Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system

Abstract

We study corner states on a flat band in the square lattice. To this end, we introduce a two dimensional model including Su-Schrieffer-Heeger type bond alternation responsible for corner states as well as next-nearest neighbor hoppings yielding flat bands. The key symmetry of the model for corner states is space-time inversion ($\mathcal{P}\mathcal{T}$) symmetry, which guarantees quantized Berry phases. This implies that edge states as well as corner states would show up if boundaries are introduced to the system. We also argue that an infinitesimal $\mathcal{P}\mathcal{T}$ symmetry-breaking perturbation could drive flat bands into flat Chern bands.

arXiv comment6 pages, 5 figures, final version

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• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Higher-order topology in monolayer graphene
• Inversion symmetric non-Hermitian Chern insulator
• Topological States in Generalized Electric Quadrupole Insulators
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Floquet higher-order topological phases in momentum space
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal