Optical evidence for non-Hermitian topological phases of two-dimensional Dirac fermions

We theoretically investigate the topological band structures of a non-Hermitian Dirac Hamiltonian in two dimensions that effectively describes a non-Hermitian Chern insulator. The optical conductivity in various phases has been calculated. Five distinct phases with different topological features are shown explicitly. We redefine the point-gapped phase for the non-Hermitian counterparts and the gapless phases with the eigenenergies coalescing into a Dirac point or bulk Fermi arc, where the exceptional points (EPs) are formed at the ends of arc, as the Fermi arc (NHFA) phases, respectively. It has been found that the evolution of topological phases can be achieved by coordinating the relative strengths of band-dependent scattering. By extending the optical response theory into the realm of non-Hermitian quantum systems, we analyze the spectral functions and the optical conductivity tensors in the respective phases in detail. We show that the mass parameter is critical for the anomalous Hall effect in the non-Hermitian system. The influence of temperature on the real and imaginary parts of frequency dependent conductivities is also presented. Our results indicate that the non-Hermiticity modifies the electron structure, so that the bulk topology is embodied in the dynamic response. We suggest an optical approach to probe new physics accompanied by non-Hermiticity in the massive Dirac systems.