Dynamical detection of topological charges

We propose a generic scheme to characterize topological phases via detecting topological charges by quench dynamics. A topological charge is defined as the chirality of a monopole at Dirac or Weyl point of spin-orbit field, and topological phases can be classified by total charges in the region enclosed by the so-called band-inversion surfaces (BISs). We show that both the topological monopoles and BISs can be identified by non-equilibrium spin dynamics caused by a sequence of quenches. From an emergent dynamical field given by time-averaged spin textures, the topological charges, as well as the topological invariant, can be readily obtained. An explicit advantage in this scheme is that only a single spin component needs to be measured to detect all the information of the topological phase. We numerically examine two realistic models, and propose a feasible experimental setup for the measurement. This work opens a new way to dynamically classify topological phases.