Study of Majorana bound states in the Kitaev model with imaginary potentials

We consider the infinite non-Hermitian finite-difference Kitaev model simulating a one-dimensional superconducting wire. Non-Hermitianity is introduced into the model using delta-shaped imaginary potentials that simulate the gains and losses of the amplitudes of Majorana bound states (MBS). In a rigorous mathematical approach, the conditions for the existence of eigenfunctions describing the MBSs are found, as well as the dependence of the eigenfunctions on the model parameters and the effect of non-Hermiticity on the MBSs. Two regimes are considered, near the topological interphase boundary and at zero chemical potential.