Pfaffian invariant identifies magnetic obstructed atomic insulators

I.M. Araya Day*, A.S. Varentcova, D. Varjas, A.R. Akhmerov

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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We derive a Z4 topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a C4T symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four C4T-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a C4T-symmetric model that interpolates between them. The phase diagram shows that C4T insulators allow ±1 and 2 changes of the invariant, where the latter is overlooked by symmetry indicators.
Original languageEnglish
Article number114
Number of pages9
JournalSciPost Physics
Issue number3
Publication statusPublished - 2023


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