Edge states in graphene-like systems

TL;DR

This paper reviews various edge states in graphene-like systems, highlighting their unique properties, topological phases, and potential for edge ferromagnetism, using a unified tight-binding model to analyze diverse phenomena.

Contribution

It provides a comprehensive, unified analysis of edge states and topological phases in graphene-like systems considering interactions, spin-orbit coupling, and magnetic fields.

Findings

Zigzag edges host non-dispersive localized states at the Dirac energy.

Graphene can host topological insulating phases like QHE, QAH, and QSHE.

Edge states exhibit topological protection and are influenced by interactions and external fields.

Abstract

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.