Edge states in trimer lattices

Alvarez, V. M. Martinez; Coutinho‐Filho, M. D.

doi:10.1103/physreva.99.013833

Cited by 95 publications

(71 citation statements)

References 57 publications

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“…They can instead be related to a Chern number, even though they appear in a quasi-1D model. These modes are very similar to those found in the trimer chain [41]. The mentioned features make the CSSH ladders versatile and exotic models, which can also be realized experimentally in several bosonic and fermionic platforms with current technology.…”

Section: Introductionsupporting

confidence: 71%

Tunable zero modes and quantum interferences in flat-band topological insulators

Zurita

Creffield

Platero

2021

Quantum

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We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

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Section: Introductionsupporting

confidence: 71%

Tunable zero modes and quantum interferences in flat-band topological insulators

Zurita

Creffield

Platero

2021

Quantum

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“…The existence of a domain wall state at exactly mid-gap energy does not necessarily occur for 1D chains consisting of sites with different on-site energies or more complicated unit cells with three or more atoms 21,22,[31][32][33][34][35] . While the states still necessarily occur at the domain wall, their energies within the gap can be tuned.…”

Section: Introductionmentioning

confidence: 99%

Tuneable topological domain wall states in engineered atomic chains

et al. 2020

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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 .

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“…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].…”

mentioning

confidence: 99%

Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons

Yan

Liljeroth

2019

Advances in Physics: X

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The fabrication of atomically precise structures with designer electronic properties is one of the emerging topics in condensed matter physics. The required level of structural control can either be reached through atomic manipulation using the tip of a scanning tunneling microscope (STM) or by bottom-up chemical synthesis. In this review, we focus on recent progress in constructing novel, atomically precise artificial materials: artificial lattices built through atom manipulation and graphene nanoribbons (GNRs) realized by on-surface synthesis. We summarize the required theoretical background and the latest experiments on artificial lattices, topological states in onedimensional lattices, experiments on graphene nanoribbons and graphene nanoribbon heterostructures, and topological states in graphene nanoribbons. Finally, we conclude our review with an outlook to designer quantum materials with engineered electronic structure. 1 arXiv:1905.03328v4 [cond-mat.mtrl-sci]

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Edge states in trimer lattices

Cited by 95 publications

References 57 publications

Tunable zero modes and quantum interferences in flat-band topological insulators

Tunable zero modes and quantum interferences in flat-band topological insulators

Tuneable topological domain wall states in engineered atomic chains

Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons

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