Corner modes of the breathing kagome lattice: origin and robustness

TL;DR

This paper investigates the nature and robustness of corner modes in the breathing kagome lattice, clarifying their trivial origin and identifying symmetry conditions that can protect their zero-energy state.

Contribution

It demonstrates that corner modes are trivial in origin but can be protected by specific symmetries, and distinguishes different phases using topological markers.

Findings

Corner modes are of trivial nature, not higher-order topological.

Protection of corner modes requires sublattice or crystalline symmetries.

Two breathing phases are identified as distinct obstructed atomic limits.

Abstract

We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order topological phase but later shown to be trivial for perturbations that were thought to protect them. Using various theoretical and simulation techniques, we confirm that it does not display higher-order topology: the corner modes are of trivial nature. Nevertheless, they might be protected. First, we show a set of perturbations within a tight-binding model that can move the corner modes away from zero energy, also repeat some perturbations that were used to show that the modes are trivial. In addition, we analyze the protection of the corner modes in more detail and find that only perturbations respecting the sublattice or generalized chiral and crystalline symmetries, and the lattice connectivity, pin the corner modes to zero energy robustly. A destructive interference model corroborates the results. Finally, we analyze a muffin-tin model for the bulk breathing kagome lattice. Using topological and symmetry markers, such as Wilson loops and Topological Quantum Chemistry, we identify the two breathing phases as adiabatically disconnected different obstructed atomic limits.