Phase vortices of the quenched Haldane model
AbstractUsing the recently developed Bloch-state tomography technique, the quasimomentum k-dependent Bloch states [sinθk/2,−cosθk/2eiϕk]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 Hf, the time-dependent azimuthal phase ϕk(t) supports two types of vortices. The first type of vortices is static, with the corresponding Bloch vectors pointing to the north pole (θk=0). The second type of vortices is dynamical, with the corresponding Bloch vectors pointing to the south pole (θk=π). In the (kx,ky,t) space, the linking number between the trajectories of these two types of vortices exactly equals the Chern number of the lower band of Hf, which provides an alternative method to directly map out the topological phase boundaries of the Haldane model.