Edge states in graphene-like systems

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.

Quantum anomalous Hall effect in graphene coupled to skyrmions

“…First, two chiral edge states are expected to occur at the boundaries of the crystal. This is confirmed by our calculations, using a recursive Green-function method [29] to calculate the surface states, as shown in Fig. 2(e).…”

Theory of edge-state optical absorption in two-dimensional transition metal dichalcogenide flakes

“…1c. At the excitation energies much higher than ∆/2, the photocarriers are excited far from the conduction and valence band edges and cannot be described by a thermalized distributions (19) and (21). It is instructive to consider the limit E ω = ∆/2 and subsequently assume that ∆ ≫ T 0 .…”

Effective model for Majorana modes in graphene

“…Interestingly, if we compare (22) to the Hamiltonian of a topological superconducting ferromagnetic nanowire: 15…”

“…Hence, there is an intrinsic identification of sublattice and valley degrees of freedom. [20][21][22] Second, electronic interactions lead to the emergence of a canted antiferromagnetic ordering that can be tuned by an applied Zeeman field, as shown in Fig. 1a.…”