Phase vortices of the quenched Haldane model

Using the recently developed Bloch-state tomography technique, the quasimomentum k-dependent Bloch states [sin (theta(k)/2), - cos(theta(k)/2) e(i phi k)](T) of a two-band tight-binding model with two sublattices can be mapped out. We show that if we prepare the initial Bloch state as the lower-band eigenstate of a topologically trivial Haldane Hamiltonian Hi and then quench the Haldane Hamiltonian to H-f, the time-dependent azimuthal phase phi(k)(t) supports two types of vortices. The first type of vortices is static, with the corresponding Bloch vectors pointing to the north pole (theta(k) = 0). The second type of vortices is dynamical, with the corresponding Bloch vectors pointing to the south pole (theta(k) = pi). In the (k(x), k(y), t) space, the linking number between the trajectories of these two types of vortices exactly equals the Chern number of the lower band of H-f, which provides an alternative method to directly map out the topological phase boundaries of the Haldane model.