Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekul\'e Bond Ordering

TL;DR

This paper investigates the stability of zero-energy modes in a disordered 2D honeycomb lattice with Kekulé bond order, revealing their robustness under certain symmetries through numerical analysis.

Contribution

It demonstrates the anomalous robustness of zero-modes in a disordered honeycomb lattice with Kekulé order, emphasizing the role of chiral symmetry.

Findings

Zero-modes are robust against disorder when chiral symmetry is preserved.

Split n=0 Landau levels maintain their integrity under disorder.

Topological defect-induced zero-modes show similar robustness.

Abstract

Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekul\'e bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekul\'e ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected.