English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this study, the Haldane model's edge states are utilized to illustratethat a zero-energy localized state forms around a single vacancy in the model.In order to complete this task, the conventional unit cell associated to theHaldane hexagonal structure is transferred onto a two-leg ladder in momentumspace, effectively forming an extended Su-Schrieffer-Heeger~(SSH) latticethrough a one-dimensional Fourier transform. Through the application of asuitable unitary transformation, the two-leg SSH ladder in momentum space isconverted into an equivalent lattice with two distinct on-site states withdifferent momentum that are suitable for the calculations. Ultimately, thedesired zero-energy localized mode formed around the vacant-site is representedby a combination of the armchair edge states. Furthermore, the scenarioinvolving two vacant sites is investigated and it is revealed that an effectivehopping interaction exists between the localized states formed around theon-site vacancies created along a zigzag chain in the lattice. This structurecan be likened to the structure of a quantum dot with two none-degenerateenergy levels. Such a hopping interaction is absent for the same vacanciescreated on the armchair chains. Finally, it is shown that introducing vacanciesperiodically on the sites of a zigzag row along a finite-width ribbon with theHaldane structure leads to the emergence of an impurity band within the energygap.

Vacancy-induced localized modes and impurity band formation in the Haldane model: a quantum dot analogy