Non-Hermitian Higher-order Dirac Semimetals

We study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs) [1]. 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 novel non-Hermitian topological phase which we call a hybrid-PT topological phases. 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 novel phases, particularly: (i) an intrinsic I-NHHODSM having hinge arcs and surface exceptional Fermi-arcs, and (ii) a novel T-symmetric skin-topological HODSM which possesses both topological and skin hinge modes. This work paves the way toward uncovering rich phenomena and hybrid functionality that can be readily realized in experiment. We have also recently studied the non-Hermitian higher-order Weyl semimetals in a separate work (see [2]). 

[1]. Sayed Ali Akbar Ghorashi, Tianhe Li, Masatoshi Sato, and Taylor L. Hughes, Phys. Rev. B 104, L161116 (2021).

[2]. Sayed Ali Akbar Ghorashi, Tianhe Li, and Masatoshi Sato, Phys. Rev. B 104, L161117 (2021).