Abstract
We generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of fourfold rotational symmetry and the time-reversal symmetry . This Pfaffian description reveals a deep and fundamental link between TIs and HOTIs, and allows important conclusions about TIs to be generalized to HOTIs. As examples, we demonstrate in the Letter how to generalize Fu-Kane’s parity criterion for TIs to HOTIs, and also present a general method to efficiently compute the index of 3D chiral HOTIs without a global gauge.
- Received 27 July 2019
- Revised 2 December 2019
DOI:https://doi.org/10.1103/PhysRevLett.124.036401
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