The oscillation of Majorana modes with near zero energy plays a very important role for ascertaining Majorana fermions. The edge states, which also have almost-zero-energy in one-dimensional Su-Schrieffer-Heeger chain (SSHc), have been extensively studied for their topologically protected properties when the on-sites have dissipations induced by independent environments. We here show that common environments shared by each pair of the nearest neighbour sites in the SSHc can result in dissipative couplings between sites, and thus change topologically trivial phase to nontrivial one. The Majorana-like oscillation for the finite-size hybridizations of two non-Hermitian edge states with complex localization lengths can be induced by the dissipative coupling. The controllable topology parameter of the SSHc plays the role of the magnetic field in the nanowire for controlling Majorana oscillation. The measurement for the oscillation is proposed. Our study provides a new way to manipulate edge states and is experimentally feasible within current technology of superconducting quantum circuits.
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