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

We classify time-reversal breaking (class A) spinful topological crystallineinsulators with crystallographic non-magnetic (32 types) and magnetic (58types) point groups. The classification includes all possible magnetictopological crystalline insulators protected by point group symmetry. Whereasthe classification of topological insulators is known to be given by the$K$-theory in the momentum space, computation of the $K$-theory has been adifficult task in the presence of complicated crystallographic symmetry. Herewe consider the $K$-homology in the real space for this problem, instead of the$K$-theory in the momentum space, both of which give the same topologicalclassification. We apply the Atiyah-Hirzebruch spectral sequence (AHSS) forcomputation of the $K$-homology, which is a mathematical tool for generalized(co)homology. In the real space picture, the AHSS naturally gives theclassification of higher-order topological insulators at the same time. Bysolving the group extension problem in the AHSS on the basis of physicalarguments, we completely determine possible topological phases includinghigher-order ones for each point group. Relationships among differenthigher-order topological phases are argued in terms of the AHSS in the$K$-homology. We find that in some nonmagnetic and magnetic point groups, astack of two $\mathbb{Z}_2$ second-order topological insulators can be smoothlydeformed into non-trivial fourth-order topological insulators, which impliesnon-trivial group extensions in the AHSS.

physical review. b./physical review. b

Topological classification under nonmagnetic and magnetic point group  symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to  higher-order topology