Non-Hermitian Higher-Order Dirac Semimetals

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.

arXiv comment4 figures

References in corpus (67)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Higher-Order Topological Insulators
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Acoustic higher-order topological insulator on a Kagome lattice
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Higher-Order Topology in Bismuth
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Topological protection of photonic mid-gap cavity modes
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Higher-order non-Hermitian skin effect
• Experimental realization of a Weyl exceptional ring
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Topological states of non-Hermitian systems
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Higher Order Topological Phases: A General Principle of Construction
• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• Second-order topological non-Hermitian skin effects
• Topological Quadrupolar Semimetals
• Higher-order topological semimetal in acoustic crystals
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Higher-order Weyl Semimetals
• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Observation of a phononic higher-order Weyl semimetal
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Topological classification of non-Hermitian systems with reflection symmetry
• Non-Hermitian second-order skin and topological modes
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Guided accumulation of active particles by topological design of a second-order skin effect
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Higher-order Dirac sonic crystals
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Parity-Time Anti-Symmetric Parametric Amplifier
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Dirac semimetals
• $\mathcal{P}\mathcal{T}$-Symmetric Topological Edge-Gain Effect
• Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations

Cited by in corpus (19)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Non-Hermitian topological phenomena: A review
• Hybrid skin-topological modes without asymmetric couplings
• Non-Hermitian Topological Phases: Principles and Prospects
• Photonic corner skin modes
• Bulk-boundary correspondence in point-gap topological phases
• Non-Hermitian boundary spectral winding
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Exceptional mode topological surface laser
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems