Electronic properties of atomic ribbons with spin-orbit couplings on different substrates

Abstract

Atomic ribbons and monoatomic chains on different substrates are proposed as spin-dependent electrical conductors with asymmetrical local density of states (DOS) and ferromagnetic occupancies along the chains. The tight-binding Hamiltonian and Green’s function techniques were used to analyze the electrical properties of both normal and topological systems with spin-orbit scattering. To make the system more realistic, electron leakage from atomic chains to various types of substrates is considered. We have shown that delocalized electrons in the substrate and spin-orbit interactions are responsible for asymmetry in the local DOS. The structure of DOS for spin-orbit nontopological chains is spin-dependent at both chain edges; however, in the middle of the chain, only paramagnetic solutions are observed. Additionally, we have found different periods of the local DOS oscillations along the chain in the presence of spin-flip and spin-orbit couplings. For topological chains, the edge nontrivial states split in the presence of spin-orbit scattering and spin-dependent Friedel oscillations appear along the whole topological chain. We have also found out-of-phase Friedel oscillations between neighboring chains along the atomic ribbon.

Topological Atomic Chains on 2D Hybrid Structure

“…In this case, the surface DOS is flat (energy independent) and can be effectively described within the wide-band limit approximation. Thus, the surface described within this approximation does not influence the chain topological states which is in agreement with the literature results [60]. The situation changes for realistic 2D square lattice substrate with the van Hove singularity in the middle of the band (panels b and e).…”

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

“…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.…”