Twisted bulk-boundary correspondence of fragile topology

Zhi Da Song, Luis Elcoro, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Original languageEnglish (US)
Pages (from-to)794-797
Number of pages4
Issue number6479
StatePublished - Feb 14 2020

All Science Journal Classification (ASJC) codes

  • General


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