On the topological immunity of corner states in two-dimensional crystalline insulators

Abstract

A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragile: the kagome lattice does not realize a higher-order topological insulator. We support this finding by introducing a criterion based on a corner charge-mode correspondence for the presence of topological midgap corner modes in n-fold rotational symmetric chiral insulators that explicitly precludes the existence of a HOTI protected by a threefold rotational symmetry.

10 pages, 5 figures. Accepted for publication in NPJ Quantum Materials

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• Engineering interfacial quantum states and electronic landscapes by molecular nanoarchitectures
• Theory of Topological Corner State Laser in Kagome Waveguide Arrays
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Corner modes of the breathing kagome lattice: origin and robustness
• Topological synchronization of quantum van der Pol oscillators
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• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
• Topological Bulk Lasing Modes Using an Imaginary Gauge Field
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Nonsymmorphic chiral symmetry and solitons in the Rice-Mele model
• Observation of Dual-band Topological Corner Modes in Acoustic Kagome Lattice with Long-range Interactions
• Observation of topologically distinct corner states in "bearded" photonic Kagome lattices
• Effective action approach to the filling anomaly in crystalline topological matter
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Real-space Obstruction in Quantum Spin Hall Insulators
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Topological Wannier cycles for the bulk and edges
• Higher-order topology protected by latent crystalline symmetries
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Extended Haldane model -- a modern gateway to topological insulators
• Nanoimprinted topological laser in the visible