Topological Atomic Chains on 2D Hybrid Structure

Abstract

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

Implementation of the Su–Schrieffer–Heeger Model in the Self-Assembly Si–In Atomic Chains on the Si(553)–Au Surface

“…A similar energy spectrum structure is expected for a trimer 1D lattice; except here, electron bands replace single states, with topological end states potentially manifesting within the energy gap. While in the original SSH chain, the topological modes precisely appear at the midgap energy, boundary topological states can also emerge at nonzero energies in extended SSH models. ,− , Moreover, it is worth noting that even in cases where the inversion symmetry is broken (due to disorders, defects, different on-site energies, asymmetrical couplings, or time-dependent perturbations), the localized nature of topological states can persist in such systems. ,, Additionally, ladder-like atomic systems such as two coupled SSH chains − and other SSH chain geometries ,− , also reveal nontrivial topological end states.…”

“… 14 , 18 − 24 , 62 Moreover, it is worth noting that even in cases where the inversion symmetry is broken (due to disorders, defects, different on-site energies, asymmetrical couplings, or time-dependent perturbations), the localized nature of topological states can persist in such systems. 19 , 20 , 46 Additionally, ladder-like atomic systems such as two coupled SSH chains 25 − 28 and other SSH chain geometries 14 , 18 − 23 , 62 also reveal nontrivial topological end states.…”

“…This system possesses time-reversal particle-hole symmetry and supports two distinct topological phases. Nontrivial topology is also observed in extended SSH models featuring various geometries, such as long-range chains incorporating next-nearest-neighbor hoppings or by altering the site period of the unit cell. ,− Moreover, the standard SSH model extends to a double-chain structure, resembling a cross-linked two-leg ladder model (Creutz ladder) or a modified Harper model. − Topological states can also emerge in two-dimensional (2D) ribbon geometries or disrupted SSH chains. − Intriguingly, ladder-like systems can unveil topological Majorana states as well. Additionally, nontrivial phases of matter are observed in driven SSH chains, sometimes termed Floquet topological insulators. , Numerous potential experimental applications of the SSH chain are observed in the domains of quantum optics and momentum lattices, wherein dynamic effects can generate nontrivial 1D structures featuring midgap topological states. ,, While this approach demands sub-Kelvin temperatures, it enables the creation of Creutz ladder systems or extended SSH structures using ultracold Fermionic atoms. , In these structures, the estimation of topological properties is conducted through quench dynamics.…”