Theory of Anomalous Floquet HigherOrder Topology
 Date
 May 26 (Wed) at 22:00  23:15, 2021 (JST)
 Speaker

 RuiXing Zhang (University of Maryland, College Park, USA)
 Venue
 via Zoom
 Language
 English
Periodicallydriven or Floquet systems can realize anomalous topological phenomena that do not exist in any equilibrium states of matter, whose classification and characterization require new theoretical ideas that are beyond the wellestablished paradigm of static topological phases. In this work, we provide a general framework to understand anomalous Floquet higherorder topological insulators (AFHOTIs), the classification of which has remained a challenging open question. In two dimensions (2D), such AFHOTIs are defined by their robust, symmetryprotected corner modes pinned at special quasienergies, even though all their Floquet bands feature trivial band topology. The cornermode physics of an AFHOTI is found to be generically indicated by 3D Dirac/Weyllike topological singularities living in the phase spectrum of the bulk timeevolution operator. Physically, such a phaseband singularity is essentially a "footprint" of the topological quantum criticality, which separates an AFHOTI from a trivial phase adiabatically connected to a static limit. Strikingly, these singularities feature unconventional dispersion relations that cannot be achieved on any static lattice in 3D, which, nevertheless, resemble the surface physics of 4D topological crystalline insulators. We establish the above higherorder bulkboundary correspondence through a dimensional reduction technique, which also allows for a systematic classification of 2D AFHOTIs protected by point group symmetries. We demonstrate applications of our theory to two concrete, experimentally feasible models of AFHOTIs protected by C2 and D4 symmetries, respectively. Our work paves the way for a unified theory for classifying and characterizing Floquet topological matters.
*Detailed information about the seminar refer to the email.