Non-Hermitian Higher-Order Dirac Semimetals

• URL: http://arxiv.org/abs/2106.14914v1
• Date: Mon, 28 Jun 2021 18:01:02 GMT
• Title: Non-Hermitian Higher-Order Dirac Semimetals
• Authors: Sayed Ali Akbar Ghorashi, Tianhe Li, Masatoshi Sato, Taylor L. Hughes
• Abstract summary: We study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs) We show that they exhibit the striking property that the bulk and surfaces are anti-PT and PT symmetric, respectively. We also find real hinge-arcs connecting the surface EFRs.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this article we study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on $C_4$-symmetric non-Hermitian systems where we investigate inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) 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 \emph{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 $\mathcal{T}$-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 $C_4$-symmetric perturbations, we discover various novel phases, particularly: (i) an intrinsic $\mathcal{I}$-NHHODSM having hinge arcs and gapped surfaces, and (ii) a novel $\mathcal{T}$-symmetric skin-topological HODSM which possesses both topological and skin hinge modes. The interplay between non-Hermition and higher-order topology in this work paves the way toward uncovering rich phenomena and hybrid functionality that can be readily realized in experiment.

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