Novel topological states in a thin strip of Haldane model.

In 1988 F.D.M. Haldane conceived the first proposal for a Chern insulator: his model $\mbox{---nowadays}$ known as the Haldane model--- describes spinless electrons on a honeycomb lattice, and it achieves a topological phase with non-zero Chern number by breaking time-reversal symmetry without net magnetic flux. The topological phase of the model is characterized by the presence of one-dimensional chiral edge states, with energy in the bulk gap and connecting the valence and conduction bands. Interestingly, if one considers a thin enough strip of the honeycomb lattice, then the chiral modes on the two edges will hybridize with each other, causing the opening of a gap in the edge spectrum. We found that, for a specific choice of the strip edge type, this gap can host a pair of zero energy modes, corresponding to topological states localized at the two ends of the strip. Moreover, we discovered that for a strip of appropriate width the model manifests an even richer phenomenology. Indeed, in such special configuration, the topological phase described above is only achievable after a topological phase transition, which can be induced through the introduction of an on-site staggered potential.