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Using the recently developed Bloch-state tomography technique, thequasimomentum $\bf k$-dependent Bloch states ${\left( {\sin \left( {{\theta_{\mathbf{k}}}/2} \right),\; - \cos \left( {{\theta _{\mathbf{k}}}/2}\right){e^{i{\phi _{\mathbf{k \right)^T}$ of a two-band tight-bindingmodel with two sublattices can be mapped out. We show that, if we prepare theinitial Bloch state as the lower-band eigenstate of a topologically trivialHaldane Hamiltonian $H_i$, and then quench the Haldane Hamiltonian to $H_f$,the time-dependent azimuthal phase ${\phi _{\mathbf{k}}(t)}$ supports two typesof vortices. The first type of vortices are static, with the correspondingBloch vectors pointing to the north pole ($\theta_{\mathbf{k}}=0$). The secondtype of vortices are dynamical, with the corresponding Bloch vectors pointingto the south pole ($\theta_{\mathbf{k}}=\pi$). In the $(k_x,k_y,t)$ space, thelinking number between the trajectories of these two types of vortices equalsexactly to the Chern number of the lower band of $H_f$, which provides analternative method to directly map out the topological phase boundaries of theHaldane model.

Phase vortices of the quenched Haldane Model