Intrinsic second-order topological insulators produced by triangular Kekulé distortion in honeycomb lattices

Chiral symmetry breaking (CSB) is promising to realize a series of exotic topological phenomena due to the coupling of Dirac fermions at inequivalent valleys. We propose a strategy to introduce CSB by applying a Kekul\'e distortion in a spinless honeycomb lattice, resulting in the emergence of a second-order topological phase as the period of the superlattice is $3m\ifmmode\times\else\texttimes\fi{}3m$ $(m=1,2,\dots{})$. Following the strategy, $\mathrm{S}{\mathrm{i}}_{x}{\mathrm{C}}_{y}$ and circumcoronene-based two-dimensional (2D) honeycomb lattices are predicted to be second-order topological insulators (SOTIs) that are identified via the topological invariants and the presence of in-gap topological corner modes. In this paper, we provide an effective approach to realize CSB in a honeycomb lattice and greatly enrich 2D SOTIs families.