# Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular lattice

## Author(s): Bradlyn, Barry; Wang, Zhijun; Cano, Jennifer; Bernevig, Bogdan A.

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1517q
DC FieldValueLanguage
dc.contributor.authorWang, Zhijun-
dc.contributor.authorCano, Jennifer-
dc.contributor.authorBernevig, Bogdan A.-
dc.date.accessioned2019-12-12T16:50:41Z-
dc.date.available2019-12-12T16:50:41Z-
dc.date.issued2019-01-15en_US
dc.identifier.citationBradlyn, Barry, Wang, Zhijun, Cano, Jennifer, Bernevig, B Andrei. (2019). Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular lattice. PHYSICAL REVIEW B, 99, doi:10.1103/PhysRevB.99.045140en_US
dc.identifier.issn2469-9950-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1517q-
dc.description.abstractIn this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be “fragile” with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the “obstructed atomic limit” of Bradlyn et al. [Nature (London) 547, 298 (2017)]. We conclude with some perspectives on topological matter beyond the K-theory classification.en_US
dc.format.extent045140-1 - 045140-13en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Ben_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleDisconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular latticeen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevB.99.045140-
dc.date.eissued2019-01-25en_US
dc.identifier.eissn2469-9969-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

Files in This Item:
File Description SizeFormat