Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model

Abstract

The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. Due to the presence of a non-dispersive flat band, the dice-Haldane model hosts a topologically rich phase diagram with the non-trivial phases accommodating Chern numbers $\pm 2$. We introduce non-Hermiticity into this model in two ways -- through balanced non-Hermitian gain and loss, and by non-reciprocal hopping in one direction. Both these types of non-Hermiticity induce higher-order exceptional points of order three. We substantiate the presence and the order of these higher-order exceptional points using the phase rigidity and its scaling. Further, we construct a phase diagram to identify and locate the occurrence of these exceptional points in the parameter space. Non-Hermiticity has yet more interesting consequences on a finite-sized lattice. Unlike for balanced gain and loss, in the case of non-reciprocal hopping, the nearest-neighbour dice lattice system under periodic boundary conditions accommodates a finite, non-zero spectral area in the complex plane. This manifests as the non-Hermitian skin effect when open boundary conditions are invoked. In the more general case of the dice-Haldane lattice model, the non-Hermitian skin effect can be caused by both gain and loss or non-reciprocity. Fascinatingly, the direction of localization of the eigenstates depends on the nature and strength of the non-Hermiticity. We establish the occurrence of the skin effect using the local density of states, inverse participation ratio and the edge probability, and demonstrate its robustness to disorder. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.

arXiv commentPublished version

References in corpus (83)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Photonic Floquet Topological Insulators
• Making Sense of Non-Hermitian Hamiltonians
• Experimental realisation of the topological Haldane model
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• The physics of exceptional points
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Anomalous edge state in a non-Hermitian lattice
• Topological energy transfer in an optomechanical system with exceptional points
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Observation of a localized flat-band state in a photonic Lieb lattice
• Topolectrical circuits
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Observation of bound states in Lieb photonic lattices
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological Flat Band Models and Fractional Chern Insulators
• Exceptional Points of Non-hermitian Operators
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Critical non-Hermitian Skin Effect
• Aharonov-Bohm cages in two-dimensional structures
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Universal non-Hermitian skin effect in two and higher dimensions
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Acoustic non-Hermitian skin effect from twisted winding topology
• Experimental realization of a Weyl exceptional ring
• Observation of higher-order non-Hermitian skin effect
• Observation of arbitrary topological windings of a non-Hermitian band
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Nearly flat band with Chern number C=2 on the dice lattice
• Topological states of non-Hermitian systems
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Experimental observation of Aharonov-Bohm cages in photonic lattices
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• The insulator/Chern-insulator transition in the Haldane model
• Observation of Exceptional Points in Electronic Circuits
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• How to escape Aharonov-Bohm cages ?
• Experimental demonstration of an anisotropic exceptional point
• Topolectric circuits: Theory and construction
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Non-Hermitian exceptional Landau quantization in electric circuits
• Exceptional Points in a Non-Hermitian Topological Pump
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Correlated phases of bosons in the flat lowest band of the dice lattice
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Observation of momentum-space chiral edge currents in room-temperature atoms
• The fate of topological-insulator surface states under strong disorder
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Magnetic suppression of non-Hermitian skin effects
• High-order exceptional points in supersymmetric arrays
• Unconventional phases in a Haldane model of dice lattice
• Anisotropic exceptional points of arbitrary order
• Topological edge states and quantum Hall effect in the Haldane model
• Three-level Haldane-like model on dice optical lattice
• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection
• Modification and Control of Topological Insulator Surface States Using Surface Disorder
• Controlling Exceptional Points with Light
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Disorder driven phase transitions in weak AIII topological insulators
• Topological Protection in non-Hermitian Haldane Honeycomb Lattices
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Predicting Large-Chern-Number Phases in a Shaken Optical Dice Lattice
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Multitude of exceptional points in van der Waals magnets
• Non-Hermitian semi-Dirac semi-metals

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