ICQM Prof. Xiong-Jun Liu’s group published a paper in PRL proposing a unified theory to dynamically characterize Floquet topological phases

Recently, Prof. Xiong-Jun Liu’s group at ICQM Peking University published a paper in Phys. Rev. Lett. reporting a progress on establishing a unified theory to characterize Floquet topological phases by quench dynamics [Phys. Rev. Lett. 125, 183001 (2020)]. This work provides a new framework for the characterization of Floquet topological phases and will advance the related research in theory and experiment.

The Floquet topological phases have been being an important research direction in topological quantum matter over the past decade, with extensively studies having been carried in various research fields, including condensed matter physics, photonic crystals, and ultracold atoms. The spatiotemporal control introduces the additional degree of freedom in the time domain, which on one hand opens a broad new route to realize richer Floquet topological phases beyond equilibrium systems, on the other hand, necessitates the time-domain information beyond Floquet bands to characterize the topological phases. As a result, for a long time the Floquet topological phases lack universal characterization and direct measurement schemes. In this work, the authors proposed a dynamical classification theory for generic Floquet topological phases based on quantum quenches form an initially static and trivial phase. The authors develop the characterization theory using quench dynamics by suddenly turning on the periodic driving to characterize the Floquet topological phases of the post-quench system. They show that the quench-induced quantum dynamics exhibit universal topological patterns in particular low-dimensional momentum subspaces, known as band inversion surfaces, from which the Floquet topological invariants can be directly obtained to fully characterize the post-quench Floquet topological phases. This result provides a simple and unified characterization, in which one can not only precisely determine the conventional and anomalous Floquet boundary modes, but also identify the topologically protected singularities in the phase bands. Besides the clear significance in theory, the proposed dynamical schemes in this work have high feasibility in the experimental realization.

The postdoc Long Zhang (PKU) is the first author of the paper. This work was supported by NSFC, MOST, and CAS.

        (a) Quench protocol.  (b) Dynamical characterization of the 1D driven model. (c) Dynamical characterization of the 2D driven model. (d) The rotation of the vector field on band inversion surfaces identifies the emergence of topological singularities in the phase bands.