| Summary: | 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.
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