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

An infinite crystal can be constructed by an infinite number of paralleltwo-dimensional (hkl) crystal planes coupled to each other. For crystals withnegligible spin-orbit coupling, we report a rigorous proof of a criterion onthe non-existence of surface states in a semi-infinite crystal with the crystalsymmetry. The forward transfer to be the same as the backward one, called asF-B dynamical symmetry, is key to realize the criterion. Based on lattice modelHamiltonian with coupling between the nearest neighbor crystal planes only, weprove that a cut crystal will not be able to accommodate any surface states ifthe original infinite crystal has reflection symmetry about every crystal planewhich results in F-B symmetry. The criterion provide a platform to simplyconclude whether surface states exist or not in a cut crystal. For any suchcrystals, the non-existence or existence of surface states depends on the cutdirection of the crystal plane. Since the spin-orbit coupling breaks the chiralsymmetry, resulting in the F-B asymmetry, surface states can emerge in the(hkl) cut crystal with spin-orbit coupling.

A criterion of the non-existence of surface states in a semi-infinite crystal