Frontiers in Physics (Jun 2022)
Takagi Topological Insulator on the Honeycomb Lattice
Abstract
Recently, real topological phases protected by PT symmetry have been actively investigated. In two dimensions, the corresponding topological invariant is the Stiefel-Whitney number. A recent theoretical advance is that in the presence of the sublattice symmetry, the Stiefel-Whitney number can be equivalently formulated in terms of Takagi’s factorization. The topological invariant gives rise to a novel second-order topological insulator with odd PT-related pairs of corner zero modes. In this article, we review the elements of this novel second-order topological insulator, and demonstrate the essential physics by a simple model on the honeycomb lattice. Novelly, the higher-order topological boundary modes can not only be tuned by the parameters but also the geometric shape of the sample.
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