Theory of anomalous Floquet higher-order topology
This event is part of the Biophysics/Condensed Matter Seminar Series.
In this talk, I will present a general framework to understand two dimensional "anomalous Floquet higher-order topological insulators" (AFHOTIs) protected by point group symmetries. Such AFHOTIs are defined by their robust, symmetry-protected corner modes pinned at special quasienergies, even though all their Floquet bands carry trivial band topology. I will show that the nontrivial topology can be diagnosed from the phase spectrum of the full time-evolution operator within one period, instead of the quasienergy bands at stroboscopic times only. In particular, the phase spectrum of AFHOTIs features robust 3D Dirac/Weyl like singularities, which cannot be removed without closing the quasienergy gap or breaking the point group symmetry. I will further demonstrate the higher-order bulk-boundary correspondence for AFHOTIs using dimensional reduction. This allows for a systematic classification of 2D AFHOTIs protected by rotation and dihedral groups