# Space-Time Phononic Crystals with Anomalous Topological Edge States

## TL;DR

This paper introduces a one-dimensional space-time phononic crystal with anomalous topological edge states enabled by time modulation, allowing subwavelength-scale topological edge mode access for miniature device applications.

## Contribution

It presents a novel space-time phononic crystal design that duplicates topological edge states across the spectrum using time modulation, enabling subwavelength control.

## Key findings

- Edge states are immune to defects.
- Time modulation enables subwavelength topological states.
- Edge states can be accessed outside the Bragg regime.

## Abstract

It is well known that an interface created by two topologically distinct structures could host nontrivial edge states that are immune to defects. In this letter, we introduce a one-dimensional space-time phononic crystal and study the associated anomalous topological edge states. A space-decoupled time modulation is assumed. While preserving the key topological feature of the system, such a modulation also duplicates the edge state mode across the spectrum, both inside and outside the band gap. It is shown that, in contrast to conventional topological edge states which are excited by frequencies in the Bragg regime, the time-modulation-induced frequency conversion can be leveraged to access topological edge states at a deep subwavelength scale where the entire phononic crystal size is merely 1/5.1 of the wavelength. This remarkable feature could open a new route for designing miniature devices that are based on topological physics.

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Source: https://tomesphere.com/paper/1904.02711