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Space-Time Phononic Crystals with Anomalous Topological Edge States
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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