Topological Phase Transition of Non‐Hermitian Systems with Particle–Hole Symmetry

Abstract

As an effective description of general open systems, the non‐Hermitian (NH) Hamiltonians have attracted much attention recently. New topological properties unique to NH have been discovered. Herein, the one‐dimensional NH systems in the presence of particle–hole symmetry are considered and demonstrate that the topological phase transition happens when the momentum of states touches the unit circle of the generalized Brillouin zone. This criterion is in agreement with the critical point that zero modes are annihilated into the continuum bands, i.e., the gap of continuum bands is closed. This criterion of phase transition is also verified for the models of the Kitaev chain and Alicea nanowire, by introducing two NH terms including the Hatano–Nelson term and complex chemical potential. It is found that the skin effect enhances the localization of zero modes. Moreover, the NH Kitaev chain and Alicea nanowire with electric circuits for further experiments are realized.