Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives

TL;DR

This paper uncovers a new class of 2D phononic topological insulators in Xenes and derivatives, characterized by nontrivial Stiefel-Whitney topology, leading to robust edge and corner vibrational modes, expanding the scope of topological phononics.

Contribution

It demonstrates that many buckled 2D Xenes exhibit nontrivial phononic Stiefel-Whitney topology due to band inversion, revealing a previously overlooked topological property in these materials.

Findings

Identification of nonzero second SW number $w_2=1$ in Xenes.

Presence of gaped edge states and topological corner modes.

Structural buckling causes double band inversion leading to topology.

Abstract

Two-dimensional (2D) Stiefel-Whitney (SW) insulator is a fragile topological state characterized by the second SW class in the presence of space-time inversion symmetry. So far, SWIs have been proposed in several electronic materials but seldom in phononic systems. Here we recognize that a large class of 2D buckled honeycomb crystals termed Xenes and their ligand-functionalized derivatives realize the nontrivial phononic SW topology. The phononic SWIs are identified by a nonzero second SW number $w_2=1$, associated with gaped edge states and robust topological corner modes. Despite the versatility of electronic topological properties in these materials, the nontrivial phononic SW topology is mainly attributed to the double band inversion between in-plane acoustic and out-of-plane optical bands with opposite parities due to the structural buckling of the honeycomb lattice. Our findings not only reveal an overlooked phononic topological property of 2D Xene-related materials, but also afford abundant readily synthesizable material candidates with simple phononic spectra for further experimental studies of phononic SW topology physics.