Role of the edges in a quasicrystalline Haldane model

Abstract

We study the role of the edges in determining the features of the topological phase in a quasicrystalline higher order topological insulator. We consider a specific model consisting of two stacked Haldane models with opposite Chern number and a $30^{\circ }$ twist, whose structure is crystallographically equivalent to that of the graphene quasicrystal. We find that the gap-opening in the low energy spectrum of the higher order topological insulator occurs at different energies when different kinds of edges are considered. Crucially, bearded bonds appear to be necessary for the gap to appear close to the charge neutrality point. In the more realistic case of zigzag edges, the gap opens symmetrically in the electron and hole sectors, away from zero energy. We explain our findings by inspecting the edge-bands of the decoupled bilayer, in the approximation of quasi-periodicity.

10 pages, 9 figures

References in corpus (6)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Reflection symmetric second-order topological insulators and superconductors
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks

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• Higher-order topology in twisted multilayer systems: a review
• Charging a Dimerized Quantum XY Chain
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Topological Interface States and Nonlinear Thermoelectric Performance in Armchair Graphene Nanoribbon Heterostructures