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.
Highlights
The topology of electronic band structures of crystals is largely restricted by the existing symmetries [1,2,3,4,5,6,7,8], and its nontriviality is reflected in the presence of gapless modes located at the crystal boundaries [9,10,11,12,13]
As far as topological classification is concerned, such a space-time symmetry can lead to a nontrivial Floquet band topology, in the same way as its spatial counterpart does in a static system, except for a possible alternation of the commutation/anticommutation relations with respect to the nonspatial symmetries [33,34]
We provide two examples in which by promoting a spatial symmetry with operator gto a space-time symmetry, the commutation relations between gand nonspatial symmetries become appropriate for supporting a nontrivial (Floquet) topological phase, whereas only a trivial phase exists in a g-symmetric static system
Summary
The topology of electronic band structures of crystals is largely restricted by the existing symmetries [1,2,3,4,5,6,7,8], and its nontriviality is reflected in the presence of gapless modes located at the crystal boundaries [9,10,11,12,13]. As far as topological classification is concerned, such a space-time symmetry can lead to a nontrivial Floquet band topology, in the same way as its spatial counterpart does in a static system, except for a possible alternation of the commutation/anticommutation relations with respect to the nonspatial symmetries [33,34]. This result leads to the following interesting question. The relations with respect to the nonspatial symmetries that are inappropriate for the spatial symmetry would become otherwise appropriate for the space-time symmetry
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