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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the bulk and boundary properties of fragile topological insulators(TIs) protected by inversion symmetry, mostly focusing on the class A of theAltland-Zirnbauer classification. First, we propose an efficient method fordiagnosing fragile band topology by using the symmetry data in momentum space.Using this method, we show that among all the possible parity configurations ofinversion-symmetric insulators, at least 17 percent of them have fragiletopology in 2D while fragile TIs are less than 3 percent in 3D. Second, westudy the bulk-boundary correspondence of fragile TIs protected by inversionsymmetry. In particular, we generalize the notion of $d$-dimensional ($d$D)$k$th-order TIs, which is normally defined for $0<k\le d$, to the cases with$k>d$, and show that they all have fragile topology. In terms of the DiracHamiltonian, a $d$D $k$th-order TI has $(k-1)$ boundary mass terms. We showthat a minimal fragile TI with the filling anomaly can be considered as the$d$D $(d+1)$th-order TI, and all the other $d$D $k$th-order TIs with $k>(d+1)$can be constructed by stacking $d$D $(d+1)$th-order TIs. Although $d$D$(d+1)$th-order TIs have no in-gap states, the boundary mass terms carry an oddwinding number along the boundary, which induces localized charges on theboundary at the positions where the boundary mass terms change abruptly. In thecases with $k>(d+1)$, we show that the net parity of the system with boundariescan distinguish topological insulators and trivial insulators. Also, bystudying the (nested) Wilson loop spectra, we determine the minimal number ofbands to resolve the Wannier obstruction, which is consistent with theprediction from our diagnosis method of fragile topology. Finally, we show thata $(d+1)$D $(k-1)$th-order TI can be obtained by an adiabatic pumping of $d$D$k$th-order TI, which generalizes the previous study of the 2D 3rd-order TI.

Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop