# Observation of topological edge states of sound at a momentum away from the high-symmetry point

## TL;DR

This paper reports a novel phononic topological insulator with Dirac cones along high-symmetry lines in a square lattice, demonstrating tunable topological edge states for sound that are robust against disorder.

## Contribution

It introduces a new type of topological phononic insulator with momentum-away Dirac cones and demonstrates tunable, robust topological edge states in square lattice phononic crystals.

## Key findings

- Dirac cones appear along high-symmetry lines in square lattice phononic crystals.
- Rotating square columns lifts Dirac points, creating a band gap.
- Topological edge states exhibit robustness against cavities and disorders.

## Abstract

Topologically protected one-way transportation of sound, mimicking the topological properties of the condensed matter, has received greatly attentions. Thus far, the topological phases and the topological edge states of sound are yielded in the vicinity of the Dirac cones fixed at the high symmetric points of the Brillouin zone. Here, we present a new type of the phononic topological insulator in the square lattice with position-variational Dirac cones along the high symmetric lines. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. By rotating the square columns, these Dirac points are lifted and a complete band gap is induced because of the mirror-symmetry-breaking. Along the topological domain wall between the phononic crystals (PhCs) with the distinct topological phases stemming from the mirror symmetry inversion, we obtain a topological edge state for the neutral scalar sound which is absence of the intrinsic polarization and is uncoupled from an external field. Within a wide rotational range of the square column, the topological edge state in our PhCs evolves from a gapless one into a gapped one with a robust edge transport against cavities and disorders. Our excellent results are promising for the exploration of the new topological phenomena in the PhCs beyond the hexagonal lattices. Furthermore, the flexibility of the rotational square columns provides an interesting platform for the design of tunable topological acoustic devices.

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Source: https://tomesphere.com/paper/1706.08206