  Unlike the edge state of a topological insulator where its energy level lives
in the bulk energy gap, the edge state of a topological semimetal hides in the
bulk spectrum and is difficult to be identified by the energy. We investigate
the sensitivity of bulk and edge states of the gapless phase for a topological
semimetal to the disordered perturbation via a concrete two-dimensional chiral
symmetric lattice model. The topological gapless phase is characterized by two
opposite vortices in the momentum space and nonzero winding numbers, which
correspond to the edge flatband when the open boundary condition is applied.
For this system, numerical results reveal that a distinguishing feature is that
the robustness of the edge states against weak disorder and the flatband edge
modes remain locked at zero energy in the presence of weak
chiral-symmetry-preserving disorder. We employ the Loschmidt echo (LE) for both
bulk and edge states to study the dynamic effect of disordered perturbation. We
show that, for an initial bulk state, the LE decays exponentially, whereas it
converges to a constant for an initial edge state in the presence of weak
disorder. Furthermore, the convergent LE can be utilized to identify the
positions of vortices as well as the phase diagram. We discuss the realization
of such dynamic investigations in a topological photonic system.

Mesoscale and Nanoscale Physics;Optics;Quantum Physics