Marginal topological properties of graphene: a comparison with topological insulators

TL;DR

This paper compares the topological properties of graphene and topological insulators, highlighting similarities and key differences, and introduces the concept of gapped graphene as marginal topological insulators.

Contribution

It clarifies the topological classification of gapped graphene, emphasizing its unique position as marginal topological insulators distinct from trivial and true topological insulators.

Findings

Graphene and topological insulators share features like quantized Berry phase and edge states.

Differences between valley and spin degrees of freedom are crucial for topological distinctions.

Gapped graphene systems are characterized as marginal topological insulators.

Abstract

The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant orbital bands, which generate the pseudo-spin degree of freedom, and, less obviously, there is a correspondence between the valley degree of freedom in graphene and electron spin in topological insulators. Despite the similarities, there are also several important distinctions, both for the bulk topological properties and for their implications for the edge states -- primarily due to the fundamental difference between valley and spin. In view of their peculiar band structure features, gapped graphene systems should be properly characterized as marginal topological insulators, distinct from either the trivial insulators or the true topological insulators.