Non-Hermitian Kitaev chain with complex on-site potentials

Abstract

We investigate non-Hermitian Kitaev chains in which imaginary potentials are added to all or only the two end lattice sites to represent the physical gain and loss during their interacting processes with the environment. By analyzing the energy eigenvalues of the non-Hermitian Hamiltonians both analytically and numerically, we find that if the imaginary potentials are added to every lattice site, the topologically nontrivial phase region will be gradually narrowed down as the imaginary potentials increase. The zero-energy modes in the nontrivial phase region remain real and thus the Majorana bound states (MBSs) at the ends of the chain are presenting steadily until the imaginary potentials become strong enough to close the energy gap and change the bulk properties. However, if the imaginary potentials are only added to the two ends of the chain, the zero-energy modes will always be real and thus the MBSs exist stably all the time even when the imaginary potentials become very strong since the corresponding bulk properties cannot be changed by these two local perturbations. Our results explicitly demonstrate the evolution and robustness of the nontrivial topological state of Kitaev chain against external perturbations.