Non-Hermitian higher-order Dirac semimetals

In this Letter, we study three-dimensional non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on C4-symmetric non-Hermitian systems where we investigate inversion (I) or time-reversal (T) symmetric models of NHHODSMs having real bulk spectra. We show that they exhibit the striking property that the bulk and surfaces are anti-PT and PT symmetric, respectively, and so belong to two different topological classes realizing a non-Hermitian topological phase which we call a hybrid-PT topological phase. Interestingly, while the bulk spectrum is still fully real, we find that exceptional Fermi rings (EFRs) appear connecting the two Dirac nodes on the surface. This provides a route to probe and utilize both the bulk Dirac physics and exceptional rings/points on equal footing. Moreover, particularly for T-NHHODSMs, we also find real hinge arcs connecting the surface EFRs. We show that this higher-order topology can be characterized using a biorthogonal real-space formula of the quadrupole moment. Furthermore, by applying Hermitian C4-symmetric perturbations, we discover various phases, particularly (i) an intrinsic I-NHHODSM having hinge arcs and surface exceptional Fermi arcs, and (ii) a T-symmetric skin-topological HODSM which possesses both topological and skin hinge modes. The interplay between non-Hermition and higher-order topology in this Letter paves the way toward uncovering rich phenomena and hybrid functionality that can be readily realized in experiment.