Phonon-induced Floquet second-order topological phases protected by space-time symmetries

TL;DR

This paper demonstrates how phonon excitations can induce Floquet higher-order topological phases protected by space-time symmetries, revealing new boundary modes in systems that are trivial without phonon activation.

Contribution

It introduces a mechanism where phonon modes promote static spatial symmetries to space-time symmetries, enabling Floquet topological phases with higher-order boundary modes.

Findings

Phonon excitation can induce Floquet topological phases.

Altered symmetry relations enable gapless boundary modes.

Examples in class D and AIII show practical realization.

Abstract

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, presumably with alterations in the commutation/anticommutation relations with respect to non-spatial symmetries. We show how a coherently excited phonon mode can be used to promote a spatial symmetry with which the static system is always trivial, to a space-time symmetry which supports non-trivial Floquet higher-order topological phase. We present two examples -- one in class D and another in class AIII where a coherently excited phonon mode promotes the reflection symmetry to a time-glide symmetry such that the commutation/anticommutation relations between spatial and non-spatial symmetries are modified. These altered relations allow the previously trivial system to host gapless modes of co-dimension two at reflection-symmetric boundaries.