provides new analytical solutions for zero-energy states in graphene quantum dots and trapezoidal structures, generalizing prior numerical findings.

Findings

Analytical solutions match previous TB and DFT results for small triangles.

Solutions extend to arbitrary size of graphene structures.

Enables study of bowtie graphene devices.

Abstract

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.