An anomalous higher-order topological insulator

Understand

Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk.

• This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure.
• We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant.
• We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index.