Scattering Dynamics and Boundary States of a Non-Hermitian Dirac Equation

We study a non-Hermitian variant of the (2+1)-dimensional Dirac wave equation, which hosts a real energy spectrum with pairwise-orthogonal eigenstates. In the spatially uniform case, the Hamiltonian's non-Hermitian symmetries allow its eigenstates to be mapped to a pair of Hermitian Dirac subsystems. When a wave is transmitted across an interface between two spatially uniform domains with different model parameters, an anomalous form of Klein tunneling can occur, whereby reflection is suppressed while the transmitted flux is substantially higher or lower than the incident flux. The interface can even function as a simultaneous laser and coherent perfect absorber. Remarkably, the violation of flux conservation occurs entirely at the interface, as no wave amplification or damping takes place in the bulk. Moreover, at energies within the Dirac mass gaps, the interface can support exponentially localized boundary states with real energies. These features of the continuum model can also be reproduced in non-Hermitian lattice models.