Metallic Graphene Nanodisks

TL;DR

This paper investigates the electronic properties of graphene nanodisks and nanoribbons, identifying conditions under which they exhibit metallic behavior through zero-energy states, with a focus on trigonal zigzag nanodisks.

Contribution

It reveals that only trigonal zigzag nanodisks possess degenerate zero-energy states and metallic ferromagnetism, with controllable degeneracy based on size.

Findings

Finite-length zigzag nanoribbons lack zero-energy states.

Trigonal zigzag nanodisks have degenerate zero-energy states.

Trigonal zigzag nanodisks exhibit large relaxation times despite small size.

Abstract

We explore the electronic properties of finite-length graphene nanoribbons as well as graphene nanodisks with various sizes and shapes in quest of metallic ones. For this purpose it is sufficient to search zero-energy states. We find that there exist no zero-energy states in finite-length zigzag nanoribbons though all infinite-length zigzag nanoribbons have zero-energy states. The occurrence of zero-energy states is surprisingly rare. Among typical nanodisks, only trigonal zigzag nanodisks have degenerate zero-energy states and show metallic ferromagnetism, where the degeneracy can be controlled arbitrarily by designing the size. A remarkable property is that the relaxation time is quite large in spite of its small size in trigonal zigzag nanodisks.