Phononic Obstructed Atomic Insulators with Robust Corner Modes

TL;DR

This paper links obstructed atomic insulators to robust corner states in phonon spectra of certain monolayers, using topological quantum chemistry and first-principles calculations, revealing potential for experimental detection and applications.

Contribution

It extends the concept of obstructed atomic insulators to phonon systems and predicts robust corner states in phonon spectra of specific monolayers.

Findings

Robust phonon corner modes are predicted in MX3 monolayers.

Corner states are insensitive to boundary conditions, indicating topological robustness.

The work bridges electronic topological insulators and phononic systems.

Abstract

Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum chemistry (TQC) theory. The boundary states in HOTIs reported so far are often fragile, manifested as strongly depending on crystalline symmetries and cleavage terminations in the disk or cylinder geometry. Here, using the TQC theory, we present an intuitive argument about the connection between the obstructed Wannier charge centers of OAIs and the emergence of robust corner states in two-dimensional systems. Based on first-principles calculations and Real Space Invariant theory, we extend the concept of OAIs to phonon systems and thereby predict that the robust corner states can be realized in the phonon spectra of $MX_3$ ($M$=Bi, Sb, As, Sc, Y; $X$=I, Br, Cl) monolayers. The phonon corner modes in different shapes of nano-disks are investigated, and their robustness facilitates the detection in experiments and further applications. This work suggests a promising avenue to explore more attractive features of higher-order band topology.