Zak phase and the existence of edge states in graphene
By P. Delplace, D. Ullmo, G. Montambaux. 2011
412 citations recorded by the source corpus.
We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, it con?firms and generalizes the results of several previous works.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/d9d15a5f2c4c0eaf3002ff60f7162d4c2563b549
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Direct measurement of the Zak phase in topological Bloch bands (2012, background): “Non-trivial Zak phases underlie the existence of protected edge states (13, 14), fermion number fractionalization (1–3), and irrationally charged domain walls (15, 16) between topologically distinct one-dimensional solids.”
- Exciton-polaritons in lattices: A non-linear photonic simulator (2016, methodology): “Another consequence of the particular spinor structure of the wavefunction in a honeycomb lattice is the existence of edge states in finite size ribbons: it has been shown that the winding of the phase of the wavefunctions around the Dirac cones can be connected to the appearance of edge states simi”
- Topological photonics (2018, background): “20, along the k⊥ direction over the first Brillouin zone (Delplace et al., 2011; Mong and Shivamoggi, 2011; Ryu and Hatsugai, 2002):”
- Floquet topological transitions in a driven one-dimensional topological insulator (2015, methodology): “This phase has been connected to the existence of edge states in graphene [65] and, interestingly, it has been measured in cold-matter systems simulating the (undriven) SSH model [49] and also in acoustic systems [66].”