Graphene nanodisk is a graphene derivative with a closed edge. The trigonal zigzag nanodisk with size $N$ contains a zero-energy sector with the $\text{SU}\left(N\right)$ symmetry. We investigate electron-electron interaction effects within the zero-energy sector. We explicitly derive the direct and exchange interactions, which explicitly break the $\text{SU}\left(N\right)$ symmetry. Then, by regarding a nanodisk as a quantum dot with an internal degree of freedom, we analyze the nanodisk-lead system consisting of a nanodisk and two leads. By employing the standard Green’s function method, we reveal Coulomb blockade effects in this system. As the chemical potential increases, a peculiar series of plateaux and dips develops in the occupation number and a peculiar series of Coulomb blockade peaks develops in the conductance, which reflect the energy spectrum of a nanodisk with a broken $\text{SU}\left(N\right)$ symmetry. It is argued that dips emerge in the occupation number due to a Coulomb correlation effect and that tiny Coulomb blockade peaks emerge due to a tunneling effect between the nanodisk and leads.

• Received 24 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.155411