Relationship between the electronic polarization and the generalized winding number in non-Hermitian systems

We discuss an extension of the Resta's electronic polarization to non-Hermitian systems. We point out that there appears a finite region where the polarization becomes zero between two gapped regions, and that there is correspondence to the generalized winding number which may take half integers. We demonstrate this argument in the non-Hermitian Su-Schrieffer-Heeger model.