Phase-factor-optimized topological transmission in a dimerized lattice with long-range hopping

We show that both the efficiency and robustness of the topological excitation transmission can be optimized by the phase factor of the long-range hopping in the dimerized lattice. This phenomenon can be explained as the fact that the phase factor in the hopping can widen the minimal energy space around the gap closing point. By redesigning the configuration of long-range hopping, we implement the perfect topological excitation transmission assisted by the phase factor from the left edge to the right edge. We demonstrate that the present optimized topological excitation transmission essentially originates from the phase transition induced by the phase factor, in which the existence of the phase transition leads to the decreasing of the gap closing points. Furthermore, we also investigate the generalized cases with longer-range hopping and find that the optimized topological excitation transmission is determined by the order of long-range hopping. Our investigation shows the significant effect of the phase factor of hopping strength on the topological excitation transmission, which is usually overlooked in relevant work.