Edge States in 1D Rhombus Lattices

Abstract

The band structure and topological properties of a 1D rhombus lattice are studied by defining three models according to the manners of intracell hopping amplitudes. Results show that in the presence of uniform intracell hopping amplitudes, degenerate topological edge states appear at the ends of the lattice. When the intracell hopping amplitudes change, the edge states change in different ways, but they are robust to a small amount of disorder. The inversion symmetry breaking modifies the degeneracy of the edge states and makes the edge states localized at one end of the lattice. Next, when local magnetic flux is introduced, the band structures of the three models are further modulated. New gaps can be opened and edge states can be induced with their different topological properties. This rhombus lattice can be a promising candidate for studying the edge states and their dependence on structural parameters and magnetic flux in 1D systems.

Exploiting Oriented Field Projectors to Open Topological Gaps in Plasmonic Nanoparticle Arrays

“…However, we expect this kind of edge states to still be robust to weak offdiagonal disorder, as the edge states from rhombus chains. 29 The appearance of these edge states matches the steps in the Zak phase, shown in panel (e). We also show one of the edge states of the lower gap for = 30 in Figure 3f, which as we see inherits the symmetry of the three-way chirality, localizing in the two sublattices closer to the edge.…”

“…This makes them more tunable but less robust than the edge states in the SSH, as they can be more easily pushed into the continuum and hybridize with bulk states. However, we expect this kind of edge states to still be robust to weak off-diagonal disorder, as the edge states from rhombus chains …”

“…24 This model can also be generalized to one-dimensional chains with larger linear unit cells 25−28 or rhombus unit cells. 29 These systems are topologically more complex than the SSH model, featuring several gaps and nonzero edge states. They can also exhibit other kinds of topological protection like square-root topology.…”

“…Due to the simplicity of the system, several generalizations of the SSH model have been made, for example, by adding hoppings between further neighbors or by extending to two dimensions in a square array . This model can also be generalized to one-dimensional chains with larger linear unit cells − or rhombus unit cells . These systems are topologically more complex than the SSH model, featuring several gaps and nonzero edge states.…”

Exploiting oriented field projectors to open topological gaps in plasmonic nanoparticle arrays

“…Due to the simplicity of the system, several generalizations of the SSH model have been made, for example by adding hoppings between further neighbors [23], or by extending to two dimensions in a square array [24]. This model can also be generalized to one-dimensional chains with larger linear unit cells [25][26][27][28] or rhombus unit cells [29]. These systems are topologically more complex than the SSH model, featuring several gaps and non-zero edge states.…”