Majorana polarization in non-Hermitian topological superconductors

Topological invariants play an important role in characterizing topological phases. However, the topological invariants of Hermitian systems usually fail to characterize non-Hermitian topological systems due to non-Hermiticity. In this work, we generalize the Majorana polarization, which is initially defined to describe Hermitian topological superconductors, as a topological edge invariant to characterize the non-Hermitian topological superconductors. The definition of the generalized Majorana polarization depends upon two inequivalent particle-hole symmetries in non-Hermitian systems. The spinless Kitaev chain model and topological superconductor model on the honeycomb lattice are considered to examine the reliability and validity of the generalized Majorana polarization. We find that the phase transitions obtained by using Majorana polarization are consistent with the commonly used complex-energy point gap descriptions, which indicates the Majorana polarization is a reliable topological invariant to characterize the topological phase transition in non-Hermitian topological superconductors. In addition, the non-Hermitian skin effect on Majorana bound states in non-Hermitian topological superconductors is also discussed.