Zitterbewegungfor ultracold atoms in the merging of Dirac points

We investigate Zitterbewegung (ZB) of the ultracold atoms in a tunable honeycomb optical lattice. By tuning the parameters of the lattice one can realize the merging of two Dirac points. The process of two Dirac points merging into a hybrid point implies a topological phase transition from a semimetallic to a band insulator phase. After merging, it presents a linear-quadratic dispersion relation which is linear in one direction and quadric in the other orthogonal direction. We show that ZB occurs isotropically before merging but occurs only in the direction of the linear dispersion after merging. Furthermore, we obtain that ZB is exponentially damping for a negative energy gap but is a stable oscillation for a positive energy gap. The frequency and amplitude of ZB can be controlled in a detectable range, so the phenomena can be observable in the ultracold atomic experiments.