Tuneable topological domain wall states in engineered atomic chains

Abstract

Topological modes in one-and two-dimensional systems have been proposed for numerous applications utilizing their exotic electronic responses 1-7 . The zero-energy, topologically protected end modes can be realized in the Su-Schrieffer-Heeger (SSH) model 8 , which has been experimentally implemented in atomic-scale solid-state structures and in ultra-cold atomic gases 9,10 . While the edge modes in the SSH model are at exactly the mid-gap energy, other paradigmatic 1D models such as trimer and coupled dimer chains have non-zero energy boundary states 4,5,11 . However, these chains have not been realized in an atomically tuneable system that would allow explicit control of the edge modes. Here, we demonstrate atomically controlled trimer and coupled dimer chains realized using chlorine vacancies in the c(2 × 2) adsorption layer on Cu(100) 9,12,13 . This system allows wide tuneability of the domain wall modes that we experimentally demonstrate using low-temperature scanning tunneling microscopy (STM). In the future, these modes may be used to realize well-defined fractional charge states or find applications in exotic quantum devices with atomically well-defined geometries 8,11,14,15 .

Particle-antiparticle duality and fractionalization of topological chiral solitons

“…In quantum topological physics, the famous Su-Schrieffer-Heeger (SSH) soliton manifests a variety of important concepts including Thouless topological charge pumping, fractional charge, particle-antiparticle (PA) symmetry and spin-charge separation 2 – 7 . Such exotic properties and potential applications have stimulated many studies: conducting polymers 7 , diatomic chain model 8 , fractionalized domain wall excitations in 1D chain and wire 9 , 10 , acoustic experimental system 11 , realization of Zak phase and topological charge pumping in the cold atom system 12 – 14 , topological photonic crystal nanocavity lasers using SSH edge mode 15 – 17 , artificially engineered SSH lattices 18 , 19 , and topological quaternary operation using chiral soliton 20 , 21 . Among such exotic properties, PA symmetry and fractionalization are essential to understand not only the pair creation but also topological properties of topological solitons.…”

Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons

“…The SSH model describes the physics of a dimerized one-dimensional chain within the tight-binding model and here we will explain how it can be implemented in artificial lattices and later, in graphene nanoribbons [86,87]. The ideas related to dimer chains can be extended to topological domain wall states in trimers and coupled dimer chains that have also been characterized experimentally and theoretically [88][89][90][91].…”

Topological Atomic Chains on 2D Hybrid Structure

“…Among many experimental fabrication methods of 1D systems one can find atomic chains grown epitaxially on silicon surfaces, such as Si(335), Si(557) [35][36][37], 1D chains with gate-defined quantum dot in 2D electron gas or chains of dopant atoms in silicon [38,39]. Alternatively, the SSH topology was found in chlorine vacancies on Cu(100) surfaces [34,40]. In such systems, the role of 2D substrate electrodes can play the surface atomic reconstruction (like Si(111)-(6 × 6)Au surface) or atomically flat graphene, silicene, antimonene or other layers which nowadays can be easily fabricated [2,31,32,41,42].…”